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NAME OF AUTHOR/NOM DE L'AUTEUR Christian Gerard SimOn

TITLE OF THESIS/TTTITEDEAAJBESE_ The Conformations of Alkyl-Substi tuted Ethylenes. A

----C- mb-ines ear Magnetic Resonance and Force Field of

Study

UNIVTRSITY/UNWERS/TE

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University of Regina

Doctor of Phi losophy in Chemistry

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' THE CONFORMATIONS OF ALKYL-SUBSTITUTED ETHYLENES.

A COMBINED NUCLEAR MAGNETIC RESONANCE AND FORCE FIELD STUDY

A Thesis

--------------Submitted to the Faculty of GribuateS_tudies and Research

In Partial Fulfilment.of the Requirements

for the degree of

,Doctor of Philosophy

in Chemistry

Faculty of .Science

# University of Regina

by

Christian Gerard Simon

Regiha, Saskatchewan

May, 1980

Copyright 1980. C.G. Simon


UNIVERSITY OF REGINA

Faculty of Graduate Studies and Research 1/4

SUMMARY OF THE THESIS

Submitted in Partial Fulfillment

of the Requirements fo'r the

DEGREE OF DOCTOR OF PHILOSOPHY

in

CHEMISTRY

by

CHRISTIAN GERARD SIMON

Doctorat 3eme Cycle

(Universite d'Orleans, France)

June, 1980

Committee in Charge:

W D. Chandler (Department Head) F.H.A. Rummens (Supervisor)

D.G. Lee S. Levine

B.D. Kybett . B.E. Robertson C. W. Blachford (Dean of Graduate Studies and Research)

External Examiner:

M. St•Jaeques. Professor of Chemistry University of Montreal

Montreal, Quebec


THESIS.

THE CONFORMATIONS OF ALKYL-SUBSTITUTED ETHYLENES. '

A COMBINED NUCLEAR MAGNETIC RESONANCE AND FORCE FIELD STUDY

Variable temperature proton NMR parameters (aPmical shifts and coupling constants) have been obtained for cis- and trans-2,2,5-trimethy1-3-hexene and for czs-2,5-dimetliy1-3-hexene using high precision experimental techniques, coupled with a powerful spectral technique (NUMARIT).

Detailed structural and energetic information for the above-mentioned molecules was obtained employing a Force Field procedure.

The general approach for the interpretation of the experimental results involved the combined use of the (AJ/A0) data calculated earlier by Rummens and Kaslander, the structural geometry calculated using the Force Field method and the theorem of Boltzmann population statistics. In many cases the technique was proven to be reliable.

No such generally useful structure-parameter stratagem was found frir the interpretation of chemical shifts. Differential solvent effects are suspected to be the cause of this failure. For the same reasons, the carbon-la spectra, obtainW for cis- and trans-2,2,5-trimethyl-:3-hexene were not useful for the interpretation of the totameric changes.

The temperature dependence .of coupling constants for trans-2,2,5-trimethyl-3-hexene is explained in terms of an anti-gauche equilibrium. The difference, in Gibbs free energy between the anti and gauche forms could be determined as AG" = 531+59J.mol (127+14cal.mol l); the Force Field method overestimates this


.01

difference by about 4KJ.mol ' (IKcal.mol l). No evidence of interaction between the isopropyl and tert-butyl rotors could be found.

In ci -2,2,5-trimethy1-3-hexene, it was concluded that the two substituents (isopropyl and ieri-butyl groups) are in anti position in the ground state. It seems clear from the experimental data that there exists a second low-lying minimum (AG" 2.1KJ.mol ' or 0.5Kcal,mol 1), not in concordance with the Force Field calculation.

The results on cis-2,5•dimethyl•3-hexene indicated a ground state with an anti-anti conformation. There exists a low energy

second conformer (AG" 1.13KJ.mo1- ' or 0.27Kcal.mol 1 ), but its

structure could not be determined. The anti•syn structure obtained from the Force Field as the second conformation was disproved by the NMR results. The latter point tb a skew-skew

structure as a likely form.

BIOGRAPHICAL

1969

CHRISTIAN GERARD SIMON

Diplorcy Universitaire d'Etudes Scientifiques, Universit6 d'Orleans (Prance).

1972 Maitrise de Physique, Universito d'Orleans.

197:3 Diplome d'Etudes Approfondies, Universite d'Orleans.


1974 Doctorat de 3 .me Cycle (specialty: solid state physics), Universite d'Orleans.

1976, 1977 Gerhard ferzberg Fellowship, Universit of Regina.

1978 Samps J. Goodfellow Scholarship, Univ rsity of Regina.

1978, 1979 Province of Saskatchewan University Graduate Scholarship, University of Regina. Province of Saskatchewan University Gradtiate Summer Scholarship, University of Regina.

1979 Teaching Assistantship, University of Regina.

1980 Research Technician, University of Regina.


ABSTRACT

Variable temperature proton NMR parameters (chemical shifts and

coupling constants) have been obtained for cis- and trans-2,2,5-trimethyl-,

3-hexene and for cis-2,5-dimethy1-3-hexene using high precision experimen-

tal techniques, coupled with a powerful spectral analysis technique

(NUMARIT).

Detailed structural and energetic information f95 the above-

mentioned molecules was obtained employing a Force Field procedure.

The general approach for the interpretation of the experimental

results involved the combined use of the (a(A0) data calculated by

Rummens and Kaslander, the structural geometry calculated using the Force

Field method and the theorem of Boltzmann population statistics. In many

cases the technique is proven to be reliable.

No such generally useful structure-parameter stratagem is found

for the interpretation of chemical shifts. Differential solvent effects

are suspected to be the cause of this failure. For the same reasons, the

carbon-13 spectra, obtained for cis- and trans-2,2,5-trimethy1-3-hexene

were not useful for the interpretation of the rotameric changes.

The'teniperature dependence of coupling constants for trans-2,2,5-

trimethyl-3-hexene is explained in terms of an anti-gauche equilibrium.

The difference in Gibbs free energy between the anti and gauche forms

could be determined as AGo 531±59J.mol-1 (127±14cal.mol-1); the'Force


Field method overestimates this difference by about 4KJ.mol (1Kcal.mol-1 ).

No evidence of interaction between the isopropyl and tert-butyl rotors

could be found,

-In cis-2,2,5-trimethyl-3-hexene, it is concluded that the two

substituents (isopropyl and tert-butyl groups) are in anti position in

the ground state. It seems clear that there exists a second low-lying

J ai-rrlinum (AG° = 2.1KJ.mo1-1 or 0.5Kcal.mo1-1) not in concordance with the

Force Field calculation.

The results on cis-2;5-dimethy1-3-hexene give definitely a

ground state with an anti-anti conformation. There exists a low energy

second conformer (Ae = 1.13KJ.mol -1 or 0.27Kcal.mo1-1), but its struc-

ture could not be determined. The anti-syn structure obtained from the

Force Field as second conformation is disproved by the NMR results. The

latter point to a skew-skew structure as a likely form.



FACULTY OF GRADUATE STUDIES AND RESEARCH

CERTIFICATION OF THESIS WORK

We, the undersigned, certify that Christian Gerard Simon

candidate for the Degree of Doctor of Phi losophy in Chemistry

has presented a thesis on the subject

Alkyl-Substituted Ethylenes. A Combined Nuclear Magnetic Resonance

The Conformations of

and Force Field of Study

that the thesis 1% acceptable in form and content, and that the student

demonstrated a satisfactory knowledge of the field covered by the thesis

in an oral examination held on June 20, 1980

External Examiner citt,LA.(1)), .... Dr. Maurice 2I-Jacq s, rofessor of Oemjstry..Uoiversi y.o Montreal._

Internal Examiners



PERMISSION TO USE POSTGRADUATE THESES •

Title of Thesis The Conformations of Alkyl-Substituted

Ethylenes. A Combined Nuclear Magnetic Resonance and Force

r Field of Study

Name of Author Christian Gerard Simon

Faculty of Science Faculty

Doctor of Phi losophy in Chemistry Degree.

In presenting this thesis in partial fulfi lment of the requirements for a postgraduate degree from the University of Regina, I agree that the Libraries of this University shal l make it freely avai lable forinspection. I further agree that permission fbr extensive copying of this thesis for scholarly purposes may be granted by the professor or professors who supervised my thesis work, or in their absence, by the Associate Dean of the Division, the Chairman of the Department or the Dean of the Faculty in which my thesis work was done. It is understood that any copying or publ ication or.use of this thesis or parts thereof for financial gain shal l not be al lowed without my written permission. It is also understood that due recognition shal l be given to me and to the University of Regina in any scholarly use which may be made of any material in my thesis.

Signature...

Date June 20, 1980

'100 cc. /am 1/2/80


ACKNOWLEDGEMENTS

It is my pleasure to.thank Dr. F.H.A. Rummens for his guidance

and supervision throughout this work.

Sincere appreciation is also expressed to Dr. J.S. Martin and

Dt. T. Nakashima for the use of their spectrometer.

I wish to thank Dr. 0. Ermer for providing a version of his

valence Force Field program.

Grateful acknowledgement is made to the University of Regina

for providing continuing financial assistance in the form of a Gerhard

Herzberg Fellowship, a University Graduate Scholarship, a Sampson J.

Goodfellow Scholarship, a Summer Scholarship and a Teaching Assistantship

in Chemistry. The National Science and Engineering Research Council

is also acknowledged for providing financial aid through temporary

employment as a technician to assist Dr. F.H.A. Rummens in his

work.

iii


TABLE OF CONTENTS

page

ABSTRACT i

ACKNOWLEDGEMENTS iii

LIST OF TABLES ix

LIST OF FIGURES xiii

PREFACE xvii

CHAPTER I FORCE FIELDS 1

1.1 INTRODUCTION 1

1.2 DESCRIPTIONi9F THE MECHANICAL MODEL 4

1.3 FORCE FIELD CONSTANTS USED 9

1.4 ENERGY MINIMIZATION 14

1.5 DESCRIPTION OF THE "CFF" PROGRAM 22

1.6 CALCULATION OF NORMAL MODES OF VIBRATION 24

1.7 CALCULATION OF CONFORMATIONAL INTER-CONVERSION , 26

1.8 CALCULATION OF THERMODYNAMIC PROPERTIES WITH FORCE FIELDS 27

1.8.1 Enthalpy 28

1.8.2 Entropy 29

1.8.3 Gibbs free energy function G 32

CHAPTER II THEORY OF HIGH RESOLUTION NUCLEAR MAGNETIC RESONANCE 35

iv


TABLE OF CONTENTS (continued)

'2.1 INTRODUCTION

page

35

2.1.1 ' Chemical shifts ' 35

2.1.2 Coupling constants 37

2.2 THEORY OF THE ANALYSIS OF NMR SPECTRA. . 38

N __Hamiltonian operator 38

2.2.2 Subspectral analysis csing the composite particle method Q 42

Subspectral analysis using the X approximation 45

2..2.4. General procedure to analyze'NMR spectra 46

2.3 CHEMICAL' SHIFTS AND STRUCTURE " 47

2.3.1 Classification of shielding effects 47

2.3.2 Interpretation of proton cifemical shifts 49

2.3.3 Interpretation of carbon-13 chemical shifts 57

2.4 COUPLING CONSTANTS AND STRUCTURE 65

2.4.1 Description of coupling •65

2.4.2 Nature of the coupling 67

2.4.3 Empirical and semi-empirical correlations, between coupling constants and structure. 69

2.4.4 Coupling constants and electronegativity effects 76

\2.51 NMR STUDIES ON ROTAMERS 79

2.5.1 Description of phenomenon 79

2.5.2 Completely averaged spectra and their temperature dependence studies ' 81

2.5.3 Dynamic equilibria and line shape analysis 86

2.6 NUMERICAL ANALYSIS USING THE PROGRAM "NUMARIT" 39

1",



•

page

2.6'.1 Introduction 89

2.6.2' Method of iteration 39

2.6.3 Error analysis 94

'CHAPTER III CONFORMATIONAL AND THERMODYNAMIC PROPERTIES OBTAINED FROM FORCE FIELD CALCULATIONS: RESULTS AND PRELIMINARY DISCUSSION 98

3.1 INTRODUCTION 98

3.2 RELEASE OF STRAIN AND CONFORMATION 98

3.2.1 Release of strain through widening of.the C=C-R valence angles 99

3.2.2 Other types of release 109

3.2.3 Repartition of steric energy 109

3.3, ENERGY IN CIS/TRANS TRANSFORMATION 111

3.3.1 Cis/trans enthalpy differences 111

3.3.2 Entropy and Gibbs energy reliability 115

3..4 STRAIN ENERGY DIFFERENCES BETWEEN ROTAMERS 117

3.4.1 - 3-Methyl-l-butene 117

3.4.2 trans-2,5-Dimethy1-3-hexene 119

3.5 INTERCONVERSION PATH AND THERMODYNAMIC PROPERTIES 121

3.5.1 cis-2,5-Dimethy1-3-hexene 121

3.5.2 trans-2,2,5-Trimethyl-3-hexene 128

3.5.3 cis-2,2,5-Trimethy1-3-hexene 134

3.5.4 4,4-Dimethyl-3-tert-butyl-1-pentene 140

APPENDIX 145

vi

No.



page

,CHAPTER IV NMR EXPERIMENTAL RESULTS 160

4.1 EXPERIMENTAL CONDITIONS 16Q

4.2 SPECTRAL ANALYSIS OF THE PROTON SPECTRA. . 164

4.2.1 cis- and trans-2,2,5-Trimethy1-3-hexene 164

4.2.2 cis-2,5-Dimethyl-3-hexene 173

4.2.3 cis- 4,4-,Di methyl -2- pen tene 177

CHAPTER V INTERPRETATION OF THE NMR DATA 189

5.1 INTRODUCTION 189

5.2 TRANS-2,2,5-TRIMETHYL-3-HEXENE 191

5.2.1 Analysis of the temperature dependence of the coupling constants

5.2.2 Coupling constants and conformational structure

5.2.3 Proton chemical shifts and conformations

5.2.4 Carbon-13 chemical shifts and structure

5.2.5 Conclusion

5.3 CIS-2,2,5-TRIMETHYL-3-HEXENE

5.3.1 Introduction

5.3.2 Analysis of the temperature dependence of several coupling constants

5.3.3 /Coupling constants and conformations

5.3.4 Proton chemical shifts and structure


5.3.6 Rotational barriers and line intensities

5.3.7 Conclusion

vii

191

197

202

209

214

216

216

218

222

231

242

249

253


ti

TABLE OF irENTS (continued)

page

5.4 CIS-2,5-0IMETHYL-3-HEXENE 255

5.4.1 Temperature dependence of coupling. constants 255

5.4.2 Coupling constants and structure 260

5.4.3 Proton chemical shifts and structure 264

5.4.4 Conclusion 269

CHAPTER VI , EPILOGUE 271

TABLE OF REFERENCES 282

Viii


LIST OF TABLES

Table ' page

1.3-1 Valence Force Field constants for olefins as given by Ermer and Lifson [3]. 10

3.2-1 Effect of a fir't alkyl substitution on the valence angles of ethylene, as found experimentally. 101

3.2-2 Force Field-derived variations of valence angles with monosubstitution of one hydrogen atom by an alkyl group in an ethylene molecule, when the molecule is in its minimum of lowest energy. 102

3.2-3 Calculated effects of alkyl monosubstitution on valence angles for ethylene molecules. 104

•

3.2-4 Effect of second substitution in cis or trans position on valence angles for monoalkyl ethylenes, as calculated for the minimu'" energy conformation.

Difference between Force Field-derived and experi-mentally obtained Valence angles for various ethylene molecules.

105

106

3.2-6 Calculated steric energies (KJ.mo1-1) in various conformations of lowest energy of olefins as calculated by the "CFF" method. 110

3.3-1 Difference in steric energy (C) and in enthalpy (M) between cis and trans isomers of various molecules as calculated with the Ermer and Lifson Force Field; comparison with the experimental enthalpy di-fferences. 112

3.3-2 Comparison .of cis/trans enthalpy differences as calculated using three Force Field methods and as obtained experimentally.

3.3-3 Comparison between calculated entropy difference .is/ Trans (for conformation of lowest energy) as obtained from Force Field technique and as deduced from experimental data.

114

116

ix


LIST OF TABLES (continued)

Table

3.5-1 Contributions to calculated steric energies for various conformations of cis-2,5-dimethyl-3-hexene.

3.5-2 Calculated thermodynamic properties of cis-2,5-dimethy1-3-hexene conformations.

3.5-3 Calculated thermodynamic properties of crans-2,2,5-trimethy1-3-hexene conformations.

3.5-4 • Calculated thermodynamic properties of cis-2,2,5-trimethy1-3-hexene conformations.

3.5-5 Cal culated thermodynamic properties of 4,4-dimethyl-3-tert-butyl-l-pentene conformations.

page

126

127

133

139

143

4 2-1 Comparison between parameters as obtained from the NUMARIT program (a) iterating all the coupling constants, (b) iterating only the coupling constants of sizeable magnitude. The example is given for the trans-2,2,5-trimethyl-3-hexene at 345.5K. . 167

4.2-2 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the trans-2,2,5-trimethy1-3-hexene at each investigated temperature. 171

4.2-3 '.ist of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the cis-2,2,5-trimethyl-3-hexene at each investigated temperature. 173

4.2-4 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the cis-2,5-dimethyl-3-hexene at each investigated temperature. 177

4.2-5 Proton chemical shifts and H-H coupling constants for cis-4,4-dimethyl-2-pentene at various temperatures. 178

4.3-1 Carbon-13 chemical shifts (in ppm from internal TMS) of trans-2,2,5-trimethy1-3-hexene as a function of temperature. 187

4.3-2 Carbon-13 chemical shifts (in ppm from TMS) of2,2,5-trimethyl-3-hexene as a function of temperature. ' 188

x


LIST OF TABLES (continued)._

Table page

5.2-1 Sets of coupling constants and Gibbs energy differences as obtained by the GBM method applied to the experi-mental data of trans-2,2,5-trimethyl-3-hexene. 196

5.2-2 Sets of coupling constants and energy separations between rotamers by the GBM method applied to the experimental data of trans-2,2,5-trimethy1-3-hexene.

5.2-3 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm upfrequency from TMS.

5.2-4 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is an ;sopropyl group, in ppm from TMS.

5.3-1 Sets of coupling constants and energy separations between rotamers obtained by the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethyl-3-hexene.

5.3-2 Sets of 4taJ coupling constants as obtained by the GBM method for the three considered transformations (see Figure (5.3-1)) ofthe cis-2,2,5-trime hy1-3-hexene, with energy separations as taken from the 3CJ and 3vj results.

5.3-3 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3-hexene. The GBM method is applied to uncorrected chemical shifts in ppm from TMS.

5.3-4 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method applied to shifts corrected for unwanted contributions for the three considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene.

5.3-5 Sets of proton chemical shifts and :heir differenck' as obtained by the GBM method applied to shifts corrected for unwanted contributions;'the enthalpy separations for the three considered transformations (see Figure (5.3-1)) are as given in Table 5.3-1.

xi

198

210

213

221

230

236

237

239


LIST OF TABLES (continued)

Table page

5.3-6 .Carbon-13 chemical shift (pom) dependence on temperature for the cis-2,2,5-trimethyl-3-hexene referenced to the methyl tert-butyl carbon C5. 243

5.3-7 Sets of carbon-13 shifts and energy separations obtained from the GBM method for the three transformations considered (see Figure (5.3-1)) of the cis-2,2,5-tri-methyl-3-hexene. The shifts are referenced to C5.

5.3-8 Sets of carbon-13 chemical shifts and their difference as obtained from the GBM method with the enthalpy separations as given in Table 5.3-1 for the three considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene.

5.3-9 Carbon-13 chemical shifts of sdme cis disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm from TMS.

5 3-10 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene (proton NMR).

5.3-11 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene for carbon-13 NMR.

5.4-1 Sets of coupling constants and energy separations between rotamers as obtained by the GBM method applied to the experimental data of cis-2,5-dimethy1-3-hexene up to a temperature of 300K.

5.4-2 Sets of proton chemical shifts and energy separations as obtained by the GBM method applied to experimental data of cis-2,5-dimethyl-3-hexene up to a temperature of 300K.

"s. •

xii

244

245

247

251

252

259

266


LIST OF FIGURES

Figure _page

1.4-1 A comparison of best-step Newton descent- and standard steepest descent. 17

1.5-1 General scheme of the Lifson-Ermer Force Field calculation. 23

2.3-1(a) Definition of the coordinate system (Oxyz). (b) Shielding and deshielding regions due to magnetic aniso-

tropy of the C=C bond; model A according to Pople [32], model B according to ApSimon et al. [28].

(c) Definition of R and 4) in Vogler's model. 52

2.4-1 Molecular fragments used for the definition of: (a) allylic coupling constants (b) homoallylic coupling constants. 73

2.5-1 Free energy profile for two stable conformations. 82

2.5-2 Temperature dependence of the NMR spectrum as a result of chemical exchange (uncoupled AB case). 88

3.2-1 Schematic description of valence angle variation with increasing size of the alkyl group substituent for monsubstituted ethylenes. 100

3.2-2 Schematic description of valence angle variation with increasing size of the alkyl group R2 for cis- and trans-disubstituted ethylenes with an isopropyl group as first substituent. 108

3.4-1 Calculated molecular geometries of the anti and gauche conformations of 3-methyl-l-butene. 118

3.4-2 Steric energy increases with successive anti-gauche transformations of the isopropyl group in 3-methyl-l-butene and in naans-2,5-dimethy1-3-hexene as obtained from Force Field calculation. 120


-Lrg OF FIGURES (continued)

Figure

3.4-3 Calculated molecular geometries for the various conformations of minimum energy of trans-2,5-dimethyl-3-hexene.

3.5-1 Calculated steric energy profile for the interconver-Sion of (aa) and (as) conformers of cis-2,5-dimethy1-3-hexene.

,3.5-2 Calculated molecular geometries of the three conforma-tions of lowest minimum energy of cis-2,5-dimethyl-3-hexene.

page

122

123

125

3.5-3 Calculated steric energy profile for the rotation of the isopropyl group of trans-2,2,5-trimethy1-3-hexene. 129

3.5-4 Calculated steric energy profile for the rotation of the tert-butyl group of trans-2,2,5-trimephy1-3-hekene. 130-

3.5-5 Calculated molecular geometries of the conformationsof minimum energy for trans-2,2,5-trimethyl-3-hexene. 131

3.5-6 Calculated steric energy profile for the rotation of the tart-butyl group of cis-2,2,5-trimethyl-3-hexene. 135

3.5-7 Calculated steric energy profile for the rotation of the isopropyl group of cis-2,2,5-trimethyl-3-hexene. 136

3.5-8 Calculated molecular geometries of conformations of minimum energy for cis-2,2,5-trimethyl-3-hexene.

_3.5-9 Calculated steric energy profile for 4,4-dimethyl-3-tert-butyl-l-pentene as obtained by driving the HC sp 2-C sp3H dihedral angle.

3.5-10 Calculated molecular geometries of the two conformations of lowest minimum energy for 4,4-dimethy1-3-tert-butyl-1-pentene.

4.2-1 Numbering system and nomenclature used for (H,H) coupling con,tants of cis- and trans-2,2,5-trimethyl-3-hexene.

4.2-2 Methine region of observed (upper spectrum) and computer simulated (lower spectrum) 90MHz proton spectra of trans-2,2,5-trimethy1-3-hexene.

xiv

138

141

142

165

168


LIST OF FIGURES (continued)

Figure

4.2-3 Temperature dependence of the methine region of the 90MHz proton spectrum for trans-2,2,5-trimethyl-3-hexene. The upper spectrum was recorded at 330K, the lower one at 270K.

page

169

4.2-4 Methine region of computer simulated (lower spectrum) and observed (upper spectrum) 90MHz proton spectra of cis-2,2,5-trimethyl-3-hexene. 172

4.2-5 Numbering system and nomenclature for (H,H) coupling constants of cis-2,5-dimethyl-3-hexene. 174

4.2-6 Methine region of the observed 90MHz proton spectrum of cis-2,5-dimethy1-3-hexene recorded at 354K under the conditions given in Section 4.2. 176

4.3-1 Numbering system of the carbon-13 atoms for cis- and trans-2,2,5-trimethyl-3-hexene. 180

4.3-2 Natural abundance 22.63MHz proton noise-decoupled carbon-13 spectrum of trans-2,2,5-trimethyl-3-hexene. 181

4.3-3 Natural abundance 22.63MHz proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethy1-3-hexene. 182

4.374 Non-olefinic region of a natural abundance proton noise-decouplied carbon-13 spectrum of trans-2,2,5-trimethyl-3-hexene. 183

4.3-5 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethyl-3-hexene. 184

4.3-6 Temperature dependence of the olefinic carbons C1 and C2 chemical shifts for cis-2,2,5-trimethy1-3-hexene. 185

5.2-1 Temperature dependence of the vicinal coupling constant (J23) for trans-2,2,5-trimethy1-3-hexene. 193

5.3-1 Schematic reoresentation of the transformations considered in the discussion of the NMR results for r:s-2,2,5-tri-methy1-3-hexene. 217

5.3-2 \Temperature dependence of the vicinal coupling constant (J23) for the Ji3-2,2,5-trimethy1-3-hexene. 220

xv


LIST OF FIGURES (continued)

Figure

5.3-3 Olefinic proton (H1) chemical shift dependence on temperature for: A - cis-4,4-dimethyl-2-pentene referenced to TMS 3 - cis-2,2,5-trimethy1-3-hexpne referenced to TMS C - cis-2,2,5-trimethy1-3-hexene referenced to TMS,

but corrected for temperature dependence of intrinsic contribution.

5.3-4 Olefinic proton (H2) chemical shift dependence on temperature for: A - cis-4,4-dimethyl-2-pentene referenced to TMS B - cis-2,2,5-trimethy1-3-hexene referenced to TMS C - cis-2,2,5-trimethyl-3-hexene referenced to TMS,

but corrected for temperature dependence of intrinsic contribution.

5.3-5 Proton chemical shift dependence on temperature for: A -.methyl proton of cis-4,4-dimethy1-2-pentene

referenced to TMS B - methine proton of cis-2,2,5-trimethy1-3-hexene

referenced to TMO C - methine proton of cis-2,2,5-trimethy1-3-hexene

referenced. to TMS, corrected for temperature dependence of intrinsic contribution.

5.4-1 Temperature dependence of vicinal coupling constant (J12) for cis-2,5-dimethyl-3-hexene.

5.4-2 Temperature dependence of the methine proton (H2) chemical shift for cis-2,5-dimethyl,-3-hexene.

5.4-3 Temperature dependence of the olefinic protons, chemical shift for cis-2,5-dimethyl-3-hexene.

xvi

page

233

234

235

258

265

268


PREFACE

Interest in high resolution NMR spectra of olefins originates

from various sources. Besides the aspect of basic structure determina-

tion that certainly ranges among the most important applications, the

conformational analysis of olefins has been tremendously advanced through

'the information obtained from chemical shifts and spin-spin coupling

constants. In addition, these parameters are dependent on the electronic

structure of the individual systems and valuable details about chemical

bonding become available.

On the other hand, the NMR spectra of olefins with known

stereochemistry have served as a source of experimental data that paved

the way for a better understanding of the mechanisms which determine

chemical shifts and coupling constants in organic molkules. NMR/

chemical structure correlations can thus be established while theoretical

investigations are stimulated.

Besides these static parameters related to molecular geometry

and bonding, the sensitivity of the NMR method to intramolecular rate

processes has led to a wealth of information related to the dynamic

'properties of molecules, including conformational equilibria. The

temperature dependence of the spectrum has thus to be studied.

The successful use of NMR spectroscopy as an analytical tool

depends on the extraction of the fundamental parameters from the spectrum.

xvii


In many cases, and particularly in this thesis, a full mathematical .

analysis using one of the computer programs available is required for

complete interpretation of the spectrum. The availability of such

sophisticated programs and of a new generation of NMR spectrometers at

the beginning of the seventies has made possible the interpretation of

more and more complex spectra. Also, up to the mid-sixties, virtually

all conformational studies carried out by NMR were based on proton

resonances, but that situation changed radically in the subsequent period

and presently a large number of studies involving carbon-13 nuclei are

reported in the literature. In this thesis, both proton and carbon-13

NMR are employed.

Studies on methyl substituted ethylenes by electron diffraction

and rotational spectroscopy have shown that in all these molecules the

preferred conformation is such that one CaH eclipses the C=C bond and is

therefore anti relative to the C-H at tire neighbouring olefinic carbon.

NMR studies on mono- and trans-dialkyl ethylenes have indicated that the same

conformational situation prevails in these molecules, although the

population of the different forms varies with the nature of the substi-

tuent(s). In these latter studies, it was proposed that the coupling

between rotors proceeds through valence electrons of the C=C moiety. The •

consequent valence angle changes would then be transmitted to the coupling

constants of the second rotor.

It was thought that variable temperature NMR studies of the two

isomers of 2;2,5-trimethyl-3-hexene and of _,1:0-2,5-dimethy1-3-hexene

would provide decisive information with regard to the above proposal.


A

The study of such cis/trans pairs of isomers would also, hopefully, shed

new light 'cm the nature of cisoid alkyl interaction. In this respect it

should, be remembered that the strueture of cis-2-butene (as obtained from

rotational spectroscopy) was the only accurate piece of inforMation

hitherto available on such cisoid interaction.

In order to succeed in this approach, additional information is

needui. The introduction of molecular Force Field calculations has as

the main purpose the provision of an estimation of energy differences

between various rotameric structures. A second objective of using Force

Field calculations was to obtain the basic structural information corres-

ponding to the minima in steric energy. This Force Field method allows

one to extend the knowledge of conformational geometries beyond the

simple molecules for which electron diffraction, rotational spectroscopy

?nd X-ray cristallography provide accurate geometries. With the help of

Force Field calculations as an auxiliary technique, structure-parameter

relations.can be investigated. Indeed, since the beginning of the

seventies, the Force Field procedure has been extensively developed and

presently, the various Force Fields contribute to obtain information on

structure and energy'of molecular conformations.

The theoretical material in this thesis is arranged in two main

sections; the first section describes the Force Field employed, while the

second one gives an extensive review of NMR/chemical structure correla-

tions as well as the methodology used in spectral analysis. The results

obtained from Force Field calculations for various substituted ethylenes

are detailed in Chapter III; this is followed in Chapter IV by a summary

xix


of the experimental data obtained by proton and carbon-13 NMR spectro-

scopy. Interpretation of the results for each molecule investigated using

a structure-parameter relationship approach is given in Chapter V, while

the epilogue of the study is given in Chapter VI.

Throughout this thesis, the energy has been expressed in J.mo1-1

except in some specific cases. These values are followed by their equiva-

lent in cal.mol-I placed between parentheses. The cis-trans system for

naming configurational isomers, being unambiguous for the molecules

studied, has been used preferentially co the Z-E system.

xx


CHAPTER I

FORCE FIELDS

1.1 INTRODUCTION

The Force Field method considers only the positions of the

nuclei in the molecule; the electronic system is not considered

explicitly as it is in ab initio energy calculations.

In this method (Force Field method) a classical approach of the

problem is employed; a set of equations in the form of the classical

equations of motion is assumed to exist for each molecule. The problem

from this point of view is one of establishing just which equations are

necessary, and of determining the numerical values for the force

constants which appear in the equations.

A great deal of experimental information regarding small mole-

cules (e.g., equilibrium bond lengths, bond angles, heats of formation)

is available. For small molecules the force constants are usually also

available from normal coordinate analysis and the Raman and infrared

spectra. A large molecule consists of the same features, but they are

combined and strung together in different ways. The problem is to

formulate the structure of a large molecule in terms of the elementary

features of these small molecules. This is both the aim and the basic

tenet of the Force Field method, to develop a universal Force Field,

1


employing force constant pertaining to small structural elements,

allowing the calculation of structures of entire molecules, both small

and large.

The Force Field method discussed here is a useful method for

determining the structure and energy of a moledUl But there are many

other properties of a particular molecule that can be found after the

structure and energy are known. These include vibrational frequencies

and thermodynamic functions such as free energy and free enthalpy of

activation for rotation.

The Force Field method has also its shortcomings; it is a semi-

empirical method, in that its force constants are found by data fitting

on a large volume of experimental data. These data must exist for a

given class of compounds before the method can be developed and applied

to any particular compound in this class.

Real molecules at roam temperature occupy a series of vibra-.

tional states, and the atoms are not at rest but are vibrating. The

energy of the total assembly varies with temperature because the mole-

cules occupy the vibrational levels according to a Boltzmann distribution.

The calculation carried out by the semi-empirical'Force Field method

gives a potential function and the molecule is regarded as being a rigid

structure at rest at an energy minimum. This type of structure is

usually adequate for many purposes; in cases where the dynamic nature of

a structure is important, one can use the vibrational levels calculated

by standard methods of statistical mechanics, using the force constants

as used for the "rigid" structure calculation.

2


There is another way to determine the structure of a molecule

by calculation: the so-called ab initio method. Regardless of other

shortcomings (truncation of wave function, neglect of correlation between

electrons) the ab initio calculation is considerably slower (factor of

103 for small molecules that increases with the size--see for example a

review by Allinger [2]). At present the accuracy of ab initio structure

calculation is not as good as with Force Field methods.

The development of a Force Field begins by imagining a mechani-

cal model of a molecule as a series of masses (atoms) attached by springs

(bonds). This general idea can be traced back to Andrew [2]. Deforma:

tion of the structure results in an energy change which can be calculated

if the forcelaws and force constants involved are known. The complete

set of force constants is referred to as the Force Field. The latter is

developed by deciding what kinds of forces and constants are needed to

reproduce the known structures of small molecules. A model is then

constructed; it may reproduce the experimental facts, but this does not

mean that the model is in every respect a faithful reproduction of the

molecule under study. It means on1S, that the information used to develop

the model is reproduced by it. If one wants to calculate properties of a

molecule, one prefers the particular Force Field that is developed from

the properties of interest. In the present study the Consistent Force

Field calculation developed by Ermer and Lifson [3] has been chosen. As

far as this study is concerned (calculation of energy conformation and

thermodynamical properties of substituted ethylenes) it is the most

accurate one available. Experimental data used for the optimization of

3


energy parameters comprised: 259 experimental vibrational frequencies of

ethylene, trans- and cis-2-butene, isobutylene, cyclohexene, 1, 4-cyclo-

hexadiene l nd trans, trans, trans-1, 5, 9-cyclododecatriene, 44 conforma-

tional data on ethylene, propene, cis- and skew-l-butene, isobutylene,

cyclopentene, cyclohexane, trans-cyclooctene, cis, cis-1, 6-cyclohexane;

ten cis/trans differences and excess values (over cyclohexene) of the

heat of hydrogenation involving the 2-butenes, the 1, 2-di-tert-butylethy-

lenes, the 1, 2-methyl-tert-butylethylenes and the five- to ten-membered

cyclic mono-olefins.

- In the next section the potential function used by Ermer and

Lifson [3] will be described.

1.2 DESCRIPTION OF THE MECHANICAL MODEL

To develop a classical valence Force Field, the molecule will

be represented as though it were a serif; of masses joined together by

springs, with Hooke's law applying within the Newtonian laws of motion.

The mechanical model thus becomes a description of the various types of

deformation, as detailed below.

(i) Bond stretching and valence angle bending

Bonds tend to have a certain "normal" length. If a bond is stretched

it is assumed that Hooke's laws apply as it would for a spring. A

similar relationship applies for bending angles. Thus a stretching

energy (Eb) and a bending energy (E0) can be defined for a molecule by

equations (1.2-1) and (1.2-2) in which the summations are over all the

4


bond lengths and valence angles in the molecule (respectively b and e).

Eb = E Kb (b-b0)2

Ee

h E He (0-8

o)2

(1.2-1)

(1.2-2)

bo and eo

are parameters representing the corresponding reference

values. It is known from vibrational spectroscopy that valence angle

deformations require much less energy than bond length deformations.

The respective force constahts differ by about one order of magnitude:

bond angles display a greater variability than bond lengths and are

more relevant for conformational calculation.

Equations (1.2-1) and (1.2-2) are strict* speaking only valid

for relatively small deformations. For larger deformations higher

order polynomial terms could be added or a Morse potential could be

employed instead. By making use,only of quadratic terms, one is thus

faced with a general limitation. in terms of molecular geometry para-

meters, Ermer [4] estimates roughly 0.1A and 15° as upper limits for

deviations of bond lengths and valence angles from their respective

reference values, as validity range for equations (1.2-1) and (1.2-2).

(ii) Torsional terms

Ti account for the energy difference between eclipsed and staggered

ethane one has to introduce a torsional term in the potential. For

ethane this term is described by equation (1.2-3):

5


E4) = li H4) (1-cos34)) (1.2-3)

where 4) is the H-C-C-H dihedral angle, 114) the force constant.

Ermer and Lifson [3] have generalized this formula to include

all torsional motions in alkanes and alkenes:

E4) = 1/2 E H 9 (1 + s cos n4)) ;1.2-4)

s and n depend on the type of the bond around which rotation occurs:

the energetical description of rotations around bonds with high tor-

sional barriers (double bonds) demands the evaluation of the influence

of higher cosine terms.

(iii) Non-bonded interactions

In addition to the terms already defined, Van der Waals interactions

exist between all pairs of atoms which are not bonded to one another,

nor to a common atom (these cases are excluded because if the atoms

are bonded together the Van der Waals interaction is taken into

account by the bond stretching, and if they are bonded to a common

atom it is at least partly allowed for in the bond bending).

The attractive part of the Van der Waals curve is a result of

electron correlation and is inversely proportional to the sixth power

of the di.,tance separating the atoms. The repulsive part of the

potential is more steeply dependent upon distance in the Lifson-Ermer

Force Field; an inverse power of 9 is used to express this behaviour.

6


Enb

= E e (2(r*/r)9-3(r*/r)6) (1.2-5)

where r* is an equilibrium "radius" and e measures the softness or

hardness of the potential. A thorough discussion of alternative non-

bonded potentials has been given by Williams et al. [5].

All the terms described up until this point are common to all

Force Fields; the remaining terms to be discussed are specific to some

workers.

(iv) Out of plane bending

For pyramidal distortion without twisting (out-of-plane bending) a

potential developed by Warshel et al. [6] has been applied. This out

of plane bending is different from torsion as it involves the inter-

actions between the three orbitals of the same atom, while the other

involves those between two neighbouring atoms.

Ex = H

xx2

(v) Cross terms

(1.2-6)

In cyclobutane, if an angle is opened bond the tetrahedral value the

repulsion between adjacent bonds is reduced and the bond lengths can

contract. Clearly, bond length and bond angle are correlated and not

as independent as equations (1.2-1) and (1.2-2) would indicate. The

apparent solution to the problem Cs to add a stretch-bend interaction

7


term into the energy expression. Thus an energy of the form repre-

sented by equation (1.2-7) is introduced,

Ebe . z E Fbe (b-bo) (0-0o) (1.2-7)

Fb6

is the force constant used to express the strength of coupling ..."--

between the bond length b and the adjacent angles 6. Similarly, a

cross term is.added for two adjacent bonds (b) and two adjacent angles

(e), and two adjacent out of plane bendings (x); this leads to energy

terms as given by equations (1.2-8), (1.2-9) and (1.2-10).

Ebb'

= E E Fbb' (b-bo) (b'-boi) (1.2-8)

Eee,= z z F66' (6-60 0 ) (A-6') (14.2-9)

EXX

1 = E E FXX'XX'

(1.2-10)

Finally the complete potential expression used can be written

in the following form:

Or:

V = Eb + EA + Enb + Ex + Ebe + Ebb' + E56 1 4. E(x 1 (1.2-11)

8


• V = 1/2 E Kb (b-bo)2 + 1/2 E He (e-eo)2 h E K (1 + s cos 0)

+ E E(2(r*/r)9 - 3 (r*/r)6) + E E F

be (b-b

o) (0-e

o)

+ E E Fbb (b-bo) (b 1-bc;) + E E Fee (e-e0) (e'-e(;)

+ 1/2 E HX

x2 + E E FXX

XX'

1.3 FORCE FIELD CONSTANTS USED

(1 .2-12)

As previously indicated, the constants have been determined

using a reasonably large set of experimental data, representing a large

variety of properties and structural features. A total of 313 observed

quantities were used by Ermer and Lifson [33, and incorporated. into the

least-squares fitting process: 259 vibrational frequencies, 44 conforma-

tional data and 10 thermodynfical quantities. •

The results are listed in Table 1 .3-1. The average absolute

differences between the 44 observed and calculated bond lengths, bond

angles and torsion angles used in the optimization of parameters, were 0

0.003 A, 0.5° and 1 .0° respectively.

9


TABLE 1.3-1 Valence Force Field constants for olefins as given 'by Ermer and Lifson [3]i

I Diagonal terms

KD'

boD

KR'

boR

KT' boT

KL' b02.

K b S' oS

Kd' bod

Kr' b or

HE, C 0

bond stretch

C —C

C (0 3 ) C (0 3 )

C ( 0 j ) '-C(?)---

H 4H C C

b C " C

'C NH

C C

11/ti C H

C C A/ C / \\

H H

1-I-i

I-I

angle bend

C r e /C

C C C.

iC

N H ,,

C 4...\ C C

if 1309.9 , 1.333

645.3 , 1.526

645.3 , 1.501

723.0 , 1.089

660.0 , 1.105

654.0 , 1.105

681.5 , 1.105105i

72.4 , 122.3

104.3 , 115.4

93.2 , 110.5


TABLE 1.3-1 (continued)

HA, Ao

H r ' '0

H 40 o

q'o

H , v o

Hy, yo

HS' 60

H , n n o

H6'

do

Ha, a0

HE

C C

C C C H

C C

C—Ce.

H C C,

C

ec

C c

C c

H

H

A—r1H

C C

_AH H

H

93.2 , 109.47

93.2 , 110.0

67.5 , 121.2

75.0 , 116.5

88.8 , 108.9

88.8 , 109.2

88.8 , 112.4

66.7 , 117.6

79.0 , 109.6

79.0 , 106.4

torsions

Fk H H /C.-.E.--C\/

\ C÷ ,C\ 37.9

H H H/ C

1'


0

I TABLE 1 .3-1 (continued)

-CNH

H 121

HT

HER

HX C

FRR 28 . 5 C

Frr

H C

H—C

c (

(

CC 32.7 N.

C

I) ( -2) 2.532

-5) ( 2.845

22.9

II Cross terms -4

, FRw = 60.2 C----e -(E= 38.4 C. )

-7.9 H

-7.9

H ,C F Ry ' = 0 C----.0 F' = 0 F4 7

YY k....NC C

fYw = -10.5 1

( 4C 4116 f rr = -10.0 ((a l FXX = 3.31

III Non bonded interactions

-7.9

H H 1/2 rAw = 1.816 H CI 1/2r*HC = 1.787

1/2 = = 0.1615 6 HH 0.0641 HC

C C 1/2 r*cc = 1.759

e1/2cc = 0.4072

The potential constants are defined in graphical form. The units are Lased on the following units for energies, lengths and angles: Kcal).mo1 -1, A and rad respectively. Reference lengths and angles are given in A and degrees. The parameters for the non bonded potential hold for expression (1.2-5).

12


In the absence of strain the local symmetries of methylene and

methyl ,groups are assumed to be C2v and C3v respectively; in addition the

sp2

carbons are supposed to be coplanar with their ligands. These

assumptions lead to a reduction in the number of adjustable parameters.

The following relations have to be fulfilled (see Table 1.3-1 for

notation):

cos yo

- cos ho cos h wo (a)

cos 60 = - ((1 + 2 cos ao)/3)1/2 (b)

no = 2Tr - 240

tpo = 2Tr - 24 - e

0 o

ao = 2Tr - e

o

(c)

(d)

(e)

(1.3-1)

Ermer andlifson [3] evaluated the torsional energy individually

for each n the torsion angles X-C-C-Y around the C-C bonds, making

altogether nine torsional angles for the sp3-ep3 bond and six for the

3 2 sr -sp bond. Then the torsional energy parameters are 1/9 and 1/6 of

13


the values for H and H07

listed in table 1.3-1 . 0

In relation (1.2-4) the values for s are -1 for C = C-C-C and

C = C-C-H rotations, and 1 for all other rotations around single bonds.

For pure twisting around the double bond a twofold cosine potential was

applied, with s = -1 and 4 15(0 0 term of = 2145 4'3140' In the cos

relation (1.2-4), n = 3 for all C-C single bonds and n = 2 for double

bonds.

doe

1.4 ENERGY MINIMIZATION

The structure of the molecule will correspond to that geometry

where the energy is at a minimum. Therefore if the energy of the mole-

cule is written as in equation (1.2-12) all one needs to do to find the

structure is to take the derivative of this equation with respect to each

of the degrees of freedom of the molecule, and find the position(s) where

each of those derivatives is simultaneously equal to zero.

There is a variety of mathematical techniques which can be used

to do this; different methods have different advantages and different

drawbacks.

Here the three minimization procedures used in the Ermer-Lifson

program are discussed: the steepest descent iteration, the Fletcher-

Powell method and the Newton-Rahson minimization procedure. A combina-

tion of these ':chniques gives satisfactory results in almost all cases

of practical interest.'

The program uses Cartesian atomic coordinates which is better

14


than the alternative of internal coordinates: it is easier to derive all

independent and dependent internal coordinates from a set of independent

easiboqbtainable Cartesian coordinates, than to evaluate the dependent

inter41 coordinates from a set of independent ones. The disadvantage

(that the potential energy.is related to Cartesian coordinates in a more

complex fashion than to internal coordinates) is 'a less serious problem.

One has then to find the minimum of a function of n variables

such as (1.4-1):

V = V(xl, x2 . . . , xn) = V(x)t (1-.4-1)

It is obvious from inspection of equation (1.2-12) that in its

domain of validity, the function used is differentiab16 which allows one

to use the three previously mentioned minimization procedures.

(1) Steepest descent minimization [7]

This method can be used when the function to be minimized has first

derivatives. Given a function V(x), it is known (if the first partial

derivatives exist) that the gradient of the function Vv(x) is a vector

pointing in the direction of t6 greatest rate of increase of V(x).

At any given point (x0) the vector vv(x0) is normal to the contour

that passes through the point (X0). The negative gradient points in

the opposite direction, which is the direction of the greatest rate of

Throughout this thesis vector quantities are italicized.

15


decrease of V(X) at this point. The procedure used in this minimiza-

tion method is as follows:

- Start at some initial point (X0).

- The general iteration step begins then; for the ith iteration one

calculates Vv(Xi).

- Move in the direction -VV(xi). To do that one has to determine a

step size hi; in the present program h i depends on the step length

(E (Ax.)2)h, x. being the jth coordinate. J . J

- Calculate the next point: (Xi+1) = (Xi) - hiVv(Xi).

- The calculation stops when relation (1.4-2) is satisfied:

V(Xi) - V(Xi4.1) < e (1.4-2)

where e is some pm-established tolerance. Figure (1.4-1) shows a

graphic representation of the possible succession of points that one

would obtain in the application of this method. In the illustration

the function to be minimized is a two-variable function f(x1, x2).

If one starts at 0 (x x02) and moves in the direction of the nega-

tive gradient, one moves in a direction perpendicular to a tangent to

a contour of f(x1, x2) and in the direction of decreasing f. This

takes to 1 (x11, x.12). Any further movement along the line 01 (in figure

(1.4-1) will increase f. Now the negative gradient at 1 is deter-

mined, and the previous procedure is repeated. In this fashion, one

proceeds to 2, 3, 4 until one reaches the minimum to whatever

tolerance is desirable. The successive steps or directions in which

• 16


Reproduced w

ith permission o

f the copyright owner. F

urther reproduction prohibited without perm

ission.

)

4

FIGURE 1.4-1 A comparison of best-step Newton descent ( ) and standard steepest descent ( ).

Reproduced w

ith permission of the copyright ow

ner. Further reproduction prohibited w

ithout permission.

to move are orthogonal to each other. One of the implications of this

fact is that if the contours of the function to be optimized are

hyperspheres in n-dimensions, the optimum would be found in one step.

The more the contours of the function depart from sphericity, the

greater is the number of computational steps required to approach the

minimum value.

If the starting point is far from the energy minimum, energy

minimization proceeds fast with this method, but it slows down as one

comes close to it. Then one switches to a different procedure which

is more powerful at small gradients.

(ii) Newton-Raphson method [8]

In the Newton-Raphson method th. function V is replaced by its Taylor

series expansion to the second term:

V = V(xo )4. E 3 V/axi(X0) (xi-x0j)

a2V/3x.ax.(Xo ) (x.-x co .) (x.-x oj.)

i,j j j (1.4-3)

The value of V, its vector of first derivatives and its matrix

(usually called Hessian matrix) of second derivatives must be known at

the location (X0). Setting 3V/3xi = 0 for all i yields the location

of the stationary point of V. From equation (1.4-3) one obtains:

18


N 2V/ax.(x ) z a vtax.ax. (x.-x .) = o

o j=1 J j oj (1.4-4)

These N linear equations must be solved simultaneously for the N

unknowns; in vector notation one can write:

X =X0 - ^-1 v17

where V v = [aV/3x]

at the starting point

A = [32v/axiaxj]

(1.4-5)

The Newton-Raphson method has two undesirable features: firstly, it

requires one to calculate the Hessian matrix of partial derivatives

and s4.condly, it cannot be used too far from the minimum, because the

Taylor-series expansion is truncated after the. second term (this means

that the actual function is assumed to be a quaJr'atic function). But

as one approaches the minimum, this approximation becomes more

accurate and the method converges faster than the steepest descent,

the procedure of which is totally dependent on the vanishing first

derivatives. A comparison of the two methods is given in Figure (1.4-1).

The Fletcher-Powell minimization to be discussed next combines the

advantages of both the steepest descent and the Newton-Raphson

methods.

19


(iii) The Fletcher-Powell method (also known as the Davidon-Fl4tcher-

Powell method) [9]

This method is devised in such a way that, if the function to be

optimized is quadratic in n variables, the iteration scheme converges

in n iterations. The main difference with the steepest descent is

that it makes use of second order information taken from the function

to be minimized. The scalar hi of the steepest descent method is

multiplied by the Hessian matrix H. The direction of minimization is

no longer the gradient vector (except if the A matrix is the unity

matrix i). Use is made of the infor; .tion contained in the differences

of first derivatives (the array of which is also called a Hessian

matrix) to determine the best direction of minimization. The basic

?"" kiprocedure involves three general steps:

- Computation of the gradient VV(Xi) at some point (Xi).

- Determination of a direction ri along which to make the desired

move; r. = Ai vv(xi).

- Motion along this direction to some new point (X14.1), using Xi4.1

Xi + hr. (where h is the step size in the direction of search)

This general procedure is repeated until the gradient at some particu-

lar point becomes sufficiently small. To use this method, the

explicit calculation of second derivatives is not needed: one has a

second order representation which contains only first-order direct

information by using the gradient at two different points and by

calculating their difference. This method is now known to be a great

improvement over simple steepest descent procedures and is less

20


computer time consuming than Newton-Raphson procedures which need

calculation of second derivatives.

Some caution has to be exercised in the energy minimization

process so as not to lose symmetry elements as has been discussed by

Ermer [20]. The molecular symmetry is reflected in the first and second

(and higher) partial derivatives of the energy function V. Hence in all

minimization techniques with simultaneous calculation of the 6xi no

symmetry elements can disappear. This holds as well for the three pro-

cedures described previously. Additional symmetry elements can, however,

'be generated by these methods, if the starting geometry happened to have

a lower symmetry than the geometry at minimum. If one wants to determine

moleculir symmetries by Force Field calculations, one should always start

the minimization with trial structures of sufficiently low symmetry, and

the initial asymmetric distortion should 'not be too small.

The various minimization procedures are different in their

efficiency. By repeating steepest descent procedures, the first deriva-t

tives, the potential energy will be reduced to around 10-1 Kcal.mo1-1.A-1 ,

whilethe reduction in energy from the previous cycle can be of the order

of 5.10-3 Kcal.mol-1. At this stage, reduction offirst derivatives can

take hours of computer time and the calculation is judged to have reached

TWhen dedling with the "CFF" program, the energy has been expressed in calorie which is the unit used in that program. For the final results the energy will be transformed from calorie into Joule (using 1 cal = 4.184 J).

21


convergence. However, three to four cycles of the quadratically conver-

gent Newton-Raphson procedure starting from the last point may not reduce

the energy overmuch (about 10-2 Kcal. mol-1 ), but the first derivatives

will be around 10-10 Kcal.mol-1 1 .A and there may be important adjustments

to the torsion angles (about 10°). The general use of a Newton-Raphson

procedure results in more reliable geometry description of molecules in

additisin to a smaller improvement in energy.

The Fletcher-Powell method can lead to derivatives of about

10-6 Kcal .mol-1 1,.A but requires several starting points to avoid

partial minima.

1.5 DESCRIPTION OF THE "CFF" PROGRAM

To illustrate the procedure used in Ermer and Lifson's CFF

program a general set-up is given in figure (1.5-1). The input consists of

the Cartesian coordinates of the trial model (through a subprogram

called "MOLDAT") plus a set of structural parameters (b0, 80, . . .) and

of constants (Kb, H8, . . .) for the potential function: The trial model

is obtained from guessed internal coordinates which are transformed to

Cartesian by the "COORD" program Eli) (which is not part of the "CFF"

program). From a line code of the molecular structure (for example ZH3

AH AH ZH3 in the case of a 2-butene; A represents an sp2-carbon atom, Z

sp-3carbon atom) the subprogram "MOLDAT" sets up a list of all internal

22


INPUT Molecular parameters (see Table 1.3-1)

INPUT Starting cartesian coordinates for the molecule under study

CALCULATION Internal coordinates

CALCULATION Steric energy (V) and its derivatives

, MINIMIZATION a- Steepest descent method b- Fletcher-Powell type procedure c- Newton-Raphson method

OUTPUT Cartesian coordinates Internal coordinates Energy (V) and its first derivatives (dV/dx)

OUTPUT Frequencies and Normal modes of vibration

FIGURE 1.5-1 General scheme of the Lifson-Ermer Force Field calculation.

23


coordinates (lengths, angles, torsion angles, non-bonded distances) that

contribute to V. Their contributions to V and to the derivatives of V

are subsequently evaluated for the individual internal coordinates and

summed appropriately through the subprogram "MOLECU". The minimization

processes performed on the Cartesian coordinates are chosen in the

routine "CALCDT", which al lows the utilization of the three previously

mentioned procedures (through subprograms called "STEEPD","NEWTON-

RANSON", "DAVIDO").

The output of the "CFF" program consists (besides a list of

energies--bond, theta, . . .--, geometry, vibrational frequencies) of the

Cartesian coordinates of the "refined" model which can be used to restart

the procedure.

1.6 CALCULATION OF NORMAL MODES OF VIBRATIONS

The "CFF" program provides also the ' equencies of the normal

modes of vibrations. These are needed in this study because they enter

in the partition functions which form the basis for the

calculation of thermodynamic properties.

The Taylor expansion of the potential energy function V(r)

around the equilibrium coordinates r0, can be written as in relation

(1.6-1):

V(r) = V(ro) Z(aV/3r.)6r.÷ 1/2 2

2Vrar.3r.)6r.6r. (1.6-1)

i j

24


The third term of (1.6-1) represents the potential energy of

molecular vibrations around the equilibrium coordinates r0. It depends

on ro and takes the form:

V(ro; 6r) = V(ro + Sr) - V(ro) (1.6-2)

or V(ro; Sr) = Sr' H(ro) 6r (1.6-3)

where H(ro) is the Hessian matrix of second derivatives. In case the

Newton-Raphson process is used for energy minimization, the evaluation of

the molecular vibrational frequencies is a fairly simple matter since the

H-matrix is available.

For small atomic.displacements, Sr, the kinetic energy of a

vibrating molecule is given in matrix notation by:

6T = 1/2 61,1 M 61, (1.6-4)

where M is a diagonal matrix of the atomic masses.

The secular equation for the normal modes of vibrations as

derived.from the Lagrangian equations of motion takes the following form:

F 6q = A Sq (1.6-5)

where Sq = m 6r, and F = M M

Solving this eigenvalue problem yields the vibrational

25


frequencies (square roots of the eigenvalues Ai) and the normal coordina-

tes (eigenvectors with relative mass-weighted CarteMan displacement

O

I

amplitudes as components). The matrix F is sixfold singular as a conse-

quence of the six vanishing eigenvalues for translation and rotation.

In the "CFF" program the problem is solved using the House-

holder-Givens/bisectioh diagonalization procedure [14. These

performed using subprograms called "FREQ" and calculations are

"NMODES". The output gives all the frequencies with their assignments,

and displays also the normal modes of vibrations when required.

1.7 CALCULATION, OF CONFORMATIONAL INTERCONVERSips

Potential energy profiles for conformational interconversions

may be evaluated relatively easily in a point by point fashion.' Conforma-

tional changes are characterized by large changes, of torsion angles which SO

may serve as a model for the reaction coordinate. The calculation is done

by choosing a torsion angle which changes substantially during the inter-

conversion, and by performing a series of constrained energy minimiza-

tions for different fixed values of the chosen torsional angle. This

angle will be called a mapping parameter, following Ermer's notation [4].

It has to be an important part of the reaction coordinate (which is.a

many-dimensional vector describing the d\splacement of all he atoms

during a rate process The torsion angl\chosen as mapping parameter

must not take the same value for two or mote different conformations

through which the interconversion proceeds., the torsional constraint

26


required for the mapping is introduced by adding a fictitious potential

to the rorce Field; following calculations done by Ermer [/0], a poten-

tial of the form Kc (4)m -4 )2 is added to the general expression (1.2-12). mo

For Kc a value very much larger than a normal torsional constant is

chosen. The mapping parameter (1)m approaches, the fixed

(Dmo' under minimi-

zation of the energy with respect to all degrees of freedom. By

performing a series of constrained minimizations for different values of

(1)mo the energy profile may then be mapped point by point. This is the

only way to obtaintransition states when they don't contain additional or

different symmetry elements relative to the neighbouring minima.

To find the.exact transition state after mapping, one has to

start with the Raximum:in the mapping curve and then apply the Newton-

Raphsoh method,: which can lead to a maximum as well as to a

minimum. Transition states are characterized by one negative eigenvalue

for the matrix of second derivatives: and this will appear in the

frequency calculation in the form of an imaginary frequency.

1 .8 CALCULATION OF THERMODYNAMIC PROPERTIES WITH FORCE FILLDS

•

From calculations based on equations (1.2-11) and (1.2-12), the

geometry of a single minimum energy conformation of a molecule and the

a4Sociated steric,energy can be obtained. Such steric energies may be

used directly to obtain energy differences between stereoisomers; energy

differences between conformations are examples where steric energies are

directly applicable; heats of formation are required for other types of

27


energy comparisons.

The energies calculated with the use of equations (1.2-11) and

(1.2-12) are appropriate for molecules in a hypothetical motionless state

at 0 K [1a]. Corrections for the thermal energy of translation, rotation

and vibration have to be made to convert steric energies into measurable

properties.

1.8.1 Enthalpy

With the knowledge of the frequencies (see equation (1 .6-5)),

vibrational enthalpy contributions Hvib may readily be obtained using the

statistical-mechanical relationship:

3 N-6 i 1 1 Hvib = RT E1 1

X. [-1_5 + exp X1 . - 11 =

(,1.8-1)

where Xi = hvi/kbT; kb is the Boltzmann constant (kb = 1.38066 10-23 J.K-1),

h the Planck constant (h = 6.6262 10-34 J.$); vi represents the frequency

of the ith vibrational state in s-1. The summation extends over all the

real non-zero frequencies calculated. To that enthalpy of vibration one

has to add the enthalpy of rotation and of translation leading to a term

of 3RT where R is the gas constant (R = 8.314 J.K-1 mol -1). The total

enthalpy is then given by relation (1.8-2):

HT = strain + Hvib + 3RT

28

(1.8-2)


1 .8.2 Entropy

Like the enthalpy, the total absolute entropy (ST) can be

calculated by an appropriate summation over all the partition functions

which depend on the various normal modes of the molecules.

The total entropy is made up of the translational entropy (Str),

the over-all rotational entropy (Sor), the internal rotational entropy

(Sir), and the vibrational entropy (Seib)'

ST = Str + Sor + Sir +Svib (1.8-3)

These different contributions to the entropy will be described

in turn.

(1) Entropy of tranaation

Str = 3/2 R ln(M),+ 3/2 R ln(T) + R ln(V) + 5/2 R

(211- k)3/2+ R In

h3 NA5/2

(1.8-4)

M is the molecular weight, T the temperature in K, V is the

molar volume. k is the ideal gas constant per molecule, h is Planck's

constant, and NA is Avogadro's number. For an ideal gas at 298.15 K

and 1 atmosphere this equation can be written as:

29


O

Str = 28.719 log(M) + 108.023

(Str is expressed in J.K-1.mo1-1).

(1.8-5)

(ii) Entropy of over-all rotation

To obtain this thermodynamic quantity it is necessary to evaluate the

moment of inertia about the centre of mass of the molecule.' This can

be done using a program called COORD made available by the "Chemistry

Department of Indiana University" [ii]. Another needed factor is the

symmetry number of the molecule 's'. This factor has been separated

into two portions, the symmetry number of, the molecule as a whole sw

and the symmetry number of the rotating portion sr. The total sym-

metry number s is the product of all the symmetry numbers of the

molecule:

S = S iT S w r (1.8-6)

sw may be defined as the number of different positions into which a

polyatomic molecule can be rotated and still appears unchanged. For a

non-linear gaseous molecule the entropy contribution for overall

rotation is given by (1.8-7)

r711 8ir2kT 3/2 11/2

Sor 1.5 R + R in ---2-- (Ix I y Iz ) h

30

(1 .8-7)


where Ix, Iy, Iz are the three components of the moment of inertia of

the molecule. The other constants have the same meaning as above.

(iii) Entropy of internal rotation

Besides over-all rotation, many molecules exhibit internal rotation

between two or more parts of the molecule. For free internal rotation

the entropy of a Single rotating group is given by:

Sir = R + R In (8Tr3kIrT) (1.8-8)

Q Ir represents the moment of the

rotating fragment about its axis.

(iv) Entropy of vibration

The molecule can be considered as composed of several harmonic oscil-

lators. The vibrational entropy is the sum of the contribution from

each of the normal modes. The total contribution is given by equation

(1.8-9):

X.

S = R z

;xp(Xi)-1 ln(1-exp(-Xd 1 vib [

(1.8-9)

where all the constants have the same meaning as in equation (1.8-1).

To these four expressions for the entropy, an entropy of mixing

has to be added each time there exists a mixture of two (or more)

indistinguishable conformations; one adds Smix = 5.761 J.K-1 .mol -1. For

a comparison of conformations of one particular molecule only Sorb Svib and

31


Smix would be relevant; for comparisons between different molecules all

entropy terms would be relevant.

1.8.3 Gibbs free energy function G

For each -compound one can calculate the Gibbs free energy

function, given by the relation:

G = H - TS (1.8-10)

where H is the enthalpy, S the entropy and T the temperature. For two

conformations with different enthalpies and entropies, we have at the

temperature T:

AG = AH - TAS (1.8-11)

where the AH and AS would be calculated from the equations in sections

1.8.1 and 1.8.2, which are valid only for gases. Under a pressure of one

atmosphere the AG defined above is called the standard Gibbs free energy

and is noted AG°. The thermodynamical property that one can

compare directly with the results given by NMR experiments are the rota-

tional barrier or activation energy Ae'0, and the standard Gibbs free

energy difference AG° between conformations.

CM-

32


1.9 A NUMERICAL EXAMPLE

To illustrate the preceding sections, calculation of energy

differences between conformers and of structure of molecules have been

performed. Betdeen cis- and trans-2-butene the energy difference calcu-

lated with the "CFF" program is in good concordance with the experimental

data (AV is 10% higher than the experimental difference, while AG is 5%

lower); this is not surprising: these two conformations were part of the

input to :ind the best parameters for the Force Field.

The geometry of the molecule in its minimum energy is well

reproduced by the calculation: differences of less than 1° are found for

all the valence angles of the two butene isomers (the largest difference

being for the valence angle C-C=C of the cis isomer (0.9° from microwave

results obtained by Kondo et al. [24])).

The performance of the program is better tested with the

barrier of rotation for each isomer: reasonable experimental data are

available and they were not included in the input data. Each isomer will

be considered in turn:

(i) Cis-2-butene

The barrier height in cis-2-butene has been determined to be 1.9

Kd.mol-1 (450 cal .mol-1) from heat capacity data [15], 3.06 and 3.13

KJ.mol-1 (respectively 731 and 747 cal.mol-1) from torsional split-

tings in the microwave spectrum [24] [26]. Making allowance for top-

top splitting in the far infrared spectrum, Durig et aZ. [1?] found a

33


value of 2.03 KJ.mol-1 (486 cal.mol-1 ). The strain energy (0)

obtained with the "CFF" program is, by far, too large (at least twice

the experimental result). The best concordance comes from the

enthalpy barrier calculated: a value of 3.01 KJ.mo1-1 (720 cal .mo1-1)

is found at room temperature. The free energy of activation is as

large as that of the strain energy and does not give a close fit with

the experimental data. (AG° = 6.3 KJ.mo1-1 or 1.5 Kcal.mo1-1)

(ii) Trans-2-butene

The barrier in this isomer has been reported by Kilpatrick and Pitzer

[15] to be 8.16 KJ.mol,-1 (1950 cal.mo1-1) from heat capacity data. By

the technique of far infrared spectroscopy the gas phase periodic

barrier was calculated to be 6.28 KJ.mol-1 (1500 cal.mol-1) by Durig

et al. [17].

Once again the "CFF" program seems to overestimate the barrier,

but this time the difference is less important (of the order of 1

KJ.mo1-1). Both the enthalpy of rotaticn and the free energy are in

the bracket of the experimental results; a A1-1 of 6.7 KJ.mol-1 (1600

cal.mo1-1) is obtained at room temperature. Under the same conditions

the free energy barrier is of 8.33 KJ.mo1-1 (1990 cal.mo1-1).

34


CHAPTER II

THEORY OF HIGH RESOLUTION NUCLEAR MAGNETIC RESONANCE

2.1 INTRODUCTION

Nuclear Magnetic Resonance has been used for a long time as a

tool to determine the structure of molecules, and also to find the -inter-

actions between molecules of solute and molecules of solvent; the spectra

obtained can be expressed by three phenomenological parameters: the

chemical shift of the nucleus, the coupling constant between any two

nuclei and the spin relaxation times. For the kind of flexible molecules

of this study, coupling constants are likely to be the most useful para-

meters followed by the chemical shifts; the relaxation times are mostly

of very limited use and will not be further considered.

2.1 .1 Chemical shifts

Originally this term was introduced to indicate that a given

nucleus could exhibit different resonance fields (or frequencies), when

contained in different molecules. Nowadays, it also expresses the

difference for nuclei of the same isotope inside the same molecule.

Chemical shifts arise from a field-induced magnetic shielding of the

nuclei by the molecular electrons and are quantitatively described by an

appropriate shielding constant ui for each nucleus. Thus, the field in

35


the immediate vicinity of a particular nucleus when an external field Ho

is applied, is given by:

H.1 = (1 - ai) HO (2.1-1)

The shielding ai is really a tensor, but in the isotropiemedia

used in this study only the average will be observed. More commonly, the

chemical shift is taken from the spectrum as the frequency separation in

Hz, from a selected reference signal. However, it is more convenient to

express the chemical shift in terms of a dimensionless scalar 6, defined

by:

..-F 6 =

v-v,= ---1 -1-- x106vref

1", ..,...,

In this thesis the following approximation will be used:

6 = v- vref x106 v

o

(2.1-2)

(2.1-3)

where vo

is the fixed frequency of the probe at a field of 21.14 T (i.e.,

90.00 and 22.63 MHz for proton and carbon-13 respectively). For all the

spectra described in this thesis TMS (tetramethylsilane) was added (about

5% v/v) to each sample. Such internal referencing leaves the intramole-

cular aspects of 6 intact, but compensates part of the intermolecular

aspect of 6.

Proton chemical shifts of a molecule are sensitive to the

36


spatial orientation of neighbouring and distant moieties. A number of

factors are involved, and in many cases it is difficult to recognize

general trends. The various mechanisms responsible for Ighielding effects

will be discussed in detail in section 2.3.

2.1.2 Coupling constants

High resolution spectra frequently exhibit an abundance of

hyperfine structure. Such fide structure arises from an indirect

coupling between the nuclear moments pi transmitted from nucleus to

nucleus through the paired electrons comprising the valence bonds. Such a

interaction between two spins i and j can be expressed as follows:

E = -Kijpi • uj

or E = /i • /j

(2.1-4)

(2.1-5)

pi and are the magnetic moments of spins i and j, whereas /i and /j

are the spin vectors. The scalar Jij is called the coupling constant and

is usually expressed in Hz. From equation (2.1-5) it is clear that J is

field independent in contrast to, the chemical shift (v-vref) which is

linearly proportional to Ho.

The interaction between the el'ectrons and nuclei arises through

the interaction of the nuclear moments, either with the orbital motion of

the electrons or with the electron spin. It is important to :tote the

37


conditions under which coupling between two nuclei can occur. Firstly,

since the interaction is transmitted via a perturbation of the electron

wave function, the nuclei must be in the we molecule..\ Secondly, the

nuclei must experience a constant interaction over a time interval which

is long compared to the reciprocal of the coupling constant expressed in

frequency units. A chemical exchange process which separates a given

pair of nuclei in a time shorter than this will effectively remove the

spin coupling; furthermore, the relaxation times of both nuclei must be

sufficiently long.

Both chemical shift and coupling constants are subject to time

averaging: rapid intramolecular motion between conformers in which a

particular nucleus has different chemical shifts or coupling constants

will produce a spectrum appropriate to the time average only of these

parameters. Slow interconversion produces a superposition of the con-

former spectra.

2.2 'THEORY OF THE ANALYSIS OF NMR SPECTRA

2.2.1 Hamiltonian operator

We consider a molecule containing n nuclei with magnetic

moments pj in.a magnetic field Ho. The actual field at a given nucleus

is altered owing to intramolecular magnetic effects and intermolecular

interactions. Assuming that all these shielding eff6cts are described

by a scalar shielding constant, the field at nucleus j is expressed by

equation (2.1-1).

38


Meinteraction energy of nucleus j with th e field Hj • is

obtained through relation (2.2-1)

E = -0.J-H. = J w..I. (2.2-1)

where w.J = Tj (1 - a.)-H 0.

If nucleus j is indirectly coupled to the remaining nuclei,

there is, in addition to (2.2-1), the spin-spin energy given by equatiqn

(2.2-2).

E = - E Kjk j u .uk = = n E /./

jk j k (2.2-2)

The total energy for nucleus j is the sum of equations (2.2-1)

and (2.2-2):

E = - n NJ . 1J . E ) k Jk k

(2.2-3)

The Hamiltonian operator, H, for the system is obtained by

summing over j, and is described by relation (2.2-4):

- Ti (E w../i j E

k E

31( 3 I..'1( ) i J

(2.2-4)

It is convenient to write H in angular units; by choosing 71 for

the unit of angular momentum we can express H by equation (2.2-5):

39


•

H = - (E v. j

Izj . + E k E Jjk j k ) (2.2-5)

(If Ho is taken to lie along the z axis; vj is then the value of vj along

z, with 2rv.J = (0. and Jjk Jjk .) 27

The problem is then the classical one of finding the stationary

states of a given spin system, i.e., of finding a set of N spin functions

which are eigenfunctions of H: 1,3

Htp.J = A. 4). J J

with j = 1, 2, . . . , N (2.2-6)

ujLetusconsider .(j = 1, . . . , N), a set of zero-order

initial spin functions: they need to be an orthonormal set of eigen-

functions of I . These u form a basis and all the tyj can be expressed

as linear combinations of these functions:

tyj = E akj uk (2.2-7)

Equation (2.2-6) will be written as:

Eakj (H-Xj) uk = 0 (2.2-8)

The result of the application of H on uk can be developed as a

linear combination of basis functions uz:

H uk = E k u

1.4 40

(2.2-9)


where H2.1( = <u 1H1uk>.

Finally we get a set of N equations for the akj:

vEaki (Hzk - Xj6k2) = 0 (k = 1, . . . , N) (2.2-10)

' This set has a non-trivial solution if and only if the deter-

minant of the coefficients vanishes:

,f 1 - 1 = 0Hu Xj dzk (2.2-11)

Equation (2.2-11) is an algebraic equation of the Nth degree

for the N characteristic roots Ai. Substituting any one of these, for

example Xj, into equation (2.2-10) leads to a set of equations for the

akj. Only (N-1) equations are independent, but a normalization require-

ment is imposed on the tpj. a Nth independent relation is obtained:

Ea` I k kj

(2.2-12)

The general procedure to solve the, problem is first to find the

set of initial functions uj, which need to be orthonormal eigenfunctions

of Iz' and second to find the components of H as defined by Oiation

(2,2-9).

To reduce the labour involved in the determination of the

components of the Hamiltonian, use of Pasic symmetry functions rather

than of simple,products (aa, as . . .) is made. As a result the basic

41


functions can be divided into classes according to their values of Fz

(Fz = E Iz (i)) and their symmetries (there is no mixing between functions . 1

with different values of Fz, and between functions of different symmetry).

The Hamiltonian can be further factorized when the system is

composed of magnetically equivalent nuclei (this is sometimes called the

composite particle method which is described in the following paragraph).

To facilitate maximum factorization of the secular determinant

the X approximation car' be used in some particular cases. The method

and the'necessary condition for application will be outlined in a later

paragraph.

2.2.2 Subspectral analysis using the composite particle method [18]

A set of nuclei is said to be chemically equivalent if each

nucleus of the set has the same electronic environment: all nuclei of a

chemically equivalent set have the same shielding constant o. This

definition has been extended to include sets of .nuclei having the same

environment when averaged over a suitably long period of time; the latter

kind of equivalence is important in molecules where internal rotation

about single bonds may occur. In many molecules ccupling constants from

nuclei within a chemically equivalent group to any particular nucleus

outside the group are equal: the group is then said to be magnetically

equivalent.

To the previously mentioned simplifications, the properties of

a magnetically equivalent group of nuclei allow a further factorization

of the Hamiltonian.

42


(i) Coupling between spins within the group does not contri-

bute to the spectrum and can be omitted.

(ii) There is no mixing between wave functions having a

different eigenvalue for the square of the total spin moment

of the group, F2.

It is worthwhile then to define the total spin for the magneti-

cally equivalent group

F(G) = E r(i) (2.2-13) i in G

Each group can be considered as a "composite" particle of

moment F(i) (the numbering is now done by magnetically equivalent group).

Defining a new basis from linear combinations of the simple basis (for

example a6, (la) the Hamiltonian can be reduced into the form:

H = E v, Fz(i) + E ji4 F(i)•F(j) (2.2-14) ' i<j J

where the summation is over the different magnetically equivalent groups.

For a group of n equivalent spin h nuclei, the maximum value for F (spin

of one group) is n/2. Allowed values of F are n/2, n/2-1, . . . , 1/2 if

n is odd; if n is even F can go from n/2 to 0. In the first case (n + 1)/2

spin states are present and (n/2) + 1 in the second. For a spin state of

total spin quantum number F, there are (2F 1) possible eigenvalues for

the Fz of the considered group. This eigenvalue ranges from F to -F

(with aFz = 1). To describe each possible spin state the notation first

43


introduced by Whitman et al. [19] will be used: S, D, T, Q, Qt, Sx, . . .

for states with eigenvalues 1/2, 1, 3/2, 2,'3 (S stands for singlet, D

for doublet, T for triplet, Q for quartet, Qt for quintet, Sx for sextet,

etc.). Each spin state has an associated statistical weight g--degene-

racy of the representation in the group--given by equation (2.2-15):

_ (2F+1) n! 9 (n/2-F)! (n/2+F+1)!

(2.2-15)

This equation applies for a state with quantum number F of a

group of n nuclei.

As suggested previously, additional factoring is present when

the Hamiltonian has a further symmetry Quirt and Martin [20] have

developed this Hamiltonian in the case of a twofold symmetry. In NMR

studies such symmetry is usually the result of a plane or twofold axis of

symmetry in the molecule, taking the conformation as an average over an

NMR time scale. By rearranging the expression (2.2-14), the Hamiltonian

can be rewritten as follows:

z vi FZ(i) + z Jij F(i)•F(j) i<j

k J44 [F(i)•F(k) F(i)*F(ki)]

+ kCF (k) + fp')] + k Jkk , F(k).F(k')

44


E [Ja[F(k),'F(2) F(k 1)*F(2')] k<2,

+ Jkk [F(k).F(V) F(k 1)•F(Q)1] (2.2-16)

The labeling follows the one used by Quirt and Martin [20]: magnetically

equivalent groups which are transformed into themselves by the twofold

symmetry operation are labeled i, j . . All other groups must appear

in pairs, labeled k, 2, . . ., such that the symmetry operation inter-

changes the primed and unprimed members of each pair. The two different

coupling constants (usually cis and trans) which connect pairs k and 2.

are written Jkz and Jzk.

2.2.3 Subspectral analysis using the X approximation

The X approximation can be defined as a neglect of off-diagonal

elements connecting diagonal elements of widely different numerical

values, i.e., Hmn « IHnn-Hmml . The familiar "first-order" treatment is

the extreme case in which all the off-diagonal elements are neglected.

More often, only some of the coupling interactions are weak; this states

that a coupling constant Jii is small relative to a difference in Larmor

frequencies v.1-v. (a less qualitative definition is that J.1 ./(v.1-v.J) is

equal to, or smaller than, the experimental linewidtii). The term Jij /2

may then be neglected wherever it occurs as an off-diagonal element,

since the difference between the connected diagonal elements includes the

quantity v . -vJ This produces valuable additional factorization of the

45


secular equation.

2.2.4 General procedure to analyze NMR spectra

The calculation of NMR spectra may be divided up into several

steps:

(i) Use is made of a complete set of basic symmetry functions

as appropriate linear combinations of basic product functions

(aa, as . . .).

(ii) The matrix elements of the Hamiltonian can be deduced

following simple rules. The diagonal elements are found using

relation (2.2-17):

N E = z v. ((i ).) + 1/4 ZEJ.. T.. jmn i zim . . ij ij 1 1 l<J

with ((Iz)i)m = + h if nucleus i has a spina in um

- 1/2 if nucleus i has a spin 8 in um

and Tij = q 1 if i and j are parallel in um

- 1 if i and j are anti-parallel in um

The non-diagonal elements follow relation (2.2-18)

Hmn

= 11 U Jij

(2.2-17)

(2.2-18)

with U = 1 when um differs from un by an interchange of spins

i and j.

0 otherwise.

46


The matrix elements between linear combinations of basic products

are evaluated through expansion.

*The energy levels are solutions of the secular equation

(2.2-11).

*Frequencies are obtained by taking the difference between

energy levels using the selection rules for Iz, Fz(G) d the occurring

symmetries.

2.3 CHEMICAL SHIFT AND STRUCTURE

2.3.1 Classification of shielding effects

It has been pointed out earlier (see 2.1) that the field

experienced by a nucleus in an atom or a molecule differs from the

applied field Ho: a free atom experiences a field which is slightly

less than Ho

due to the motion of the electron(s) around the nucleus.

Extension of the treatment of shielding in free atoms to that

of atoms in molecules is complicated by several factors. An under-

standing of these factors is important as they are related to the way'in

which molecular structure affects the chemical shift. When a hydrogen

is chemically bound, the circulation of electrons is modified in two ways.

Firstly, the electron density at the proton will not be the same as in

the hydrogen atom. Secondly, the distribution of electrons around the

proton is no longer spherically symmetric. Chemical bonding can also

restrict the circulation of electrons, the degree of restriction being a

function of the orientation of the bond with respect to the applied field.

47


In the theoretical treatment of shielding in molecules, the

shielding is separated into two terms: the first term is a function of

electron density at the nucleus, the second term takes into account the

restriction imposed on circulation of electrons by chemical bonding.

They are referred to respectively as local diamagnetic and paramagnetic

shieldings.

In addition to the local shielding effects, significant contri-

butions to the shielding may arise from the circulation of electrons

associated with other atoms or•groups in the molecule. A shielding of

this type is called "long-range shielding." This type of shielding

arises only if the magnetic suspectibility of the electrons is aniso-

tropic (i.e., if the circulation induced by the applied field is different

for some orientations of the molecule in the applied field from others).

These effects are referred to as "remote effects" or as "neighbour aniso-

tropy contributions."

For organic compounds chemical shifts are measured, most of the

time, in the liquid phase. In this case, intermolecular effects must be

included in any discussion of chemical shifts. A solvent can contribute

to the shielding of an atom in a molecule by its influence on the

electronic structure of the molecule and by direct magnetic field contri-

butions in case of a magnetically anisotropic solvent. Choosing a non-

reactive internal standard such as TMS minimizes some of the unwanted

solvent effects.

Many effects thus contribute to the value of 6, and most of the

time these 3's are not direct indications of the electron density around

48


the nucleus being investigated. Quantitative quantum mechanical evalua-

tion of shielding in various molecules appears formidable, if not hope-

less at the present time. For many systems this shift can be evaluated

by empirical correlations; when these correlations fail, contributions

such as from neighbour anisotropy are often qualitatively invoked. Only'

when deviations are encountered, the molecule is examined to see what

property it possesses that could account for the observed discrepancies.

In the present thesis the analysis of chemical shift variation

with respect to the temperature as representative of variation in

structure will follow the aboye described qualitative approach. Chemical

shifts of many olefins have already been investigated and several trends

in their variations have been suggested (see for example Martin and

Martin [22]).

2.3.2 Interpretation of proton chemical shifts

Despite the disparity of the different effects involved, some

semi-empirical relations have been put forward as an interpretation of

proton chemical shifts in alkenes. In this section, contributions due to

magnetic anisotropy of C=C, C-C and C-H bonds and to electric effects of

the C-H dipoles, also due to non-bonded H....H interactions, are reviewed.

These effects are particularly useful for the interpretation of the methine

proton of an isopropyl group.

(i) Magnetic bond anisotropy

The existence of field-induced moments at atoms in the molecule other

49


than the one undergoing the NMR transition, can be felt at the nucleus

being investigated (neighbour anisotropy contributions). This effect

can be best explained in an acetylene molecule HC-CH. The field at

the proton will be strongly dependent upon the orientation of the mole-

cule with respect to the direction of the applied field. When the

applied field is parallel to the internuclear axis, the magnetic field

generated from diamagnetic electron circulations along the CEC bond

will shield the proton, while in a perpendicular orientation, this

same effect around CEC will result in deshielding at the proton. The

magnitude of the induced moment at the CEC bond (and hence the field

at the proton from this neighbour effect) for the parallel and perpen-

dicular orientations will depend upon the susceptibility ofkthe CEC

bond for parallel and perpendicular orientations, xi/ and x1 respec-

tively. This effect can be paramagnetic as well as diamagnetic: both

paramagnetic and diamagnetic neighbour effects must be qualitatively

considered when interpreting proton shifts. With axial symmetry

(along z for example) in solution (averaging factor) the effect (for a

three dimensional molecule) is expressed by the McConnel equation [22].

1 A a= T

R-3 'x (1-3 cos20z) (2.3-1)

where 6x stands for (X71-x)and ez is the angle between the z-axis and

the vector joining the source of the effect and the atom under investi-

gation, R is the length pf this vector. In the absence of special

substituent effects, the anisotropy of the double bond in alkenes will

t 50


be the dominating factor that influences the resonance frequencies.

It is generally agreed today (see Gunther and Jikeli [23]) that pro-

tons above or below the plane of the double bond and near the z-axis

(see figure (2.3-1))are shielded, whereas deshielding exists in the (x, y)

plane. The early calculations, made by Till.* [24] and Pople et aZ.

[25] disagree with respect to the sign of the effect near the x-axis,

where shielding [25] as well as deshielding [24] has been predicted.

Only the second alternative seems supporteu by the majority of experi-

mental findings; for example, in s trans-1, 3-butadiene the protons

near the x-axis of the second double bond are deshielded [28].

Similar results are found for the inner protons of the diene systems

of 1, 3-cyclopentadiene and 1, 3-cyclohexadiene [21.

In another calculation ApSimon et al. [28] found that shielding

might also occur in the (x, ',y) plane of the double bond. Then, to

substitute the older picture for the shielding cone of the C=C bond

represented by model A on 'figure 0-1) a new model (B on the same

figure) was proposed. however, in view of the experimental data used, •

Rummens [29] as well as Gunther and Jikeli [23] believe that it is

premature to discard model A in favour of model B. The latter authors .

estimate that model A is supported by more experimental evidence (for

example in 1, 3-butadiene the central protons that come close to the

y-axis of the second double bond are the most strongly deshielded).

However, it should be noted that in model A the shielding cone

is obtained by using the McConnell equation (2.3-1) which is applicable

only to bonds with axial symmetry; furthermore, the results emerging

51


z

(a)

/2

A

(c) C

(b)

FIGURE 2.3-1 a) Definition of the coordinate system (Oxyz) b) Shielding and deshielding regions due to magnetic aniso-

tropy of the C=C bond; model A according t.,) Pople [32], model B according to ApSimon et al. [28].

c) Definition of R and m in Vogler's model [.32].

52


from any point dipole approximation must be used with circumspection

in unsaturated hydrocarbons; this approximation is valid only for pro-

tons which are remote from the anisotropic centre'of the magnetic

dipole (here the double bond). It has also been noted by Kondo et

[30] and confirmed by Vogler [32] that an R-2 dependence is present to

account for the total effect. The modification on equation (2.3-1)

performed by ApSimon et al. [28] is more appropriate for a double bond

anisotropy, which would make model B more suitable.

To find the proton shieldings in conjugated hydrocarbons,

Vogler [31] calculates the local anisotropy contributions in the frame-

work of an extended theory using the coupled Hartree-Fock perturbation

theory. He finds an anisotropic shift Ad depending on both R and 0

(as these are defined in figure (2.3-1)). Only for small R (< 2 A) and 0

small 0 (< 15°) the theory gives a shielding. With R > 3 A, only

deshielding can occur independent of angle 0; furthermore, the

difference between minimum and maximum anisotropic effects is much

smaller with the Vogler theory than with the ApSimon procedure. For a 0

distance of 2A this difference goes.from 0.5ppm (Vogler) to 1 .5ppm

(ApSimon). In the case of ethylene the difference between experimental

data and Vogler's value is 0.02ppm; a value of 0.29ppm represents the

contribution from the local anisotropy to the shielding.

Not only the anisotropy of a C=C double bond exists, but also

the anisotropy of a C-C or a C-H is not negligible. It has ben

indicated by several workers (see for example references [32], [28])

that the anisotropy of a C-C bond is of the same order of magnitude as

53


that of a C-H bond. However, in a recent study, ApSimon et al. [33]

have concluded that it is impossible to calculate reliable magnetic

susceptibilities and susceptibility anisotropies of C-C and C-H bonds

from the collection of chemical shifts reported by Pretsch et al. [34],

while reasonably reliable values for the magnetic anisotropies of C=C

double bonds can be obtained.

Raynes [35] has developed an expression for the calculation of

the contributions of magnetically anisotropic X-Y bonds of freely

rotating -XY3 groups to the shielding of protons of a freely rotating

methyl group elsewhere in the molecule (both groups must have coplanar

axis of symmetry). With slight modification the expression can be

simplified to calculate the contribution of the same group to the

shielding of a fixed proton, or the contribution of a fixed C-H bond

to a freely rotating methyl group, These expressions are applicable,

only for remote moieties.

(ii) Non-bonded interactions

In crowded molecules the local anisotropy effect cannot account for

all of the chemical shift variation of the protons. several causes

have been suggested for these discrepancies. The original idea by

Reid [36] that a shift to lower field could be due to Van der Waals

interactions between a pair of crowded hydrogen atoms, has been

favoured by Jonathan et al. [37] and Memory et a:. [38], though Pople

et 2Z. [39] have been critical of some of Reid's assumptions. Bartle

and Smith [40], however, have preferred to attribute the entire

54


discrepancy in phenanthrene to sigma-bond anisotropy effects, con-

cluding that thgre is little, if any, Van der Waals contribution to

the chemical shift of the overcrowded proton in this molecule.

Finally, Cheney [41] has proposed a bond-polarization mechanism where-

by non-bonded electron repulsions between overcrowded hydrogens are

alleviated through charge transfer on to the attached carbon atom;' by

this method he has obtained the empirical expression (2.3-2) relating

the magnitude of the steric shift 6H to the component of the inter-st •

hydrogen repulsion force directed along the H-C axis.

< st . - 105 E cos ei exp(-2.671 r.) O .

(2.3-2)

(where ri is the H....H distance, ei the angle between the C-H bond

and the H....H connection).

On the purely theoretical side, Marshall and Popll [42] and

Yonemito [43] have provided, respectively, variation and 'perturbation

methods for estimating the downfield shifts due to Van der Waals

interaction in simple systems. In both cases the shielding constant

varies as R-6. For a distance or four Bohr radii (1 Bohr radius

= 5.29 10-1 °m) Yonemoto [43] find.. a deshielding by 0.3ppm, which is

three times larger than the result reached using Marshall and Pople's

[42] expression. According to C.W. Haigh et al. [44] Yonemoto's

method gives predicted down-fi ld shifts due to Van der Weals inter-

actions in aromatic Moletules 'n excellent agreement with the observed

discrepancies. However,. it has been noted by C.W. Haigh et al. [44]

55 p


that the relationship of Yonemoto which describes a system of two isolated

hydrogens interacting at long range, cannot strictly be applied when

the separation of the nuclei is less than about 7 or 8 Bohr radii, as

electron exchange effects then become non-negligible; in the range

(< 5-Bohr radii) at which intramolecular steric deshielding of protons

becomes important, it is the repulsive exchange forces and not the

attractive dispersion 'forces which dominate the interactions between

the hydrogen atoms.. •

(iii) Electric field contribution

Even in those systems where the local diamagnetic term dominates the

observed proton shift, there are alternative interpretations for the .

trends. In addition to the trends in the population of the hydrogen

(78) orbital as a consequence of the electronegativity of the attached

group, Buckingham has proposed [45] an electric field model to account

for changes in the electron density of a bound hydrogen atom: the

bonding electron density will be distorted in an attempt to avoid the

negative region of the space. If the electric field arises from

within the molecule (polar group, polarized bonds this effect will

not be averaged to zero: a distortion of the bonding electron density

can result. The contribwoon, calculated by Buckingham [45], to the

proton shielding from this effect, AGE, is given by equation (2.3-3):

AGE = A Ez + B E

2

56

(2.3-3)


where A and B take the respective values A = - 2x10-12 and B=-1x10-18esu

for protons. If we take pcH = 0.33D, with the positive end at the

hydrogen, only the linear term is of appreciable value (0.08ppm) for

the cis-2-butene (the two methyl hydrogens being in anti-position with

respect to the olefinic proton). The majority of applications of

equation (2.3-3) have been to the interpretatioh of the observed

,shielding brought about by polar substituents, protonation, and inter-

molecular interaction. Day and Buckingham [46] advise caution in such '

applications. They calculated the changes in the 19F shielding of HF

due to a negative point charge and compared the results with those

predicted assuming that the HF molecule was in a uniform electric

field equal to the field produced by the point charge at the fluorine

nucleus. Poor agreement was obtained eves when the point charge was 0

as far as 8A from the fluorine nucleus. This result suggests the need

to allow for field gradients. Attention to this question has been

given specially in the case of carbon-13 shielding and will be dis-

cussed in the next section.

2.3.3 Interpretation of carbon-13 chemical shifts

TheWidespread interest in carbon-13 NMR has ensured that the

shielding of this nucleus has received a great deal of attention at both

the semi-empirical and ab initio levels of approach. The relative

complexity of quantum chemistry has led to consider the chemical shift in

terms of constitutive or substituent representative parameters. The type

of molecules studied in this work made the theoretical approach virtually

57


impossible. Only correlations between carbon-13 chemical shifts and

structural and physicochemical parameters can be attempted.

(i) Influence of the steric effect

The carbon chemical .shifts are usually much more sensitive to steric

interactions than are proton chemical shifts, and non-additive carbon-

13 substituent effects have been discussed in terms of steric crowding.

The a and $ substituent parameters (substitution on the closest and

next to closest atom) which are usually low field, are influenced by

steric factors, but the most noticeable contribution occurs for sub-

stituent groups separated by three bonds froM the carbon of interest

(y-effect), as observed by Buchanan and Stothers [47] and Grant and

Paul [48], for example. It was noted by Grant and Cheney [49] that,

in this case, the substituent increments reflect the angular and

distance dependence of interacting groups. The mechanisms of the

steric effect on carbon-13 chemical shift has been explained by Grant

and Cheney [49]. A model has been proposed by Cheney and Grant [50]

to explain the observed shielding of the carbon t. ler the steric

influence of a remote substituent (y-effect). This wdel involves an

electronic charge polarization in the C-H bond as a result of the non-

bonded hydrow-hydrogen repulsive forces. The increase of ,negative

charge is associated with an electron expansion causing a decrease of

<1/r3> and of the paramagnetic term (upfield shift). Similar to

proton shifts a semi-empirical expression has been derived by Grant

and Cheney [49] for the steric contribution to carbon-13 chemical

58


0 shift of a C-H bond:

(5ste

13c = 1680 E cos ei exp(-2.671 ri) ppm

i

(2.3-4)

where the various parameters have the same meaning as in expression

(2.3-2). This formula is reasonably successful in predicting the

chemical shifts of cyclohexane and derivatives (as demonstrated by

Dalling and Grant [5/]), but it fails quantitatively in other cases as

for tricyclene derivatives as shown by Lippmaa et al. [52]. It is now

pointed out that the C-H polarization theory is insufficient, since

diamagnetic y-effects are caused by interactions of many other groups

than hydrogens.

Schneider and Weigand [53] applied the steric perturbation to

shielding as well as deshielding situations, to interactions with

heteroatoms and to carbons not in y-position. For that they proposed

to define the shielding force vector on the Ci-H bond by equation

(2.3-5), which is derived from the Warshel and Lifson [54] potential

for non-bonded interactions:

F = 0.6952x10 (18e/r*) [(r*/r04 -(r*/r07] cos 8. (2.3-5)

This,equation applies to hydrogen-hydrogen interactions,

(eh= 4.109 10-3, r* = 3.632) as well as to carbon-hydrogen interactions

(e = 26.10x10-3, r* = 3.575); ri and ei have the same meaning as in

equation ;(2.3-2). Arguing that repulsive non-bonded interactions are

59


extremely sensitive to sma I change in r, they have applied equation

(2.3-5) only to fully relax d molecular structures as obtained by

Force Field energy minimization. They found an adequate linear

correlation between resonance shift and the force previously defined

(despite its dependency upon the Force Field used to find the molecu-

lar structures).

Seidmaniand Maciel [55] have attempted to explore the geometri- .

cal dependence of .methyl-group shielding in systems such as alkenes by

making ab initio calculations using the modified-INDO'finite perturba-

tion theory (FPT/INDO). The conformational dependences of the methyl-

group carbon-13 •shieldings in the n-butenes were qualitatively as

predicted by y-effect trends; nevertheless they,find that this effect

cannot be explained alone by the steric mechanism proposed by Grant

and Cheney [49]. For Seidman and Maciel [55] carbon-13 shielding

appears to depend, in part, on the precise details of the electron,

distribution at a carbon atom rather than on the total electron

density. Calculations for various alkanes [55] point to the conclusion

that the y-effect is related to the details of the conformation of the

CH3-C-C-CH

3 system. Similarly, Gorenstein [56] argues against the

attribution of y-carbon carbon-13 chemical shifts in hydrocarbons to

electron polarization and increased carbon electron density arising

from steric interactions. He proposes that it arises from a

generalized gauche-effect attributed to valence bond-angle and

torsional angle changes. Advantages claimed by Gorenstein for this

interpretation include explanations of upfield carbon-13 shifts in

60


cyclohexanes (between gauche and trans) and of the 1, 5-interaction.

In contrast to the well established upfield steric effect of

y-substituents, downfield shifts are observed for groups separated by

four bonds (1, 5-interaction) in a syn-axial orientation as found by

Grover et al. [57]. This alternation in sign between 1, 4- and 1, 5-

interactions cannot be understood by the bond polarization model.

(ii) Correlations between carbon-13 shift and electronegativity

Even if the downfield shift of a carbon atom substituted by an electro-

negative group has been known since the early days of carbon-13 NMR, a

quantitative relation between carbon-13 shift and electronegativity

has only been derived recently. In their study of the dependence of

6C-X in methyl, ethyl and phenyl derivatives on the electronegativity

of the X substituent, Spiesecke and Schneider [58] have observed the

expected increase of the chemica\shift with the electronegativity of

X. Several correlations have been proposed for.certain classes of

compounds. A more general representation of the dependence of carbon-

13 shifts on electronegativity results from a study made by Phillips

and Wray [59]. The screening of a carbon atom, substituted by four

ligands, is expressed in terms of effective electronegativities,

considered as being simple perturbations of the Higgins electronegati-

vity of a group by other substituents.

(iii) InfZuence of bond polarization electric field effect's

Like for proton shifts, an electric field effect has been invoked to

rc

61


explain the discrepancies between the theoretical and observed values

of the chemical shifts. Equation (2.3-3) is still valid and the

shielding of a nucleus is expressed as the sum of square electric

field effects, E2, and linear field effects E. Parameter A of equation

(2.3-3) is now positive and takes a value of 30.x10-12 according to

Horsley and Sternlich [60]. This means that if the shielding of a

carbon atom of a C-H bond increases when an electric field acts on the

molecule, the proton of the same C-H bond is deshielded. The

deshielding. symmetry distortion of a Ci atom electron cloud by a

fluctuating C-X dipole is given by equation (2.3-6) where ri is the

distance from the middle of the C-X bond to Ci, Ix is the first

ionization potential of X, and Pcx the polarizability of the C-X bond.

‹E2

3 Ix Pcx r.-6 (2.3-6)

The polarization of electrons at a Ci-Y bond by an intramolecular point

charge? has been approximated by Schneider and Freitag [61], by

equation (2.3-7):

AQ = P Z-1 7r

-2 cos

c.y c.y c.y (2.3-7)

where AQc is the charge separation induced by a static electric 1y

field, P the polarizability of the C.-Y bond, Z its length, r Pc •y ciy

its distance from 8 its angle with the acting electric field vector.

Neglecting higher order terms, equation (2.3-7) represents E and is

62


expected to be observable over large intramolecular distances, whereas,

owing to the r-6 term, the Van der Waals effect,<E2 , falls off

sharply. In view of some inadequacies of equation (2.3-3) (see the

electric field effect on the proton shift) it has been suggested to

take into account the effect of the field gradient. Batchelor [62]

has demonstrated that an improved description of linear field shifts

is achieved by the addition of an extra linear term arising from the

field gradient at the nucleus of interest. Batchelor divided the

shielding into contributions from uniform-field linear electric field

(i.e., quadratic field-dependent contributions are ignored) and from

field-gradient electric field shifts. His method of distinguishing

between the two contributions is to determine first the shielding

change for quaternary carbon atoms for which the uniform-field contri-

bution is ignored and the total of the observed shift is attributable

to the field-gradient contribution. Raynes [63] expresses some doubts

about the validity of such a procedure, in particular because of the

omission of long-range factors affecting the local site symmetry.

This may be of relevance since Batchelor data fitted the parameters

required to describe the uniform electric field shift and the field-

gradient shift. He showed also that these parameters depend upon the

site symmetry of the carbon-13 nucleus. These ideas were later applied

by Batchelor et al. [64] to conformational effects. Most of the

information in organic molecules comes from the orientation of the

electric field in the molecule; the field gradient is much less

orientation-dependent (20% frbm Batchelor's estimation), The authors

63


introduced a plane of zero shift; if the carbon possesses a z-axis of

symmetry, this plane is the (x, y) plane. A charge placed in this

plane would not affect the chemical shift of this atom if the first

order of the electric field is the only term considered. The direc-

tion of any uniform field shift induced at this atom will depend on

whether the field source lies above or below this plane: an upfield

shift is caused by a positive charge placed on the negative side of

the (x, y) plane. The positive side of this plane is defined as the

one containing the most polarizable bond(s) attached to the carbon

under study. Conformational information should be uncovered by the

knowledge of the position of this plane and of the charges creating

the uniform field.

Interested by the same effect, Seidman and Maciel [65] used a

modification of the'finite perturbation 'theory of the INDO theory to

calculate the effects of point chargeymonopoles with a proton

charge) and dipoles on‘carbon-13 shielding in ethane, ethylene, ace-

tylene, when these charges are about 4 tc 5 bonds from the different

carbon-carbon bonds (5 to 7A). One of the more important findings of

Seidman and Maciel is the much greater effect of the monopole or point

dipole when located on the x-axis (see figure (2.3-1) for the definition

of this axis) as compared with location on y- or z-axis. For example

in ethylene, the closest carbon to the charge displays a shielding of

2.62 ppm with the charge on the x-axis compared 'to -0.03ppm and 0.08ppm

when the charge is on the z- and y-axis respectively. They also

related_the polari-zation-of-o- and-m-electrons -for-ethylene-and

64


acetylene to the changes of shieldings. The polarization of C-H bonds

is suspected to play an important role.

2.4 COUPLING CONSTANTS AND STRUCTURE

2.4.1 Description of coupling

In an unsymmetrical molecule of the type X-CHa = CHb-Y

(assuming that X and Y have no influence) the Ha and Hb resonances appear

as doublets. The phenomenon has its origin in the magnetic field

associated with each individual spinning proton. The magnetic field

associated with the spin of the nearby proton, Hb, contributes to the net

field experienced by Ha. If Hb.has a spin, its magnetic moment is

aligned with the applied field and the total magnetic field. at Ha is

slightly stronger than that provided by the applied field of the NMR

instrument alone. Consequently, less applied field is required to

. achieve resonance,thap in the absence of Hb, and tie finds a slight down-

field shift (corresponding to a upfrequency shift). But only half of the

Hb nuclei have a spin; the rest haves spin in which the magnetic moments

are aligned against the field. For these molecules, the net magnetic

field at Ha

is slightly weaker than that given by the applied field

alone. The NMR spectrometer m at th'n provide slightly more magnetic

field in order to achieve r

downfrequency shift).

The nature of the spectra will depend upon the number of bonds

through which spin spin coupling can be transmitted. For proton-proton

onance condition with Ha (resulting in a

65


coupling in saturated molecules of the light elements, the magnitude of

the coupling constants falls off rapidly as the number of bonds,between

the two nuclei increases and is usually negligible for coupling of nuclei

separated by more than three bonds. Long-range coupltpg (coupling over

more than three bonds) is often observed in unsaturated molecules. The

relevant mechanism for the r-electron contribution to the coupling

between non-bonded protons (in situation as in X-CHa = CHb-Y) is the

exchange coupling of the a and 7 electron spins. Once the /s orbital

around proton Ha has been magnetically polarized, via "contact inter-

action" (this mechanism is described in the next section), by the nuclear

spin of Ha, it in turn polarizes the spin of the carbon electron in the

sp2-a orbital of the CH bond. The second electron is affected by the

electron to which it is bonded because their spin must be antiparallel,

so that the spin polarization is transmitted from one to the other with a

change of sign. Then, as postulated by McConnell [66], a a-7 exchange

polarization effect between the sp2-a electron on the carbon and the 7

electron on the same atom transmits the spin polarization to the 7 cloUd.

Because of the extensive delocalization of the it system, this r electron

spin polarization is easily spread over the whole molecule. The spin

polarization at an atom can be coupled back to another CH bond, where it

magnetically interacts with the proton (here Hb), thus ensuing the spin-

spin coupling of distant protons. In contrast to this, for protons separated

by carbon-carbon single bonds, the magnetic polarization is entirely

transmitted through the a bonds.

66


2.4.2 Nature of the coupling [67]

There are various contributions to the magnitude of the spin-

spin coupling constants; they are transmitted via the electron density in

the molecule and consequently are not averaged to zero as the molecule

tumbles (in the liquid state). Major contributions come from three

effects: the spin-orbital effect, the magnetic dipolar effect (indirect

or through-space coupling) and the Fermi-contact coupling which accounts

for most of the effect.

(i) spin-orbital effect

It involves the perturbation that the nuclear spin moment makes on the

orbital magnetic moments of the electrons around the nucleus. For a

nuclear spin quantum number of 1/2, the orbital magnetic moments of the

electrons will depend upon the nuclear magnetic quantum number IN

(= ill); the field at the nucleus being split will depend on the

moment of the other nucleus. The Hamiltonian for the interaction on

the first atom that is felt at the nucleus being split is:

H = n-2 1N .% 3r

(2.4-1)

where yN and ye are the gyromagnetic ratio for the proton and the

electron respectively. L is the electron orbital angular momentum, I

the nuclear spin moment, and r is the distance between the inter-

acting atoms.

67


(ii) dipolar effect

This mechanism corresponds to a polarizatiOn of paired electron

density in a molecule by the nuclear moment. The polarization of this

electron density depends on whether I = ;5 or I = -11, and the modified

electron moment is felt through space by the second nucleus. The

di polar interaction Hami 1 tonian between the (el ectron magnetic moment

S) and the- riuole'ar magnetic moment 71Y) can be written:

8 - 30.zq(S.r))Ye YN k r3 ' r (2.4-2)

The interaction between the electron spin moment and the nuclear

moment polarizes the spin in the parts.of the molecule near the

splitting nucleus. This spin polarization spreads over the entire

wave function, and modified the field ,at the splitting nucleus, which

acts directly through space on the nucleus being split. The direc-

tion of, the effect depends on the I value of the splitting nucleus.

(iii) Fermi-contact term

This term involves a direct interaction of the nuclear spin toment•

with the electron spin moment such that there is increased probability

that the electron near the nucleus will have spin kt.i!t is antiparallel 4'

to the nuclear spin. Thus, if the splitting Amcleus has an a spin,

the spin of the electron in its vicinity will most frequently be 8.

For a directly bonded nucleus the effect on the nucleus being split

will be the opposite: the spin in its vicinity will be a, and thus.

68


the nuclear spin has a greater probability to be in the 0 state. In

this way the nucleus being split receives information from the

splitting nucleus. In the theory of spin-spin coupling constants,

the "contact term" is represented by the interaction operator: .

7r , H = $3 yN ye n-2 dkrkN I St • /N (2.4-3)

--where sk is the spin of electron k'_t ip the spin of nucleus N and rkN

the distadve of electron k---to nucleus N. The expectation value of

o(rkN) vanishes tiniest the electron is right at the nucleus tthus in

an 8 orbital).

2.4.3 Empirical and semi-empirical correlations between coupling

constants and structure

The coupling constants are sensitive'tomany aspects of mole- .

cular structure. Nonetheless, coupling constant data are now available

,for such a large number of nuclear species that it is possible to look

for general trends and periodicities.

Semi-empirical methods for the calculation of spir-spin

coupling constants based on the Hartree-Fock theory have been develOped

in the last ten years. The most widely used is the finite perturbation

theory (FPT) of Pople et al. t68]. These methods have permitted to

perform quantitative calculations and to find relations between

structural and electronic properties and coupling constants. It is well

known that proton-proton coupling constants depend on the number and the

69


nature of the intervening atoms, the hybridization state of the latter,

the conformation of the bonds forming the H....H coupling path and the

nature of the substituents, their electronegativity in particular.

Extending earlier work done by Karplus [00], on the effect of

.valence angle changes on vicinal coupling constants, Rummens and

Kaslander [70] have performed extensive INDO FPT calculations on

dependence of proton-proton coupling constants with these angles in

ethylene, propylene, cis- and trans-2-butene. A comprehensive list of

(db/d8)--where a are valence angles--parameters has been compiled and the

changes are found to be additive. For coupling' constants involving

------tmethy4-groups„only the conformationally averaged data were given.

Individual data referring to anti and gauche conformation§ were- later

calculated by Rummens et al. [71]. The results indicate that in-path

angle changes have smaller effects on vicinal couplings than exo-path

angles (which have one bond in the coupling path). Twisting the C=C

double bond in cis-2-butene by angle up to 20° leads only to minor

changes in ,the couplings.

(i) Vicinal coupling constants and dihedral angles.

Relations between vicinal coupling constants and dihedral angles have

been thoroughly' studied. All the methods invariably predict a strong

conformational dependence of the vicinal proton-proton coupling

constants on this angle. The prediction of this conformational

dependence is one of the relatively successful applications of the

early theoretical methods. Using the valence bond theory (0) for a

• 70


six-electron fragment, Karplus [72] derived the following relations

between the vicinal coupling constant in ethane and the dihedral

HCCH' angle 0:

.•

8.5 cos20 - 0.28 0 < < 90

3, UHH =

9.5 cos2 - 0.28 90 < < 180

(2.4-4)

Later, Karplus [69] modified relation (2.4-4) and obtained:

3JHH' = A + B cos0 + C cos 20 (2.4-5)

For a C-C bond length of 1.543A, sp3 hybridized carbons and an average

excitation energy equal tot_9eV, Karplus [69] gave the following values

for the constants: A = 4.42,1z, B = -0.5Hz, C = 4.5Hz. INDO FPT work

has been done by Maciel et aZ. [73] on this conformational effect.

For the dihedral angle dependence in the ethane molecule, the authors

obtained a curve similar to that given by equation (2.4-5), but with

the minima displaced somewhat from the 90° and 270° values of

suggested by Karplus [69]. They have also investigated the dihedral

angle dependence of the vicinal proton coupling constant in propene

and acetaldehyde. The variations of, 3JHH, versus for the three

molecules resemble each other closely, with lower maxima and higher

minima for the two latter molecules. Theoretical plots of JHH , in

ethane as a function of the dihedral angle have also been given by

71


Pachler [74] who used the extended HUckel theory (EHT), by Govil [75]

who compared different sum over states (SOS) treatments (and found

the EHT to perform best) and by Gopinathan and Narasimhan [76] who

applied the INDO FPT and the SOS EHT techniques.

(ii) steric contributions to long-range coupling constants

The four-bond couplings in the fragment of figure (2.4-1a) are called

allylic. 4Ju is denoted as cisoid, 4Ju w as transoid. The .1.3 .2.3

orientation of H3 relative to the carbon skeleton is characterized by

the dihedral angle H3C3C2C1 denoted (180° different from defined

for the vicinal coupling constant). KarplUs [77] and Barfield [78]

studied allylic couplings using the 7-electron theories. Barfield

used the valence bond sum over triplet method, and suggested an

identical cos20' dihedral angle dependence of the Tr-electron contribu-

tion to both, the cisoid and the transoid, coupling constants. , The

average value of the n-electron contribution predicted by Barfield

[78] was -1.65Hz,and by Karphs [77] -1 .7Hz. Later ,Barfield et at.

[79] studied the dependence of the transoid and cisoid couplings in

propene on the angle 01, using the INDO FPT method as well as a •combina-

tion of the VBSOT and SOS EHT treatments. The calculated values for

cisoid coupling turned, out to be negative for the whole range of 0'.

A comparison with experimental data by the same authors [79] indicated

that the INDO FPT method overestimates the magnitude of the cisoid

coupling constant, whereas the "combined" (SOS EHT) curve appears to

agree better with experiment. Analogous curves have been drawn by

72


a

\

/ H2 C1

\ H

.• ,

\ /t

i H2 C C'3

H 1\ /

/ 2 N

.•` . ., b

I

a

FIGURE 2.4-1 Molecular fragments used for the definition of a) allylic coupling constantsb) homoallylic coupling constants.

73


'Barfield et, al. [79] for transoid coupling, ,and in this case, both

treatments appear to reproduce the experiMental data approximately

equally well. For this coupling the zig-zag path (W3C3C2C1H1

figure (2.4-1)) for 4' = 180°, corresponds to the most positive value

of the coupling constant. The INDO VT-Calculated average valu.s of

the transoid coupling constant (4taJ) was -1.19HZ and of the cisoid

(4caJ) -2.05Hz. These may be compared with the experimental values,of

-1.42Hz and -1.78Hz obtained by Rumniens et ai. [71]. Barfield and

Sternhell [80] have studied the conformational dependence of homo-

allylic coupling (the five-bond coupling in the fragment !depicted in

figure (2.4-1b)). The model system chosen by these authors is the 2-

butene. Here the conformational dependence of the homoallylic

coupling constant may be'discussed in terms of the two dihedral

'angles H1C1 C2C3(4)) and C2C3C4H2 (01), both mevured'in a Clockwise

direction from the plane defined by the carbon skeleton. Barfield and

Sternhell [80] applied both the INDO FPT and the VBSOT methods. This

latter was designed to yield the 7r-electron contribution only. This.

contribution was equal for the cis- and trans-2-butene and could be

adequately represented by the expression.:

5JHH2

= 4.99 sin24 sin24 1

(2.4-6)

The INDO FPT' results corresponded to somewhat more'complicated curves

and were similar for the cis- and trans-conformations of 2-butene.

For the orientation corresponding to the closest proximity of the

74


coupled protons in cis-2-butend, the calculated coupling constant

; becomes negative, whidh the authors interpreted-as evidence of,a

direct mechanism. Deduction of the Tr-contribution led Barfield and

Sternhel.l [80] to anticipate a small:a-contribvtion even in the highly

favourable arrangements.

( i i,i) Coupling constants and bond lengths

Several approaches have resulted in a semi-empirical correlation

between the values of 3JHH

and the C-C bond engths. Karplus [69]

derived the following relation on the basis of the VB ippfoximation

with a six-electron fragment H-C-C-H:

•

3JHH

3Jst (1-2.9 (rCC - 1.35)) (2.4-7)

where 3Jst is the standard value of the coupling constant

3JHH in

ethylene (rcc in ethylene being taken equal to 1.35A°). Coope'r and Manatt

[81] found the next relationship (Equation (2.4-8)) during a systema- .

tic analys'is of the experimdntal data on the coupling constants in the

conjugated carbocycles:

3JHFt, ' = -36 4 rCC + 58.46 (2.4-8)

*Ammon and Wheeler [82] have proposed Equation (2.4-9) based on the

data for fulvenes and suitable for both double and conjugated bonds:

75


a

3JHH

= -28.6 rCC + 43.5 (2.4-9)

Finally Solkan and Sergeyev [83] performed a series of calculations of

in ethylene, while varying the carbon-cal-bon bond disfance in the 0

range from 1.3 to 1.4A. The linear approximation of this dependence

results in the following relationship for the cisoid coupling:

30"/HH = -28.5 rCC + K (2.4-10)

where K stands for the part of the coupling constant not directly

depending upon the bond length. Solkan and Sergeyev [83] noted that

all the relationships are quite cloge to one another, with an increase

of 3JHH by about 0.6 to 0.7Hz with a decrease in the C-C bond length

0 by 0.02A.

2.4-4 Coupling constants and electronegativity effects

The nature of the substituents, in particular their electro-

negativity, can change the value of the various coupling constants quite

considerably. These changes are certainly correlated with inductive

effects controlled by electron densities on the carbon atoms of the

coupling pathway.

A simple linear relationship between vicinal coupling constants

and Pauling electronegativities has been proposed by Karplus [69]:

3cJ = 3cJu (1 - 0.604)'

76


(2.4-11)

3tJ = ZtJU (1 - 0.254x) .

in which Ax is the difference in Padling electronegativities between the

attached group and an hydrogen atom; 3tJu and 3cJu a're the values taken

by the coupling constants in the ethylene molecule. Several other

authors have studied the influence of electronegativity of the substituent

on H-C-C-H coupling. In particular, using the Huggins [84] electronega-

tivity, Banwell and Sheppard [85] proposed the following relationship:

3vJ = 7,9 - 0.74x U2.4-12)

where Ax is the difference between the Huggins electronegativity of the

atom attached to the alkyl group and that of hydrogen. Later, Abraham

and Pachle [88] applied a least-squares treatment to 103 vicinal coupling

constants from various sources and desc4Obed the electronegativity effect

Kith equation (2.4-13):

3vJ = 9.4x1 - 0.804x

where 4x has the same meaning as for equation (2.4-12).

(2.4-13)

Rumens and Kaslander [70] estimated the inddctive effect in

arguing that hybridizational effect and electronegative effect are

separable on .the basis that hybridizational changes do not affect the

electron' density on the rehybridizing carbon atoms. After accounting for

77

•


steric hindrance contributions (see previous section), they postulate

that,the remaining non-explained quantities were the result of electro,

negative effects. Methyl substitution effects were deduced from

ethylene, propylene and 2-butene molecules. Results appear Consistent

and amounting to -2.22Hz per methyl group for the vicinal olefinic

coupling, 3cJ. Similarly, values of -3.17Hz (comparing ethylene to

.propylene) and of -2.91Hz (comparing ethylene to trans-2-butene) for 3tJ

appear compatible enough to conclude in the correctness of the hypothe-

sis. For the cisoid allylic coupling, 4caJ, the inductive effect has

been found to be virtually nil, and Rumens and Kaslander [70] did anti-

cipate that.the same should be true..for the transoid allylic coupling,

4 taJ .

The difficulty in finding reliable quantitative relations between

coupling constants and the electronegativity of groups lies partially in

the difficulty to find reliable electronegativities for alkyl groups.

Hinze et al. [87], followed by Huheey [88] have made real progress

toward the deriqtion of an electronegativity for groups and radicals,

based on an extension of the definition of electronegativity for atomic

orbitals originally given by Pritchard and Summer [89]. While Hinze

et al. [01 linearly related electronegativity with the occupation of one

orbital, Huheey [88] used the charge in that orbital for the relation.

This led Huheey,[88] to suggest the dependence of/the charge transfer

ability of the substituent group upon the electronegativity (thus its

electron donating or withdrawing ability) of the substituted fragment.

Hinze et al. [87] also -noted the dependence of the electronegativity (as

78


defined by Pritchard and Summer [89]) upon hybridization of the atom and

particularly upon the amount of s-character of its bonding orbital. Then

the two effects--hybridization by steric effect and nuclear charge

exchange--are not entirely separable. Changes in hybridization will have

a twofold consequence:

(i) increase in 8-character will increase the coupling directly

(ii) increase in the a-character in the'bonding.orbital will result

in a decrease of the a-character and of the electronegativity

of the substituent groUp. •

2.5 NMR STUDIES ON ROTAMERS

2.5.1 Description of the phenomenon

If a molecule can exist as rotational isomers (rotamers), the

stable forms may possess confOrmations in which the various nuclei find

themselves in different magnetic environments, giving rise to different

chemical shifts, and where the spin-spin coupling Constants also differ A

as. a result of changes in bond angles and bond lengths.

Whether these isomers can be detected experimentally by the

observation of their separate NMR spectra depends first of all on their

abundances at a particular temperature and secondly on the lifetime of

each species. The first factor is merely an instrumental limitation, but

the second is immutable in that it is connected with the inherent time-

scale of the spectroscopic technique. The fact that radiofrequencies are

employed ensures that only those species which have lifetime of the order

79

4.


of 0,1s. or longer can be observed. This corresponds to activation

energies of 20-25KJ:mo1-1 (5-6Kcil.mo1-1), indicating that the rotation

.must be highly hindered. Most generally one observes a spectrum in which

both the chemical shifts and. the spin-spin coupling constants are

statistically weighted averages of these parameters for the possible

rotamers. Nevertheless, if the rotamer populations can be varied by

changes in temperature (or in the permittivity of the solvent),, then, in

principle, it is possible to obtain values for the free energy

differences AG° of the rotamers as well as for their individual chemical

shifts and coupling constants.

Apart from these two extreme situations, there is. the inter-

mediate region where the transition from a single averaged spectrum to

the superimposed separate spectra of the individual rotamers occurs, and

it is here that NMR is the most valuable, particularly in cases where

rotamers are of equal energy and where their populations ratio is there-

fore fixed. In the latter situation'even though the chemical conforma-

ti ns are identical, a particular nucleus can exchange its position with

another in a dynamic equilibrium. The uncertainty in establishing its

magnetic surrounding' on the NMR scales results in a broadening of. ts., 4P

resonance signals and studies of the line-shapes in this situation can

provide information concerning, the rate processes involved and hence the

free energy of activation AGE of the process.

Over the last decade refinements of both the classical and

quantum-mechanical theory have, been rapid, and have now reached the stage

where the line-shapes of quite complex systems can be analyzed. New

80


experimental techniques involving nuclear relaxation time measurements

have also become available.

2.5.2 Completely averaged spectra and their temperature dependence

studies

A simple case of rotational 'isomerism which occurs\ bout a

single' bond' with only two stable conformations can be considered; the

free energy profile of such a transforiatioh 4s schematically Shown in

figure (2.5-1). If the interconversion of the isomers-is very fast, then

the NMR spectrum at ambient temperature yields only the statistically

averaged vicinal coupling constant <J> which 'is related to the mole

fraction qi and the characteristic spin-spin coupling Constants qi of the 0

individual r9tamers by equation0(2.5-1):

<J>* = E q, • Jii

.A similar equation could be written for the statistically

averaged chemical shift <d>, but the sensitivity of chemical shifts to

macroscopic environmental changes (see reference [90]) usually precludes

their Use in the type of analysis to be described here.

Assuming that the two energy forms of the molecule have

degeneracies nl and n2 (subscript 1 refers to the high energy form)‘, then

.the equilibrium constant is given by equation (2.5-2):

K 21. 2.1..exp eq q2 n2

81


•uopsp.wacl lnotam pamgaid uoRonpoidai Jaqpnd •JaLIMO 1q6pAcloo ay} uopsp.wed tam peonpoidelj

38

GIBBS FREE ENERGY—'---0-

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

or (2.5-2)

•

eq = nnl exp ( exp (-AH) 2

RT

AS and AH are respectively .the entropy and enthalpy variations;

R has its usual meaning of perfect gases constant.

In this case bne has q1 + q2 = 1; combining equations (2.5-1)

,and (2.5-2) yields to equation (2.5-3):

(J1 Keg + J2) <

= ql jl q2 J2

- (1 + Keg) (2.5-3)

- The determination of the values of the spin-spin coupling

constants J. and of the free energy difference AG from the temperature

dependence of <J> was first advocated by Gutowsky, Belford and MacMahon

[91]. It is this method (often called GBM method) which will be used

here. To apply such a method one has to assume that changes in coupling

constants with temperature variation are only the result of changes in the

relative populations of the various rotamers. This implies that the

potential minima must be sharp enough to make contributions to the

coupling constants from torsional oscillations insignificant.

The other assumption underlyin such treatment is that AG is not

temperature dependent (then AG is equal to AG°): very commonly AS is

assumed to be zero and AH to be.temperature independent. With two

different conformations the problem is reduced to the finding of three

parameters instead of four. This problem is solved by calculating the

83


best least-squares fit of equation (2.5-3).

In relation (2.5-3) the unknowns are AG (equivalent to AG°'and

AH° under the assumptions made), Jl and J2. In practice, the procedure

of the least-squares analysis is as follows:

(i) A value of AG° or AH° is fed in, which allows the calculation of

q1 and q2 (using q1 + q2 = 1) from equation (2.5-2),

(ii) for each temperature, these values, when combined with the

experimental measurements of <J> and equation (2.5-3) allow the best-

fit values of J1 and J2 to be obtained,

(iii) these J1 and J2 values lead to a value- for the function

defined by equation (2.5-4):

0 = (<3>Toleas. - <J>

T,calc.)2 (2.5-4)

This procedure is repeated with systematic variations of AG°

(or AH°) until a'minimum value is obtained for 0 which yields the

most probable values for the NMR and thermodynamic parameters.

The method is composed of 2 least-squares analysis; fitting of

the <J> measured at n different temperatures and then, minimization of

the error by choosing the best third parameter AG° (which gives a minimum

value for 0).

If there are m non-identical rotamers, equation (2.5-3)

involves (2m-1) unknowns. Measurement of <J> at (2m-1) different tempera-

tures should be sufficient. However, the accuracy in the measurements

of this coupling constant in the examined temperature range asks for an

84


overdetermination, therefore the fitting procedure to find J assuming a

value for AG°.

To find the uncertainty of such a liethod, GutowskY, Belford and

MacMahon [91] supposed a parabolic 0 function near the minimum for all

variables. Defining an uncertainty (d <J>) in the measurements, they

obtained:

- 0 C (ArY)24xpl min min ' (2.5-5)

where a is the consider0 variable, Cmin the coefficient of the parabolic

expansion. exp is defined by (2.5-6):

0exp

=E (a <J>T)2 (2.5-6)

A solution fOr Aa is then straightforward (a can be a J value

or.a AG value). Such an estimate gives only an order of magnitude of the

error (it is normally an overestimation).

The basic assumptions in the method are that AS = 0 and that

the temperature dependence of the measured quantity, <J>, is not signifi-

cantly affected by the temperature variation of 6H, J/ and J2. There is

also the question of the accuracy of the 'best-fit' parameters so

obtained.

Govil and Bernstein [92] were able to check these assumptions

in the case of CHBr2CFBr2 by measuring the average NMR parameters at high

temperature, using the above treatment to obtain the three unknowns, and

85


I

then by comparing these values with those obtained by direct measurement

of the spectrumpat such low temperatuYes that the individual spectra of

the rotamers were obtained. The two methods gave very different results,

and in this particular case the authors [92] were able to show that the

a_sumptions of AS ! 0 and of the temperature independence of J1, J2 and

'AH were not the maor cause of the discrepancy. The real reason was that

the observed temperature dependence of the coupling at high temperatures

was not sufficient to allow a precise evaluation of the unknowns. In

conclusion, the erroneous results obtained, and the controversy

, surrounding the application of thiS method, are due entirely to the

neglect of the basic assumptions involved, rather than to any inherent

defect in the method.

To obtain the best results in any applicatiOn of this technique,

it is essential

(i) to pr•uvide some estimate of the intrinsic temperature dependence

of the parameters involved

(ii) to obtain a sufficient variation in the measured quantity with

temperature to provide well-defined values of the three unknown

parameters, or, if not possible,.to determine by another method one

of the three unknowns.

2.5.3 Dynamic equilibria and line shape analysis

If a magnetic nucleus can undergo exchange between two

different positions in a molecule as a result of internal rotation, it

often experiences a different effective magnetic field in the two sites

86


and thus exhibits different chemical shifts. This means that, in an

assembly of molecules where the exchange rate is slow, the residence

time of nuclei at each site is long compared to the reciprocal chemical

shift difference, and two different NMR signals Will)e observed. If the

rate of exchange is increased by raising the temperature, eventually a

single resonance signal will be observed, whose position will be inter-

mediate between those of the previously separate signals. In this limit,

the exchanging nuclei experience an effective field which is a weighted

average of the fields at the different sites. At intermediate rates, an

analysis of the change in sine-shape as the signals coalesce can there-

fore yield the rate constants and activation energy of the process

(figure (2.5-2) shows such variations).

In order to arrive at a quantitative measure of the activation

energy of these processes, it is necessary.to study the change in,

appearance of the spectrum as a function of temperature and the complete

line-shape analysis must be performed. Gutowsky et al. [93] we're the

pioneel in this field, and they showed how the phenomenological equa-

tions of Bloch [94] could be modffied to account for the exchange of

magnetism from one site to another during the interconversion of the

isomers. Such a classical approach is valid when the exchanging groups

are not involved in spin-spin coupling, but a quantum-mechanical basis

is required if coupling is involved. The complexity of the solution in

the latter case makes the use of a computer program a necessity. Such

sophisticated programs have been developed, in particular by G. Binsch

et al. [95].

87


Fast exchange

Near fast

exchange

Coalescence

Intermediate exchange

Slow exchange

Stopped exchange

FIGURE 2.5-2 Temperature dependence of the NMR spectrum as'a result of . chemical exchange (uncoupled AB case). "

88


2.6 - NUMERICAL ANALYSIS USING THE PROGRAM "NUMAR1T"

2.6.1 Introduction

To analyse the complex proton NMR spectra, the program to 0.6

used must fulfill certain requirements. One of the molecules studied

represents an ABCD6X9 system and only' few programs can handle such big

systems. The X approximation must be available, because an ABCD6E9 would

be too large and would demand a lot more computer time. The program also

has to include the composite particle method in order to save space and

time during the calculation. I)

The "NUMARIT" program developed by A.S. Quirt, J.S. Martin,

K. Worvill [96] seems, at the moment, the best suited for the analysis of

the spectra obtained with the molecules under present study. It includes

the preceding features, and in addition it makes full use of factorihg

resulting from bgofold frame symmetry.

The output consists of energy levels, keys connecting energy

levels and transitions, transition lists with associated quantum numbers

useful in subspectral analysis, bar plots on the line printer, spectral

simulations on a Calcomp plotter. The shifts and couplings may be

iterated to fit an observed spectrum using the method first developed by

Castellano and P,*hner-By in their program "LAOCN3" [97] (sometimes

cal'l'ed' the BBC thod).

2.6.2 Method of iteration

The method developed by Castellano and Bothner-By is one of the

89


two methods most often used for NMR analysis. The other one uses

Reilly and Swalen's approach [98] Recently Castellano and Bothner-By's

method has been even more widely employed. Three reasons for this trend

have been put forward by C.W. Haigh [99):

(i) this method is less likely to run into convergence- difficulties,

(ii) the statistics employed is matheillticalt% impeccable, ,_,.---

(iii) in the Reilly-Swalen me needs to determine all the

energy levels. The,castglano ..ands Bothner-By approach merely requires

to initially-sOecifY a sufficient number of transitions to make the

problem overdetermined.

In the BBC method, when it is desired to calculate a spectrum from a

guessed-at set of shifts and coupling constants, the Hamiltonian of the

system under consideration is determined following the procedure

described in section (2.2). The eigenvalues of determinant (2.2-11) are

the stationary state energies of the system, Xm, and the frequencies of

transitions vi are just the differences. of these eigenvalues:

v. = X -X 1 k m(2.6-1)

Comparison of a calculated spectrum with an observed spectrum

may suggest adjustments in the values of the input parameters (chemical

shifts and coupling constants) which will improve the agreement 'etween

the two spectra. However, al experimental spectrum, consisting of a set

of measured transition frecitiencies and approximate intensities is

unlikely to be exactly interpretable. The best values for' the parameters

90


(chemical shifts and coupling constants) are those which make the sum of

the squared residuals of the observables (in this case transition

frequencies only) a minimum. For each parmeter pj the coindition is

described by relation (2.6-2)

( ) E (vobs -vcalc ). = 0 N:ij

vobs is a constant, and only (vcaic)i = f(pi):

Dvcal

1=E1 (vobs-‘'calc)i (a p. )i 0

(2.6-2)

(2.6-3)

where st, is the number of transition frequencies observed and (vobs-vcalc)i

is the difference between the observed and calculated frequencies for the

th i transition.

In the procedure, only transition frequencies are considered;

the weight of each frequency is 1 or 0, depending on whether the observed

frequency is used or not (some programs include a weighing factor).

In the presence of molecular symmetry, parameters occurring in

sets may have equal Values. In such'a case equation (2.6-3) must be

modified and take the form:

+ . . .) z (v -v 2 ap. ap . obs calc) i

= 0 j k

(2.6-4)

where the parameters p are grouped according to their symmetry as

indicated by indices j, k, . . . . It is assumed that if the variations

91


of the parameters are small a linear relationship with Avi is "applicable:

Av. 3v. 3v.

rj

_ rj

4 rjor Avi = Api an. (2.6-5)

The coincidence between calculated and observed lines occurs if:

ay.

J E (°Pi) APj = (nobs vcalc)i

Or ip matrix notation: '

DA=N

(2.6-6)

(2.6-7)

where 5 is the matrix of partial differentials, A is the vector of

corrections to the parameters, N is the vector of residuals in the

frequencies. The number of available independent transition frequencies

must exceed the number of 'unknown parameters (overdetermination of the

problem) for the method of least-squares analysis to be applicable.

Standard least-squares procedure is to form the system of normal

equations:

DAt At DA = D.

92

(2.6-8)


D t-D is a real symmetric matrix with a non-vanishing determinant. The

normal equations will thus have the solution A = 0 only when bt N = 0,

that is when equations (2.6-3) and (2.6-4) are satisfied for all the

paraMeters. The convergence is thus to the desired leas -squares fit.

When A t 0, a correction will'be made to the paramet ))-squares

give

the least-squares solution If the transition frequencies were linearly

dependent on the parameters.

After solving the eigenequation (2.2-11) using initial values

as parameters, frequencies of transitions are calculated applying

relation (2.6-1). There remains the problem of finding the appropriate

partial differentials-, (av/apj). These differentials are just the

differences:

av1 , DA aI, t m n apj . api %Am A p, ap. ap.

. J J (2.6-9)

As demonstrated. by Bothner-By and Castellano [/00], the

differentials of the eigenvalues are identical to the diagonal elements

ofri .(g1/apj). S, where S and are the eigenvector matrix and its

transpose (equation (2.2-8) i$ equivalent to A = S • H S). The

differentiation of H in the basis repreientation is straightforward, so

the evaluation of (axopj) requires only the knowledge of the eigen-

vectors; thus one has to solve equation (2.2-8).

The general procedure to find the best parameters to fit the

• 93


experimental spectrum can then be decomposed as follows:

(i) Using the non iterative capability of "NUMARIT" an approximate

Hamiltonian H is Calculated following the rules described in section

2.2 and using trial parameters.

Eigenvalues and eigetvectors are found by solving equations

(2.2-11) and (2.2-10).

(iii) After calculation of frequencies of transitions (see relation

(2.6-1)) an output is given. Line transition numbers are matched with

line frequencies.

(iv) Assignment of observed frequencies to these line numbers is per-

formed (the number of frequencies assigned must.be.larger than the

number of unknown parameters).

(v) An iterative run of "NUMARIT" is performed. The first two steps

are the same as for a non-iterative calculation.

(TWAfterdeterathlationofv. all the elements of matrix 6 are

calculated (avinpj).

(vii) The least-squares analysis is then performed; if A t 0 each

parameter is varied and put back into a new Hamiltonian to go once

more through the cycle. The iteration ends when A = 0; the final

parameters are obtained with a certain precision.

2.6.3 Error analysis

The determination of errors of optimum parameters p, obtained

by a least-squares method applied to a large number of experimental data

(the measured frequencies of the lines of the spectrum) involves normally

94


a two-step procedure: first, the error of the experimental data must be

properly characterized; second, a law of propagation of errors from the

experimental data to the optimum parameters .has to be applied. In the

"NUMARIT" program, error in parameter analysis is given by the variance-

covariance matrix Z. The error for a set of variables is completely

characterized by this matrix: its diagonal elements are the variances

ai2, and its off-diagonal elements represent the covariance. This matrix

is always symmetrical but diagonal only when the variables are

completely independent. A measure of the interdependence between.two,

variables xi and xk is given by e coefficient r defined by relation

(2.6-10):

Ci r = (2.6-10) aiak k

where Cik is the element of the matrix t corresponding to the ith row and

the kth column; ai and ak are the square root of the diagonal element on

the ith and kth rows respectively. The error calculation will give the

matrix E corresponding to the experimental frequencies. This matrix is

supposed to be diagonal in the case of NMR spectra (no correlation

between frequency errors of different lines); each diagonal.eTemeht is

calculated using relation (2.6-11) when all line measurements are of the

same quality:

z . E E2

2 i=1 i a = Z - q

95

(2.6-11)


Here t is the number of lines assigned (numberof'conditions of the type

of relation (2.6-6)) and q is the number of independent parameters

iterated. e. represents the difference between final computed frequencies •

and experimental frequencies.

To find the variance-covariance matrix e of the calculated

parameters, the propagation law has to be applied. The relationships between

-frequencies and parameters ai.e generally non-liAlear and the calculation

is carried out by finding the values of their first derivatives. 'If the

matrix 8, previously defined, is known, the transformation from ev to e

can be expressed by the following matrix multiplication:

At 8v (2.6-12) D •

where 5t and D have the same meaning as in equation (2.6-8). The

expression of the errors associated with the parameter pi is:

E s. 2

cr. - mj i

det(Dt •D)(k-(1) (2.6-13)

wherea. isthestanciami deviationoftheParameterj,m. the minor of

-t^ the coefficient (D D)„, the other parameters have the same meaning as in

expression (2.6-11). There are advantages, however, 'to transforming to a

new set of variables before computing the errors. The new set of

variables should be the linear combinations of the parameters which cause

96


the matrix I) to be diagonal. The standard deviation is then easier to

compute and takes the form described in relation (2.6-14):

c. 2 i 1 -

b dbb(t-q) (2.6-14)

In this equation, dbb is the bth diagonal element of the diagonalized

matrix, cb is the standard deviation of the bth linear combination of

parameters, obtained from the basis set of parameters and the bth eigen-

vector. These values are printed out as "standard deviation"; the

coefficients of these combinations are called "error vectors" in the

program output (there are as many "standard deviations" as there are

iterated parameters ) .

97


CHAPTER III

CONFORMATIONAL AND THERMODYNAMIC PROPERTIES

OBTAINED FROM FORCE FIELD CALCULATIONS;

RESULTS AND PRELIMINARY DISCUSSION

3.1 INTRODUCTION

Conformational and thermodynamic properties of several

substituted ethylene molecules have been investigated using the empirical

"CFF" Force field method described in Chapter I. Steric energies as well

as geometrii'al variations with the substitution are described in the next

section. Mono- and disubstituted ethylenes have been studied. A wti-

cu.for emphasis is put on the rotameric interconversion in cis- and trans-',

2,2,59trimethy1-3-hexene and in cis-2,5-dimethyl-3-hexene. In addition

the different conformations of minimum energy are given for 3-methyl-l-

butene and trans-2,5-dimethy1-3-hexene. To appreciate the behavior of

the Force Field in the case of large strain the rotameric interconversion

path for the 4,4-dimethyl-3-tert-butyl-l-pentene is also reported.

3.2 RELEASE OF STRAIN AND CONFORMATION

When substituting an hydrogen atom by a bulkier alkyl group in

an ethylene molecule, several mechanisms could release the strain

98


created; widening of the C=C-C and inner H-C-C valence angles, non-planar

distortions of the C=C double bond and rotation of the.substituent around

a C-C single bond are some of these possibilities.

3.2.1 Release of strain through widening of the C=C-R valence angles

(R = H, C)

When substituting one hydrogen in ethylene by an increasingly

bulky group, the increased steric interaction between the substituent R

and H2 (see figure (3.2-1) for notation) would cause them to move apart.

At the same time, the movement at R would produce a reflex movement of H1,

which suffers little compression. 'Distortion at H2 would propagate to

H3. Mechanisms of these kinds have been investigated by Rummens et al.

[101] and by Cooper et aZ. [102], using IR and NMR spectroscopy; experi-

mental evidence seems to support this picture when replacing a methyl

group by an ethyl group (in going from propene toscis-l-butene--whith is

the conformation of lowest minimum. energy for this molecule) as can be

seen in table 3.2-1. However, the replacement of one hydrogen atom of

the ethylene molecule by a methyl (or an ethyl) group does not lead to

the expected widening of the C=C-H2 valence angle, but to a reverse

effect (even if this effect is small). Meanwhile, the mechanism

described previously is well followed in the geometries obtained using

the "CFF" method, for all the substitutions (see table 3.2-2). The size

of the alkyl substituent is not the only factor affecting the value of

the valence angles; these angles depend also on the type of interaction

between H2 and R. For example, the calculated valence angles are of the

99


1

ex

A

FIGURE 3.2-1 Schematic description of valence angle variation with 'increasing size of the alkyl group substituent for mono-substituted ethylenes.

100


TABLE 3.2-1 Effect of a first alkyl substitution on the valence angles of ethylene, as found experimen,tallyl

81 82 e3 e4 ref.

H 121.7 121.7 121.7 121.7 a

methyl 124.3 120.5 119.0 121.5 b

ethyl(*) 125.4 117.5 c

ethyl(**) 126.7 121.1 119.0 119.8 c

(*)gauche-1-Iptene, one methylene C-H eclipses the double bond. (**).scis-l-butene, in which the C sp 3-Csp 3 bond eclipses the double bond. aData taken from K. Kuchitsu, J. Chem. Phys. 44,906 (1966). bSee reference [121].

cData taken from S. Kondo, E. Horita and Y. Morino, J. Mol. Spectro-scopy, 28, 471 (1968).

tFor notation see Figure (3.2-1).

101


I 4.

)

TABLE 3.2-2 ,Force Field-derived variations of valence angles with mono-substitution of one hydrogen atom by an alkyl group in an ethylene molecule, when the molecule is in its minimum of lowest energy.

R . 0.1 02 8-J 04

H 121.4 . 121.4 121.4 121.4

methyl 123.9 122.2 120.5 120.9

isopropyl - 123.8 122.3 t 120.1 120.8

tert-butyl' 127.0 124.1 118.4 119.8

For notation see Figure (3.2-1).

c.

\

102


same magnitude for 3-methyl-l-butene and propene (where a C-H bond

eclipses the double'bond), and for 3,3-dimethyl-l-butene and s cis-l-butene

(where a C sp 3-C sp3 eclipses the double bond) as can be seen in table

3.2-3.

A second substitution in trans position in 3-methyl-l-butene

tends to reduce the effect of the first substitution (in the case shown,

the isopropyl group) as can be seen in table 3.2-4. This influence is

understandable in view of the previously proposed mechanism, which leads

to opposite effects on all four (C=C-) angles for the first and second

alkyl subttituents. For both the cis and trans substi,Jtions,both

valence angles H-C=C and C=C-R on the side of the second substituent

(with reference to the double bond) are opened up, while the angles on

the other side are closed down. With•a second substitution in trans

position, the difference between experimental and calculated valence

angles seems reduced compared to the differences for the corresponding

monosubstituted molecule; table 3.2-5 shows such a result for the methyl

substitution (between propene and trans-2-butene). With a second

substitution in cis position, the repulsive forces between the bulky

groups open up the el C=C-H valence angle to a value of 130.2° when the

second substituent is a tert-butyl group. This large value (compared to

120°) is at the limits of validity of the potential used: the deviation

from the reference value is large and quadratic energy terms for wide

angles may not be exact. This direct interaction between the two bulky

groups with a cis substitution leads to a widening of the Al C=C-H

valence angle much more pronounced than the closing of the same angle

103


TABLE 3.2-3 Calculated effects of alkyl monosubstitution on valence angles for ethylene moleculesT

R 81 e3 e4

methyl 123.9 122.2 120.4 120.9

A, ethyl, 124.0 122.3 120.1 120.8

:isopropyl(*) 123.8 122.3 120.1 120.8

`ethyl(*) 126.8 123.7 119.0 120.0

B isopropyl 127.1 123.9 118.3 119.8

,t-butyl \ 127.0 124.1 118.4 119.8

A gives the angleS when one (methyl, methine or methylene) C-H bond eclipses the double bond. B gives them for conformations with one C ' 3-C 3 eclipsing the double bond. . sP gP (*) indicates the conformation of lowest Minimum energy(scis-l-butene for ethyl substitution) when several possibilities are given.

tfor notation see Figure (3.2-1).

t

104


TABLE 3.2-4 Effect of second substitution in cis on trans position on valgnce angles for monoalkyl ethylenes as calculated for the minimum energy conformation.

R1 R2 R3 1 62 63 64

121.4 121.4 121.4 121.4

isopropyl H H 123.8 122.3 119.9 120.8

isopropyl methyl H 128.1 128.1 117.2 117.9

isopropyl isopropyl H, ' 128.5 128.5 116.8 116.8

isopropyl tert-butyl H 130.2 129.7 115.7 115.5

isopropyl H methyl 123.5 121.4 120.8 123.4

isopropyl H isopropyl 123.4 121.0 121.0 , 123.4

isopropyl H tert-butyl 122.7 119.5 122.7 126.4

105


TABLE 3.2-5 Difference between Force Field-derived and experimentally obtained valence angles for various ethylenic molecules. Comparison with errors obtained using an additivity rule (where each 2-butene molecule is considered as the geometri-cal results of the addition of two propene molecules)T

081 A82 083 A84

propene -0.4 1.7 1.4 -0.6

trans-2-butene -0.2 -0.2 -0.3

(*) (-0.3

-1. 3.1 3.1 -1.

cis-2-butene 1.1 1.1 0.9 0.9

(**) [ 1.3 1.3 0.8 0.8

(*)calculated using A01 = Aer(propene). + A04(propene)

AO2 = a 2(propebe) + AO3(propene)

(**)calculated using Ae2 = 681(propene) + A02(propene)

A83 = A03(propene) + AO4(propene)

'AO = 0calc - 0expl

106


with a second substitution in trans position relative to R1 (see figure

(3.2-2) and table 3.2-4).

As in the case of a monosubstitution, the effects created by a

second substitution With a methyl or with an isopropyl group are of the

same order; this can be best explained by postulating tat the opening of

the C=C-H valence angle is mainly caused by the repulsion between the

inner hydrogens eclipsing the double bond (in the calculated conformations

of minimum energy for the two molecules one of the methyl hydrogens of 6

the cis-4-methyl-2-penterie and the methine hydrogen of the cis-2,5-dimethyl-

3-hexene are in almost the safe position).

Instead of reducing the difference between experimental and

calculated valence angles, as is the case for a trans second substitution,

a cis second ,substitution lead to an additivity of the errors found for

the corresponding monosubstituted ethylenes (see table 3.2-5 for the

description). Table 3.2-5 shows the difference (experimental to

calculated) for the cis-2-butene. If this effect is general, it can lead

to substantial errors in the case of bulky substitutions; the cis-2,2,5-

trimethy1-3-hexene an example. Estimation of these errors can be made

from the s cis- and jr.,:yhe-l-butene (combining both substitutions lead to the

cis-3-hexene molecule with one methylene C-H for one group, the C-C bond

for the other ethyl group eclipsing the double bond). The -rule of

additivity of errors leads to an overestimation for three out of the four

valence angles. The valence angles 61, e2, 03 are overestimated by 1.2°,

1.9°, 2.8° respectively, while 84 is underestimated by 0.6° 0 1 is

referring to the ethyl group with one C-H methylene eclipsing the double

107


1

FIGURE 392-2 Schematic description of valence angle variation with increasing size of the alkyl group R2, for cis- and trans-. disubstituted ethylenes with an isopropyl 41.oup as first substituent (R1).

/ 108


bond).

3.2.2 Other types of release

Non-planar double bond deformations involve a hard-potential;

for none of the conformations calculated to correspond to the lowest

energy minimum was such a.deformation found to release the strain. Such

a torsion of 4.1° was obtained only for the cis-2,2,5-trimethy]-3-hexene

where it is combined with an out-of-plane methine hydrogen for the

isopropyl group:

Widening of the inner C8/22-C8p3-H angle' is negligible in all

the trans substitutions (the variation is less than 0.4° around the

equilibrium value of 109.4°). For a cia substitution the variation is -

more substantial and takes a value of 2.2° for the cis-2,2,5-trimethy1-3-

hexene.

None of the bond lengths is affected appreciably by an increase

in crowdiness of the molecule; for example •C 3-C 2 bond lengths a're not sp sp varying by more thanj).5 percent around the equilibrium position of

0 1.501A for most of the molecules under study; this variation should not

be a major41i factor in the discussion of the results of NMR spectroscopy

(see Cooper and Manatt [81]).

3.2.3 Repartition of steric energy

Contributions to the total strain energy for various substituted

ethylenes in their conformation of lowest energy are detailed in table

3.2-6. It is remarkable to see, in the case of cis- and trans-hexenes,

109


Reproduced w

ith permission o



ission.

TABLE 3.2-6 Calculated steric energies (KJ.mol-1) in various conformations of lowest energy of olefins as calculated by the "CFF" method. Between parentheses values in Kcal.mol-,are given.

trans-2,5- cis-2,5- trans-2,2,5--cis-2,2,5- 4,4-dimethyl-3-methyl- dimethyl-

ethylene 1-butene 3-hexene dimethyl- trimethyl- 3-hexene 3-hexene

trimethyl- 3-t-butyl-3-hexene 1-pentene

frond stretching 0.004 0.193 0.423 0.385 1.013 1.280 6.222 - (0.001) (0.046) (0.101) (0.092) (0.242) (0.306) (1.487)

Bond angle bending 0.017 0.594 0.803 7.067 3.117 11.899 20.782 (0.004) (0.142) (0.192) (1.689) (0.745) (2.844) (4.967)

Torsional strain 0.000 0.025 0.050 0.067 0.063 10.791 5.263 o (0.000) (0.006) (0.012) (0,016) (0.015) (2.579) (1.258)

Out of plane bending 0.000 0.000 0.000 0.000 0.000 0.000 0.013 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.003)

Non-bonded inter- 1.197 8.527 13.949 14.418 21.209 20.635 42.652 action (0.286) (2.038) (3.334) (3.446) (5.069) (4.932) (10.194)

- Cross terms 0.000 0.071 0.222. -1.167 0.255 -1,640 -2.828

(0.000) (0.017) (0.053) (-0.279). (0.061) (-0.392) 4-0.676)

Total steric energy 1.218 9.406 15.443 20.769 25.652 42.965 72.107 (0.291) (2.248) (3.691) (4.964) (6.131) (10.269) (17.234)

Reproduced w



ithout permission.

that the non-bonded energy is about the same within each cis/trans pair

(this kind of energy is even smaller for the cis- than for the trans-

isomer of 2,2,5-trimethyl-3-hexene). At short distance the non-bonded

potential becomes so hard that only the soft bond angle bending and the

torsions can release the strain efficiently. However, the non-bonded

energy increases with the size of the alkyl substituent (for example when

replacing an isopropyl by a tent-butyl group). Among the substituted

ethylenes studied, the cis-2,2,5-trimethyl-3-hexene and the 4,4-dimethyl-

3-tert-butyl-l-pentene are\ the only ones for which angle bending alone

cannot release the strain optimally, so they must resort respectively to

C=C twisting and to C-C torsional deformations.

3.3 ENERGY IN CIS/TRANS TRANSFORMATION

3.3.1 cis/trans enthalpy differences

In the initial discussion of their results, Ermer and Lifson

[3] pointed out that in the least-square process for finding the para-

meters of the Force Field they gave a considerably lower weight to data

obtained from solutions as compared to data obtained from the gas phase;

discrepancies of up to 7.1KJ.mol-1 (1 .7Kcal.mol-1) have been noticed

between gas- and solution phase data. Of 'the molecules given in table

3.3-1, the 2-butene and the 2-pentene enthalpy differences are the only

ones taken from equilibration measurements in the gas p'lase. However, Air

the calculated enthalpy difference (using equations 1 .8-1 and 1.8-2) for

the 2-pentenes is 45 percent larger than the experimental value. Such a

111


TABLE 3.3-1 Differences in steric energy (AV) and in enthalpy (iH) between cis and trans isomers of various molecules as calculated with the Ermer and Lifson Force Field; comparison with the experimental enthalpy differences.*

11)

Compound O calc AHcalc

AHexpl P11 P21

2-pentene e(i) 5.19 e(i) 5.36 3.68a e(i) 0.41 e(i) 0.45 (1.24) (1.28) (0.88)

e(ii) 0.63 e(ii) 1.3 (0.15) (0.31)

'OM 4.24 'OM 4.69 e(iii) 0.15 e(iii) 0.27

4-methyl- 5.02 5.65 4.18b

0.20 0.35 2-pentene (1.20) (1.35) (1.00)

2-butene 4.85 5.31 5.23c 0.07 0.02 (1.16) (1.27) (1.25)

4,4-dimethyl- 17.8 17.7 16.14 0.10 0.10 2-pentene (4.25) (4.24) (3.86)

2,2,5,5-tetra-methyl- 47.3 48.4 -38.9b 0.22 0.24 3-hexene (11.3) (11.6) (9.3)

aData taken from D. R. Stull, E. F. Westrum Jr. and G. C. Sinke, The chemical thermodynamics of organic compounds, J. Wiley and Sons, Inc. (1969). bData taken from reference [128].

See reference [106]. dData taken from J. D. Rockenfeller and F. D. Rossini, J. Phys. Chem., 65,267 (1961).

(i) refers to the difference between the two conformers of lowest energy.

(ii) refers to the energy difference between the cis conformer of lowest energy and the tiosconformer of second lowest energy.

(iii) refers to the energy difference between the cis conformer of lowest energy and the equilibrium mixture obtained for the trans conformers when their Gibbt enely separation is 4.05KJ.mo1-1.

e

'Pi 2 1"calc AHexpl l/aexpl P2 = IAHcalc

AHexpl

I/AHexpl *Units: the energies are given in KJ.mo1-1; between parentheses their

values are in Kcal.mo1-1. 112


difference is not inside the average absolute difference given by Ermer

and Lifson [3]. For this molecule, the possibility of having two

appreciably populated trans rotamers at room temperature cannot be

rejected. A difference in enthalpy between these two rotamers of

4.1KJ.mol-1

(0.97Kcal.mo1-1) is found using the "CFF" method; thi-S- feads

to 10 percent of the population being in the second conformation. The

difference between calculated and measured enthalpy differences is then

lowered to 1.3KJ.mol-1 (0.30Kcal.mol-1). For the other molecules listed,

part of the disk.repancy between calculated and experimental cis/trans

enthalpy differences has been claimed by Ermer and Lifson [3] to be

caused by the presence of a polar effect in solution. Allinger and

Sprague [103] estimated this effect to account for 4,2KJ.mo1-1 (1Kcal.

mol-1); if such an increase from solution in acetic acid to gas is

present, the discrepancy for the 2,2,5,5-tetramethyl-3-hexene decreased

from 9.5KJ.mol-1 to 5.4 KJ.mol-1 (from 2.3 to 1.3Kcal.mol-1). The

overestimation of the difference then drops to 13 percent.

A comparison of results using various Force Field potentials is

attempted in table 3.3-2. The data displayed show that the potentials

used are equivalent; a slight advantage seems to go to Allinger and

Sprague's results,. A major drawback of these authors' potential lies in

too hard a potential to take account for the non-bonded interactions as

suggested by White and Bovill [104]. This leads to approximate geomet-

ries; for example, in the case of the cis-2-butene, Allinger and Sprague

[/03] found a C2 geometry (one of the methyl group is twisted in order to

release the strain), while'Ermer and Lifson [3] as well as White and

113


TABLE 3.3-2 Comparison of cis/trans enthalpy differences as calculated using three Force Field methods* and as obtained experi-mentally.

White and Bovill [/04]

Ermer and Lifson [3]

Allinger and Sprague [/03] Expl

2-pentene 5.23 5.19 3.56 3.68a

(1.25) (1.24) (0.85) (0.88)

4-methyl-2 2.05 5.02 4.18b

pentene (0.49) (1.20) (1.00)

2-butene 5.48 4.85 4.85 5.23c

(1.31). (1.16) (1.16) (1.25)

2,2,5,5- 47.30 43.30 38.9b

tetramethyl- (11.30) (10.35) (9.3) 3-hexene

aData taken from D. R. Stull, E. F. Westrum Jr. and G. C. Sinke, The chemical thermodynamics of organic compounds, J. Wiley and Sons, Inc. (1969). bData taken from reference [128].

cSee reference [1OS]. *For the three methods, the steric energy difference is taken „as representing the enthalpy difference.

114


Bovill [104] have a minimum energy when the conformation geometry has a A

C2v symmetry with two methyl hydrogens eclipsing the double bond as has

been established by microwave spectroscopy,[14].

3.3.2 Entropy and Gibbs energy reliability

From the frequencies calculated for the conformations of

minimum energy, entropy differences between cis and trans isomers have

been obtained according to equations (1.8-3) to (1.8-10. A comparison

of these values'vith entropy differences obtained from experiments is

given in table 3.3-3. The errors in absolute entropy for the values

given by the American Petroleum.Institute (API) have been estimated by .

Golden et al. [105] to be of the order of f2.9J.mo1-1.K-1 (f0.7e.u.).

Considering the fact that AS values are derived from differences in

absolUte values, they probably have error limits of at least,t2.9J.mol 1.K-1

(f0.7e.u.). Egger and Benson [106] and Golden et al. [105] used the

method of iodine or nitric oxide catalyzed isomerization of olefins to

find the values quoted in table 3.3-3. The calculated entropy differences,

AS ciAltrans, fall within the error limits of the various experimental

data. The standard deviation (from the experimental data) for AS is

about 3.3J.mo1-1.K-1 (0.8e.u.), which would give an uncertainty on AG of

1KJ.mo1-1.K-1 (240cal.mol-1.K-1) at room temperature. The uncertainty in

T AS as compared to the value of T AS itself, leaves one to wonder if the

calculated cis/trans enthalpy difference is not as good a comparison as

is the calculated Gibbs energy difference to the experimental Gibbs

energy difference. In view, however, of the excellent agreement between

115


TABLE 3.3-3 Comparison between calculated entropy difference cis/trans (for conformations of lowest energy) as obtained from Force Field technique and as deduced from experimental data.

Compound AS (cis-trans) T = 298K AS-(cis-trans) T = 400K

From "CFF" calc. Expl From "CFF" calc. Expl

(i)-1.1 (-0.26) 5.9 (1.4),a, (i)-1.4 (-0.33) 5.7(1.37)a2-pentene di (ii) 3.6 (0.86) 1.7 (9.4)- d (ii) 3.3 (0.80)

(iii) 0.25 (0.06) * (iii) 0.72 (0.17)

2-butene 3.5 (0.83) 5.23(1.25)a 3.2 (0.77) 5.4(1.3)°4.35(1.04)a ,,2.0(0.5)a

4-methyl- 2.2 (0.53), 5.06(1.21)a 1.92 (0.46) 2.9(0.7)a2-pentene

aFrom D. R. Stull, E. F. Westrum Jr., G. C. Sinke, The chemical thermo-dynamics of organic compounds, J. Wiley and Sons, Inc. ()969); the entropies are deduced from thermal data. •

bSee reference [106]; asee reference [105]. The values taken from references [105] and [106] are obtained from iodine-catalized isomeriza-tion of olefins. d (i) describes the entropy difference between the conformations of lowest energy; (ii) gives the entropy difference when the trans isomer is in its second conformational energy minimum; (iii) gives the expected value when the Gibbs energy difference between the two trans-2-pentene rotamers is taken equal to 4.06KJ.mo1-1 (0:97Kql.m91-1). Units: the values are given in J.mo1-1.0; between parentheses, these quantities are given in cal.mo1-1.K-1.

116


experimental and "CFF" calculated vibration of frequencies (see reference

[3]), it is highly likely that the calculated AS values are far more

reliable than the corresponding experimental data.

3.4 STRAIN ENERGY DIFFERENCE BETWEEN ROTAMERS

4'

3.4.1 3-methly1-1-butene

The preferred conformation for the 3-methyl-l-butene is such

that thefflethine C-H fragment of the isopropyl group eclipses the C=C

double bond and therefore anti relative to the olefinic C-H (see

figure (3.4-1)). This result confirms the assumption made by Bothner-By

et al. [207] in their early studies of this molecule by NMR spectroscopy.

zn Rummens et aZ.'s [71] estimation, the population difference between

the anti and'gauche forms is small. These authors estimated (from

variable temperature proton spectra) that AG° = 0.54KJ.mo1-1 (0.13Kcal.

mol-1) between the anti and gauche conformations. "CFF" calculations for

steric energy differepce give a value of AV = 4%7KJ.mo1-1 (1.13Kcal.mo1-1).

Such a value is unacceptable in the opinion of Rumens et al. [71].

According to the "CFF" calculation the strain is mainly

released through an opening of the C=C-C valence angle between the two

rotamers (from 124° in the anti form this angle increases to 127.1° in

the gauche form). This is combined with an opening of the -C-C-C angle

bearing the C-C bond eclipsing the C=C double bond. In the gauche form,

the steric hindrance is further alleviated by a small twisting of the

entire isopropyl group by 6°. The important geometrical features of the


I

U rn

I

I

118

•

I


two rotamers are given in figure (3.4-1). A more detailed description of

them can be found at the end of this chapter.

3.4.2 trans-2,5-dimethyl-3-hexene

Following a study by Rummens et aZ. [108], four different

rotamers corresponding to energy minimum have been investigated. In

their notation, there is a singlet (aa) state, a 4-fold degenerate (ag)

state [(ag+), (ag-), (g+a), (g-a)], a 2-fold degenerate state consisting

of the (gg) and (g-g-) rotamers and another 2-fold degenerate state of

the (dig-) and (g-g+) rotamers. Energetically the two rotors are almost

independent and the calculated steric energies for the two latter (gg)

states are almost identical (the difference amounts to 0.05KJ.mol or

0.01Kcal.mol-1). The energy increase for each anti-gauche transformation

is not exactly constant and the difference in strain energy between (aa)

and (gg) is not quite twice that of (aa) (-0,g) (10.7KJ:mo1-1 instead of

10.0KJ.mo1-1 for two AVaa g which. is 2.55 instead .of 2.38 in,Kcal.mol-1)

as can be seen from figure (3.4-2). This amount of AV = 5.KJ.mol-1

(1.19Kcal.mol ) is close to the one calculated for the similar transfor-

mation in the 3-methyl-l-butene (which is 4.73KJ.mo1-1 or 1.13Kcal.mo1-1).

However, experimental evidence (seeRummens et al. [71]) suggests much

smaller difference in energy between the rotamers than the calculated value.

Once again the discrepancy between calculated and experimental values is

around 4.2KJ.mol-1 (1.Kcal.mol-1). Such an overestimation seems to be a

general feature of the "CFF" method developed by Ermer and Lifson [3]

when a rotameric C sp 2-C sp3 transformation involving an isopropyl group

119


Reproduced w

ith permission o



ission.

Iierot. J-2.5 - dimethy1-3-hexerte

20.

AI

0.

5.68 (1.36)

4.97 (1.19)

1

f +, 7,51-11+

14.2 (3.40)

ethylene

3-methyl-1-butene ,40 f reze•nede

4.72 (1.13)

8.19 (1.96)

FIGURE 3.4-2 Steric energy increases with successive anti-gauche transformations of the isopropyl group in 3-methyl-l-butene and in trans-2,5-dimethyl-3-hexene as obtained from Force Field calculation (the figures between parentheses are steric energy differences in Kcal.mo171).

Reproduced w



ithout permission.

occurs. If the value of 550J.mol (130ca1.mol-1) for AG° found for

3-methyl-l-butene is also applicable to both the anti-gauche transforma-

tions of trans-2,5-dimethy1-3-hexene, then all states ((aa), (ag), (gg))

are appreciably populated at room temperature and any NMR experiment at

this temperature would involve the four conformations.

The successive geometrical changes for each anti-gauche trans-

formation are drawn in figure (3.4-3); they are described more thoroughly

in the appendix following the chapter. Each anti-gauche transformation

has the tendency to open up the adjacent C=C-C valence angles while it

closes the opposite C=C-C angles. The two discernable (gg) states have

the same valence angles.

3.5 INTERCONVERSION PATH AND THERMODYNAMIC PROPERTIES

3.5.1 cis-2,5-dimethyl-3-hexene

The path of lc st energy displayed in figure (,3.5-1) has been

obtained by "driving" the torsional angle around one of the Cop 3-C op2

bonds by steps of 10 to 20° to give a smooth conformational change. The

computer calculated %retry of the conformation of lowest energy has a

C2v symmetry; both methine hydrogens are in anti position with respect to

the closest olefinic fragment (this conformation will be referred to as

the (aa) conformation later). The conformation with one of the methine

bonds in ayn position (referred to as (as) conformation) presents only a

Cs symmetry; its steric energy is 12.5KJ.mo1-1 (3.0Kcal.mo1-1) higher

than the energy of the (aa) conformation. In between these o conformations,

ia 0

121


Reproduced w

ith permission o



ission.

a

II

II

.0

C 4

C

II

1221 C • — C

1;'

H

D IY . /'

C

109 6Se

!.H

C

4, '•.•

X1.334 /s 'C

C 111 31 (7'4. 0H " — • H

6 'I; 12-

II

113 90 C

4.3 34C C

141

H

C

II

C 111111, • • • C

FIGURE 3.4-3 Calculated molecular geometries for the various conformations of minimum energy of trans-2,5-dimethy1-3-hexene as obtained by Force Field calculation.

Reproduced w



ithout permission.

(;;

.06

28S I\J

22.5 (539)

•

H 54\

.,341 133J// 18 \ ri

H 9 129y

[ 7 \

17.3 (4.1.1)

I

I 0 160 270 360

mapping coordinateeN)

FIGURE 3.5-1_ Calculated steric energy profile for the inter-conversion of (aa) and (as) conformers of cis-2,5-dimethy1-3-hexene (the figures between pai-entheses are energies in K.cal.mo1-1).

Reproduced w



ithout permission.

another (shallow) minimum can be seen in the energy path; it corresponds

to a geometry of low symmetry (C1) with one methine hydrogen in gauche

position. The C sp 3-C sp2 single bond bearing the other isopropyl group

is twisted by almost 6°, making the methine C-H stick out of the plane

containing the C=C-C part. The most important geometrical features for

these conformations are given in figure (3.5-2); a more complete picture

of them can be seen in the appendix following this chapter.

Only a few more comments need be made about the calculated

structural and energy parameters of the various conformations and transi-

tion state shown in figure (3.5-2) and table 3.5-1. For the (aa), (as),

(ag) conformers only angle bending and non-bonded energy are of

appreciable magnitude. The (as) conformation has higher bond angle

bending and torsional strain energtei than .t.e (aa) conformation; this is

partly compensated by a smaller non-bonded energy in the (as) state as

can be perceived in table 3.5-1. Much of the strain for the third

conformation (ag) is from the angle bending terms; the repulsive forces

between the two isopropyl groups open the C=C-C valence angles to values

reaching 132.1° and 133.9° (as said previously these values are at the

limits of validity of the method). In this same conformation, release of

the strain is partly obtained through a torsion of 1.8° of the double

bond.

Thermodynamic properties for these various conformations and

for the transition state are given in table 3.5-2. Because of the

extremely low calculated barrier between the (as) and the distorted (ag)

states (5.8KJ.mo1-1 or 1.4Kcal.mo1-1) most of the interest lies in the

124


C.

C.

1.333

i/C 11727

0

H

C\\\

03 a 0, t",: . 0.A

, ..-07 ..., C \ 1.331 ( '

C 0.8 At? A -.• - 9 cu-> 4

C 1,„ •••:.

•••

C 111.40

\sO0

.0

\O/

C \ 1.333 / .1

4

(aa)

n2.42 C 00.3 o

CO

tIGURE 3.5.-2 Calculated molecular geometries of the three conformations of lowest minimum energy of cis-2,5-dimethy1-3-hexene.

125


TABLE 3.5-1 Contributions to calculated steric energies for various conformations of cis-2,5-dimethy1-3-hexene.*

(aa) (as) (ag)

0.385 0.25 0.561 Bond stretching (0.092) (0.059) (0.134)

Bond angle bending 7.067 (1.689)

11.51 (2.75)

22.55 (5:39)

Torsional 'strain 0.067 10.88 (2.60)

2.50(0.616) (0.597)

Out of plane bending 0.0 0..0 (0.0)

0.0(0.0) (0.0)

Non-bonded energy 14.42 12.5 (2.98)

16.4(3.45) (3.93)

-1.17 -1.74 -3.98 Cross terms (-0.28) (-0.42) (-0.95)

20.77 33.34 38.1 Total steric energy (4.964) (7.97) ' (9.1)

*Units: the energies are given in KJ.mol-1; between parentheses, these quantities are given in Kcal.mol-l.

126 4


TABLE 3.5-2 Calculated thermokynpic properties of cis-2,5-dimethy1-3- hexene conformations

(aa) (as) (ag) TS*

° strain

198

• AH

AS

AG

20.8 12.6 17.3 (4.96) (3.00) (4.14)

22.5 (5.38) 1

602 12.0 18.8 21.8 (143.8) (2.88) (4.49) (5(21)

298 615 12.1 18.5 20.8 (147.1) (2.89) (4.43) (4.97)

398 634 12.1 18.3 , 19.9 (151.6) (2.89) (4.38r (4.75)

198 363 -1.55 15.1 -25.1 (86.6) (-0.37) (3.60) (-60)

298 422 , -1.34 14.0 -29.1 (100.7) (-0.32) (3.34) (-6.95)

398 477 -1.17 13.5 -31.8 (114.1) (-0.28) (3.22) (-7.6)

`198 530 12.3 15.8 26.8 (126..6) (2.95) (3.78) (6.40)

298 490 12.5 14.4 15 29.5 (2/7.2) (2.99) (3.43) (7.04) .„..

398 444 12.6 13.0 32.5 (106.1) (3.01) (3.10) (7.77)

The values for the (aa) state are absolute (given in italics); those for the other conformations are relative to (aa). Units: the energies are in KJ.mo1-1, the entropies are in J.mo1-1.K-1. Between Orentheses, these values are given in Kcal.mo1-1 and in cal.mol-I.K-1 respectively. The temperatures are in K. *TS represents the transition state between (aa) and (ag).

127


• Alt

(aa) to (as) barrier which is calculated to be 31.8KJ.mo1-1 (7.6Kcal.mo1-1)

at 298K. The large difference between the entropy of the (as) conforma-

7 tion and that of the transition state, and its large variation with

temperature leads to values of enthalpies of rotation (about 21KJ.mol-1

or 5Kcal.mol-1) much lower than the corresponding Gibbs energies. How-

ever, all these values are small enough so that a fast exchange (on the

NMR time scale) beiween these states can be expected at room temperature.

According to the "CFF" calculation, the (aa) conformation is

12.6KJ.Mo1-1 (3.0Kcal.mo1-1) more stable than the (as) conformation.

Their Gibbs energy difference (increasing with temperature) reaches

12.5p.mol-1 (3.0Kcal.mol-1) at room temperature„whereas the enthalpy

difference (almost temperature independent) is 12KJ.mo1-1 (2.9Kcal.mo1-1).

Even with an overestimation of this difference by about 4.2KJ.mol-1

(1Kcal.mol-1) (as suspected for several rotameric energy difference--see

Rummens et aZ. [71]), the (aa) conformation is populated to the extent of

99 percent,at room temperature.

3.5.2 trans-2;2,5-trimethyl-3-hexene

By constraining one torsional angle and "driving" it to

successively increased or decreased values, the pathways of lowest energy

given in figures (3.5-3) and (3.5-4) have been obtained. In both'cases

the two rotors (the isopropyl and tert-butyl groups) are uncoupled. Two

conformations of minimum energy have been found; the more stable shows a

Cs symmetry (called I in figure (3.5-5)), while the other does not

present any plane of symmetry (this is the conformation called II in the

128


\ 123/

40.0

<173 \

\ 122.3)

O 12645 \

E

13.31 (3.18)

30.0

6

25.,64L6.13)

20.0 180 • 270

H

<126 3 \

10 9 (2.6)

mapping parameter

H?,

" H

360

FIGURE 3.5-3 Calculated steric energy profile for the rotation of the isopropyl group of trans- , 2,2,5-trimethy1-3-hqxene (the .figures between parentheses are energies in Kcal.mol_ ').

Reproduced w



ithout permission.

Reproduced w

ith permission o



ission.

1 a >-0

33.5

29.3

20.9 I I 180 210

MAPPING COORDINATE ------pr 360

FIGURE 3.5-4 Calculated steric energy profile for the rotation of the tert-butyl group of trans-2,2,5-trimethy1-3-hexene (the figures between parentheses are energies in Kcal.mo1-1).

Reproduced w



ithout permission.

Reproduced w

ith permission o



ission.

X

C

I

114.52 122.

114.07 C 1.334

126.41 122.72

C 113 02

'Ti

112.40

II

FIGURE 3.5-5 Calculated molecular geometries of the conformations of minimun}'energy for trans-2,2,5-trimethy1-3-hexene.

Reproduced w



ithout permission.

figure ). The transition state for transformation I to II has one of the

carbons of the isopropyl group in syn position. During the entire trans-

formation, one of the Csp 3-Csp 3 bOnd of the tert-butyl group is eclipsing

the double bond. The energy barrier which separates these conformations

is small (13.3KJ.mo1-1 or 3.18Kcal.mo1-1), and the rate of exchange would

be too fast to be detected by using the NMR method.

The three-fold symmetry described in figure (3.5-4) has been

obtained by "driving" one of the torsional angles on the tert-butyl side.

Once again the barrier to rotation is small.

Rotational barriers, enthalpy and Gibbs energy differences are

given in table 3.5-3. The Gibbs energy difference at room temperature

between I and II has a value of 4.6KJ.mo1-1 (1.1Kcal.mo1-1). According

to this value, 76 percent of the sample population would be in conforma-

tion I. Following the results obtained by Rummens et al. "7/1 the steric

energy difference between anti and gauche rotamers in isopropyl substi-

tuents is overestimated by 4.2KJ.mo1-1 (1Kcal.mo1-1). If such a correc-

tion would be applied to the present results, it would lower the

difference in steric energy to around 0.4KJ.mol-1 (0.1Kcal.mol-1).

Accepting this value as a correct value 63 percent of the population

should be in conformation II at room temperature.

The geometries outlined in figure (3.5-5) are more thoroughly

described in the appendix at the end of the chapter. The release of

"strain for the gauche isomer (conformation II) is achieved mainly through

valence angle opening; this angle bending energy accounts for 2.6KJ.mol-1

(0,63Kcal.mo1-1). Torsional deformation amounting to 0.2KJ.mo1-1

132


TABLE 3.5-3 Calculated thermodynamjc properties of trans-2,2,5-trimethyl-3-hexene conformations

I II TI*

TII*

AVstrain 25.6 5.69 13.3 7.11 (6.13) (1.36) (3.18) (1.70)

T

198 680 5.48 11.0 3.87 (162.5) (1.31) (2.62) (0.93)

AH

AS

AG

298 695 5.19 10.2 3.23 (166.3) (1.24) (2.43) (0.77)

398 717 4.81 9.37 2.56 (171.4) (1.15) (2.24) (0.61)

`198 359 2.38 -8.53 -14.7 (85.9) (0.57) (-2.04) (-3.52)

298 427 1.92 -11.9 -17.4 (102.1) (0.46) (-2.84) (-4.15)

398 491 1.76 -14.1 -19.3 (117.4) (0.42) (-3.38) (-4.62)

`198 607 5.02 12.7 6.81 (145.2) (1.20) (3.04) (1.63)

298 568 4.60 13.7 8.40 (135.8) (1.10) (3.27) (2.01)

398 522 4.10 15.0 10.2 (124.7) (0.98) (3.59) (2.44)

+The values for conformation Dare absolute (given in italics); those for the other conformations are relative to that of (I). Units: the energies are given in KJ.mo1-1, the entropies in J.mo1-1.K-1. Between parentheses, these values are given in Kcal.mo1-1 and in cal.mo1-1.K-1respectively. The tempdratures are in K.

*T represents the transition state for the tert-butyl rotation, while T1 represents that for the isopropyl rotation.

133


(0.05Kcal.mo1-1) in addition to the increase of 2.7KJ.mo1-1 (0.64Kcal.mo1-1)

for the non-bonded interaction completes the distribution. Included in

these results is a slight out-of-plane position (6.7°) for the C sp 3-C sp3

bond eclipsing the double bond.

3.5.3 cis-2,2,5-trimethy1-3-hexene

Following the procedure described for the' trans isomer, the

lowest energy profiles given in figures (3.5-6) and (3.5-7) have been

determined. When constraining the H-C sp 2-C sp3-H fragment of the

isopropyl group and "driving0 it, the tart-butyl group is also rotating

due to the through-space coupling with the isopropyl group (see figure

(3.5-7)). But, if the constrained angle is on the tert-butyl side, with

the isopropyl in anti position, the isopropyl group appears uncoupled.

This is the consequence of the *non-reversibility of the process when

"driving" one angle at a time, as already mentioned by Anet and Yavari

[I09]: the computer-driven process follows the lowest energy path for

any given constraint. The calculation leads to three conformations of

minimum energy. The lowest energy is obtained with one of the C sp 3-C sp3

single bonds of the tert-butyl group eclipsing the adjacent C-H olefinic

bond with the methine part of the isopropyl group eclipsing the double

bond; this structure, which has a Cs symmetry is denoted I or (as). In

the second minimum one of the C-C bonds of the tort-butyl group eclipses

the double bond (rotation of 60° from conformation I around the C op 2-C sp3

bond), and this conformation II can be noted (aa). The third minimum

(conformation III) displays a highly strained structure. No symmetry is

134


Reproduced w

ith permission o

f the copyright owner.

Further reproduction prohibited w

ithout permission.

48.0

7 -3 I 46.0 O E

w z w z

=

7( 44.0

tA

42 0

4.72 (1.13)

2.72 (0.65)

C

\ )

180 270 MAPPING COORDINATE .•

1 360

FIGURE 3.5-6 Calculated steric energy profile for the rotation of the tert-butyl group of cis-2,2,5-trimethy1-3-hexene (the figures between parentheses are energies in Kcal.mol-l).

Reproduced w



ithout permission.

Reproduced w

ith permission o



ithout permission.

95.0

a 70.0 0

0,

0 "

CD g 0

45 0 — 1-

180 270 mapping parameter

.0

‘ss 31.8 113.3

H

37.2 (8.9)

,s;k 41.0 161.7 H

25.5 (6.1)

H 360

FIGURE 3.5-7 Calculated steric energy profile for the rotation of the isopropyl group of cis-2,2,5-trjmethyl-3-hexene (the figures betwqen parentheses are energies in Scal.mor I).

Reproduced w



ithout permission.

its

present in this conformation. Whereas between con rmations I and II the

strain is mainly released through opening of valence angles, tonformation

III has a twisted double bond (4.1°), and none of the bonds of either

alkyl group is eclipsing the double bond; the extra torsional disOace-

ments apparently reduce the strain with the position of\the methine

fragment.18° out of the syn position. Geometries for these conformations

are given in figure (3.5-8); a more detailed description f the structures

,appears in the appendix at the end of this chapter.

The calcUlated rotational barrier between the (as)\and (aa)

conformations is very small as can be seen in table 3.5-4. A fast

exchange between them is occurring at temperatures of usual NMR experi-

ments. The steric energy difference between the (as) and (aa) conforma-

tions is small (2.72KJ.mo1-1 or 0.65Kcal.mo1-1). But the presence of an

extra small vibrational frequency in the (aa) conformation (there is one

frequency with a smaller value than 100cm-1 for the (as) conformation

(35cm-1), while there are two for the (aa) conformation (40 and 23cm-1)

gives a somewhat larger enthalpy difference. The Gibbs energy difference

reaches a sizeable value (about 5.4KJ.mo1-1 or 1.3Kcal..mo1-1 ); this would

lead to a population difference between the (as)"and (aa) states at room

temperature. The presence of a measurable population of rotamer III is

improbable; the Gibbs energy difference between conformatiOns II (also

called (aa)) and is 33KJ.mo1-1 (8.0cal.mo1-1), 28KJ.mo1-1 (6.7Kcal.

mol-1) of which is caused by the strain present. The presence of only

two rotameric conformations at low temperature seems well warranted.

137

141


C

H4

114.83 (

'C itt.3

C 107 2 'top

111.83

I 109.87 129.12 130.22 c~ 1.333

C 11408

115.45 115.70

III

\ 134 12 41 135.77

111: 1431 0 1 1,1.75

.7 11291 112.4

H:

II cat.)

iso-propyl

tell°

FIGURE 3.5-8 Calculated molecular geometries of conformations of minimum energy for cis-2,2,5itrimethy1-3-hexene.

•

I •

138


TABLE 3.5-4 Calculated thermodynamic properties of cie-2,2,5-trimethy1-3-hexene conformations+

(as) as III TS*

k 43.0 2.72 a strain

. (10.27) (0.651) T

198 ' 695 6.53 31.9 (166. (1.56) .. (7.62)

AH 298 71 5.98 31.5 (1 9.9) (11.43) . (7.52)

398 732 5.48 (175.0) (1.31)

AS

AG

198 366 4.48 (87.6) (1..07)

298 435 • 2.18 004.1 (0.52)

398 500 0.79 (119.4) (0.19)

' 28.2 (6.74)

31.1 (7.43)

-5.69 • (-1.36)

' -7.45 • (-1.78)

4.73 (1.13)

6.42 (1.53)

5.17 (1.24)

3.95 (0.943)

-12.6 (-3.02)

-17.7 (-4.24)

-8.58 -21.3 (-2.05) (-5.09)

198 622 5.65 33.1 8.91 (148.7) (1.35) (7.92) (2.13)

298 581 5.31 33.8 10.5 (138.9) (1.27) (8.09) 2.50

398 533 (127.5)

5.15 34.7 12.4 (1.23) (8.30) (2.97)

The values for the (as) state are absolute (given in italics); those for the other conformations .are relative to that of the (as) state. Units: the energi::: are given in KJ.mol-1, the entropies are in J.mo1-1.0. Betwden parentheses these quantities are given in Kcal.mo1-1 and cal.mo1-1.K-1 respectively. The temperatures are in K.

*TS is the transition state for the tert-butyl rotation.

1 39

e


3.5.4 4,4-dimethyl-3-tert-butyl-1-pentene

By driving the H-C sp 2-C sp3-H torsion angle, the energy path

drawn in figure (3.5-9) has been obtained. This profile brings two

conformations of minimum energy. A strain energy barrier of 51KJ.mo1-1

(12.2Kcal.mo1-1) separates both rotamers. Their geometries have a low

symmetry (C1) which is close to be (Cs)

energy; this conformation possesses its

anti position. The other minimum shows

180° around the Csp 2-C sp3 bond from its

lowest energy (i.e., in syn position).

in the case of the lowest minimum

lone methine hydrogen in (almost)

the alkyl group rotated about

poSition in the conformation of

As can be seen in figure (3.5-10),

both rotamers have a highly distorted alkyl group. The strain is

partially released (for the minimum of lowest energy) through a rotation

of one of the tert-butyl group from its staggered position relative to

the methine C-H fragment. This distortion reduces the strain because

this structure avoids the juxtaposition of two pairs of methyl groups of

the tert7butyl groups (which would be present if both tert-butyl groups

were staggered relative to the methine C-H). For these highly strained

conformations, relief is also obtained through stretching of the Ca-CB0

bonds (see figure (3.5-10) for notation); a value of 1.562A is found for 0

these bonds, while the equilibrium length is 1.526A.

The nergy difference separating both minima is calculated to

be 17.1KJ.mo1-1 (4.1Kcal.mol-1 ). This corresponds to enthalpy and Gibbs

energy differences of 17KJ.mo1-1 (4.06Kcal.mo1-1) and 18KJ.mol

(4.3Kcal.mo1-1) respectively as is shown in table 3.5-5'. Due to the

small variation in difference in entropy, these values can be assumed to

140


Reproduced w

ith permission o



ithout permission.

120.0

2 03 t 95.0

0

0

70 0

H

C \ /23.6/

\ H

50.88 (12.16)

C C

5H 128._5,

\ H

17.15 (4.1).

L 180 270

mapping parameter,

360 0 —11..

FIGURE 3.5-9 Calculated steric energy profile for 4,4-dimethy1-3-tert-butyl-1-pentene as obtained by driving the HCET2-Csp31-1 dihedral angle (the figures'between parentheses are energies in Kcal.mo1-1).

Reproduced w



ithout permission.

Reproduced w

ith permission o



ission.

CV``

3 "Si/ CH:

1:566\‘ \ • CH

3 I \ FI 105.79 C.

r

1.344

c‘; . " eb. - 1"/ Jig 61 CA ) " " • • CH3

0, • . -A1.335 /".'-

Ci7 ---\-- s.0

3

Q. HC2C,H 345.99

LHC2C"Cp .7234.99

L ViC2Ca Cp ,.: 97.24

L H C„ H =784 5 5

kHc2c.„cfr 77. 77

HC2CaC,= 297.37

0,9 CH3 si

••- CH3"

• • Oi.70 ‘ °4

A, H

H H

FIGURE 3.5-10 Calculated molecular geometries of the two conformations of lowest minimum energy for 4,4-dimethy1-3-tert-butyl-1-pentene.

Reproduced w



ithout permission.

TABLE 3.5-5 Calculated thermodynamic properties of 4,4-dimethyl-3-tert-butyl-l-pentene conformationsT

anti syn TS* 0

AV strain

T

72.0 (17.2)

17.2 (4.10)

51.0 (12.2)

198 877 17.0 53.6 (209.7) (4.07) (12.8)

AH 298 897 17.0 52.7 (214.3) (4.07) (12.6)

398 923 17.1 51.5 (220.5) (4.08) (12.3)

198 385 -3.19 -15.7 (91.9) (-0.76) (-3.76)

AS 298 465 -3.09 -20.4 (111.2) (-0.74) (-4.88)

398 543 -3.00 -23.8 (129.7) (-0.72) (-5.68)

198 801 17.7 56.8 (191.5) (4.22) I (13.3)

AG 298 758 17.9 58.7 (181.1) (4.29) (13.6)

398 706 18.2 61.1 (168.8) (4.36) (14.6)

tThe values for the anti form are absolute (given in italics); those for the other conformations are relative to the anti form. Units: the energies are given in KJ.mo1-1, the entropies in J.mo1-1.K7 1 Between parentheses, these quantities are given in Kcal.mo1-1 .1<-1 respectively. The temperatures are in K. TS* is the transition state.

143

\


be temperature indepeident. These large quantities, even if somewhat

overestimated, indicate that this molecule should be exclusively in the

anti form at room temperature.

Following the opinions expressed by several authors (see for

example [2.70] and [M]) as well as the results of the above study

7) (particularly sections 3.1 to 3.3' the reliability of the Force Field

approach is acknowledged to be greater in the prediction of structural

observations than in energies. The geometric parameters will therefore be

used with more confidence in the discussion of the experimental NMR data

than will be the various kinds of energies obtained by the Force Field

method for the same molecules.

144


APPENDIX

In the following pages, the internal coordinates of the various

molecules studied as obtained from the Force Field calculation are given

in full detail. The numbering system of the atoms is shown for the

conformation of lowest energy of each molecule. An example of how to use

the tables is given below for the propene molecule (the distances are in 0 A, the angles in degrees).

Example: •

8 112.54

6 1153

7;""; 1 9 c.; —' cr cc?) -- ---k?' (Y)

6,e•:,---/

S. c?,t'' Y 11- ( ' e 3 2

/ 'ND 1 eii Sic)..--QT:1 sy—--0

4 5

R12 = 1.090 R23 = 1.334

1 is a hydrogen atom, 2 and 3 are carbon atoms.

TH123

= 122.18

NA NB NC ND atom (D) RCD THBCD ' PHABCD

1 2 3 4 H 1.090 120.47 180.00 4 3 2 5 H 1.090 120.89 0.00 1 2 3 6 C 1.503 123.88 0.00 2 3 6 7 H 1.106 113.53 0.00 2 3 6 8 H 1.105 112.54 239.74 2 3 6 9 H 1.105 112.24 120.26

145


3-METHYL-1-BUTENE

10 9

11-°•,„ / 7 13 2--;6 1

)' \ 14 % 15 3===2

/ 1 5 4

(anti) form

R12 = •

1 '090 R23 = 1.334 TH123 = 122.35

NA' NB. NC ND atom (D) A RCD THBCD PHABCD

1 2 3 5 H 1.091 120.10. 180.00

5 3 2 4 H 1.089 12P.78 0.00

1 2 3 6 C 1.508 123.80 0.00

2 3 6 7 H 1.107 109.42 0.00

2 3 6 8 C 1.532 110.10 241.33

2 3 6 12 .

C 1.532 110.10 118.67

3 6 8 9 H 1.106 113.'9 298.74

3 6 8 10 H 1.106 112.49 58.89

3 6 8 11 H 1.106 112.73 178.41

3 6 12 13 H 1.106 112.73 181.59

3 6 12 14 H 1.106 112.49 . 301.11

3 6 12 15 H 1.106 113.19 61.26

146


3-METHYL-1-BUTENE

(gauche) form

The numbering of the atoms is the same as for the (anti) form.

R12 = 1.089 R23 =

1.334 TH123 = 123,80„.

1 is a hydrogen atom, 2 and 3 are carbon atoms.

NA NB NC' -ND atom (D) RCD THBCD PHABCD •

1 2 3 5 H 1.091 118.33 179.92

5 3 2 4- H 1.090 119.82 -0.02

1 2 3 6 C 1.505 127.10 359.88

2 3 6 7 H 1.107 107.37 , 235.36

2 3 6 8 C 1.535 109.57 .118.43

2 3 6 12 C 1.530 113.70 354.55

3 6 8 9 H 1.106 112.97. 297.33

3 6 8 10 H 1.106 112.66 51..48

3 6 8 11 H 1.106 112.77 177.04

3 6 12 13 H 1.106 112.17 182.73

3 6 12 % 14 H 1.106 113.00 301.74

3 6 12 15 H 1.106 113,56 62.97

1 147


TRANS-2,5-DIMETHYL-3-HEXENE

14 25 (aa) form

13=13 ,7 9, 5 10

111 3==-4 2( 22

4/ \ .21-2324

T20 \

k 18 19

R12 = 1.509

1, 2, 3 exe carbon atoms.

R23 = 1.335 TH123 = 123.38

NA NB NC ND atom (D) RCD THBCD PHABCD

1 2 3 4 H 1.091 120.99 0.00

1 2 3 6 C 1.509 123.38 180.00

4 3 2 5 H 1.091 120.99 180.00

2 3 6 7 H 1.107 109.50 0.00

2 3 6 12 C 1.532 110.01 241.32

2 3 6 8 C 1.532 110.01 118.68

3 6 8 9 H 1.106 113.19 61.21

3 6 8 10 H 1.106 112.47 301.08

3 6 8 11 H 1.106 112.75 181.56

3 6 12 13 H 1.106 112.75 178.44

3 6 12- 14 H 1.106 112.47 58.92

3 6 12 15 H 1.106 113.19 298.79

3 2 1 16 H 1.107 109.50 0.00

3 2 1 17 C 1.532 110.01 241.32

3 2 1 21 C 1.532 110.01 118.68

• 2 1 17 18 H 1.106 112.47 58.92

2 1 17 19 H 1.106 113.19 298.79

2 1 17 20 H 1.106 112.75 178.44

2 1 21 22 H 1.106 112.75 181.56

2 1 21 23 H 1.106 112.47 301.08

2 1 21 24 H 1.106 113.19 61.21

148 •

I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

TRANS-2,5-DIMETHYL-3-HEXENE

(ag) form

The numbering of the carbon atoms is the same. as for the (aa)

conformer.

R12 = 1.511 R23 = 1.334

N123 = 122.80


1 2 3 4 H 1.091 119.55 0.04

1 2 3 6 C 1.507 126.49 179.94

4 3 2 5 H 1.090 122.49 179.82

2 3 6 7 H 1.107 107.30 125,46

2 3 6 12 C 1.539 113.90 6.21

2 3 6 8 C 1.535 109.41 242.28

3 6 8 9 H 1.106 112.95 62.74

3 6 8 10 H 1.106 112.66 302.61

3 6 8 11 H 1.106 112.79 183.03

3 6 12 13 H 1.106 112.13 177.02

3 6 12 14 H 1.106 113.03 58.05

3 6 12 15 H 1.106 113.61 296.72

3 2 1 16 H 1.107 109.65 359.78

3 2 1 17 C 1.532 109.9.4 .241.04

3 2 1 21 C 1.532 109.92 118.50

2 1 17 18 H 1.106 113.20 298.87

2 1 17 19 H 1.106 112.47 59.00

2 1 17 20 H 1.106 112.75 178.52

2 1 21 22 H 1.106 112.75 178.51

2 1 21 23 H 1:106 , 112.47 58.99

2 1 21 24 H 1.106 113.20 298.86

149


TRANS -2,5-01METHYL-3 -HEXENE

(gleg+) anct,(g-g-) forms

The numbering of the atoms is the same as for the (aa) conformer.

1.509 R23 = 1.334 THBCD = 126.01 R12 =

1, 2, 3 are carbon atoms.

NA NB NC ND ' atom (D) RCD THBCD

1

1

4

2

2

2

3

3

3

3

3

3

3

3

3

2

2

2

2

2

s, 2

•

2

2

3

3

3

3

6

6

6

6

6

6

2

2

2

1

1

1

1

1

1

3

3

2

6

6

6

8

8

8

12

12

12

1

1

1

17

17

17

21

21

21

4

§

5

7

12

8 •

9

10

11

13

14

15

16

17 21

18

19

20

22

23

24

H

C

H

H

C

C

H

H

H

H

H

H

H

C C

H

H

H

H

H

H

„

1.089

1.509

1.089

1.107

1:629

1.536

1.106

1.106

1.106

1.106

1.106

1.106

1.107

1.536

1.529

1.106

1.106 ,

1.106

1.106

1.106

1.106

121-:06

126.01

121.07

107.20

114.31

109.26

112.94

112.66

112.80

112.07

113.07

113.66

107.20

109.26

114.31

112.94

112.66

112.80

112.07

113.07

113.66

PHABCD

0.10

179.86

179.65

125.90

6.56

242.52

62.88

302.76

183.18

176.84

57.92

296.48

234.10

117.48

353.44

297.12

57.24

176.82

176.84

i 57.92

.r296.48

150


TRANS72,5-DIMETHYL-3-1HEXENE

(g+g-) and (g-g+) forms

The numbering of the atoms is the same as for the (aa) conformer,

R12 =•1.509 R23 = 1.334 TH

123 = 126.,02

NA NB NC ND atom (D) RCD THBCD PKAgaD

1

1

4

2.

2

2

3

3

3

3

3

3

3

3

3

2

2

2

2

2

2

2

2

3

3

3

3

6

6,

6

6

6

6

2

2

2

1

1

1

1

1

1

3

3

2

6

,, 6

6

8

8

4, . 8,

12

12

12

1

1

1

17,

17

17

21

21

21

ti

4

6

5

7

12

8

9

10

11

13

14

15

16

17

21

18

19

20

22

23

24

H

C

H

H

C

C

H

H

H

H

H

H

H

C

C

H

H

H

H

H

H

1.089

1.509

1.089

1.107

1.529

1.536

1.106

1.106

1.106

1.106

1.106

1..106

1.107

1.536

1.529

1.106

1.106

1.106

1.106

1.106

1.106

121.07

126.02

121.07

107./19

114.31

109.28

112.95

:112.66

112.79

112.07

113.07 le,113.66

107.19

109.28

114.31

112.66

112.95

112.79

112.07

113.66

113.07

359.96

180.00

180.00

125.87

6.56

242.49,

62.91

302.78

183.20

176.81

57.89

296.46

125.87

242.49

6.56

302.78

62.91

183.20

183.19

63.54

302.11

m

151


CIS-2,5-DIMETHYL-3-HEXENE

(aa)' form

9

j

R12 = 1.50?


2F 23 16

„p.24 g0 / 17-19

2 18

5

R23 = 1.333 TH123 = 128.51

NA

1

1

4

2

2

2

.3

3

3

3

3

3i

3,

3

3'

2

2 .

2

2

2

2

NB NC ND atom (D) 'RCD BCD PHABCD

2' 3 4 H 1.091 116.82 180.00

12 3 6 C 1.502 128.51 0..00

3 2 5 H 1.091 116.82 0.00

Q 6 7 H 1.104 111.41 0.00

3 6 a 12 C 1.534 109.87 119.04

,3 6 8 C 1.534 109.87 240.96

4,6 8 9 H 1.106 112. 3 59.64

16 8. 10 H 1.106 113.24 299.48

6 8 11 H 1.106 112.71 179.11

6 12 13 H 1.106 112.71 180.89

6 12 14 H '1.106 113.24 60.52

. 6 12 15. H 1.105 112.43 300.36

2 1 16 H 1.534 111.41 0.00

2 1 17 C 1.534 109.87 119.04

2 1 21 C 1.106 109.87 240.96.

1 17 18 H 1.106 112.71 179.11

1, 17 19 H 1.106 112.43 59.64

1 17 , 20. H 1.106 113.24 299.48

1 21 22 H 1.106 112.43 59.64

1 21 23. H 1.106 113.24 299.47

' 1 21 24 ' H 1.106 112.71 179.11

a ., .t • . I 1 1 1 152



(as) form

The numbering of the atoms is the same 0 for the (aa) form.

= 1.500 R12


R23

1.333 TH123 = 129.98

NA NB NC ND atom (0) RCD THBCD

•

PHABCD

1 2 3 4 H 1.091 116.29 180.00

1 2 3 6 1.500 129.20 0.00

4 3 2 5 H 1.091 116.06 0.00

2 3 6 7 H 1.103 111.40 0.00

2 3 6 12 C 1.534 109.24 119.05

2 3 6 8 C 1.534 109.92 240.95

3 6 8 9 H 1.106 112.48 59.49

3 6 8 10 H 1.106 113.23 299.32'

3 6 8 11 H 1.106 112.69' 178.98

3 6 12 '13 H 1.106 112.69 181.02

3 6 12 14 H 1.106 113.23 60.6e

3 6 12 15 H 1.106 112.48 300.51

3 2 1 16 H 1.108 105.87- 180.00

3 2 1 17 C 1.529 112.43 295.78

3 2 1 21 C 1.529 112.43 64.22

2 1 17 18, H 1.106 112.30 172.45

2 1 '17 19 H 1.106 112.38 ' 53.61

2 1 17 20 H 1.104 114.58 292.78

2 1 21 22 1.106 112.38 53.61

2 1 '21 23 H 1.104 114.58 292.78

2 1 .21 24 H 1.106 112.30 172.45

153



(ag) form

The numbering is the same as for the (aa) form.

R12

= 1.497

1, 2, 3 are carbon atoms. .

R23 = 1.331 TH123

= 133.98

NA

1

1

4

2

2

2

3

3

3

3

3

3

34.

3 3

2

2

2

2

2

2

' NB MC ND atom (0) RCD THBCD PHABCD

2 3 4 H 1.091 114.34 178.49

2 3 6 C 1.496 132,.11 358.18

3 2 5 H 1.092 113.97 1.47

3 6 7 H 1.100 112.41 354.57

3 6 12 C 1.534 109 95 114.41

3 6 8 C 1.536 109.77 235.93

6 8 9 H 1.106 112.40 59.74

6 8 10 H 1.106 113.32 299.51

6 8 11 H 1.106 112.64 179.15

6 12 13 H 1.106 112.70 180.46

6 12 14 H 1.106 113.21 60.12

6 12 15 ft 1.106 112.50 299.97

2 1 16 H 1.107 105.63 133.45

2 1 ' 17 C 1.537 109.38 248.51

' 2 1 21 C 1.523 117.27 14.86

1 17 18 H 1.106 112.77 174.96

1 . 17 19 H 1.106 112.66 55.37

1 17 20 H 1.106 112.94 295.26

1 21 . 22 H 1.106 ;3.65 48.79

1 21 23 H 1.105 114.11 285.41

1 21 24 H 1.106 111.31 167.24 r

154


TRANS-2,2,5-TRIMETHYL-3-HEXENE

(anti) form 16 15

17,4, / ,18 12..mo..°\ 10 13•1

14 2-- --1t 212 / z is \ -23

11 \ _6%0s 24

R12 = 1.334


26' 27 "7 -21

R23 = 1.512 19 zo TH123

= 122.66


1 2 3 4 C 1.532 109.91 241.27

1 2 3 5 C 1.532 109.91 118.73

3 2 1 6 C 1.511 126.41 180.00

2 1 6 7 C 1.539 108.30 239.17

2 1 6 8 C 1.539 108.31 120.84

2 1 6 9 C 1.534 113.02 0.00

3 2 1 10 H 1.091 119.52 0.00

6 1 2 11 H 1.089 122.72 0.00

1 2 3 18 H 1.107 109.66 0.00

2 3 5 12 H 1.106 112.76 181.48

2 3 5 13 H 1.106 113.20 61.13

2 3 5 14 H 1.106 112.46 301.01

2 3 4 • 15 H 1.106 112.75 178.52

2 3 4 16 H 1.106 112.46 59.00

2 3 4 17 H 1.106 113.20 298.87

1 6 7 19 H 1.106 113.05 181.36

1 6 7 20 H 1.106 112.70 61.34

1 6 7 21 H 1.106 112.99 301.46

1 6 8 22 H 1.106 113.05 181.37

1 6 8 23 H 1.106 112.70 61.34

1 6 8 24 H 1.106 112.99 301.46

1 6 9 25 H 1.106 112.99 180.00

1 6 9 26 H 1.106 113.36 299.41

1 6 .9 27 H 1.106 113.37 60.59

155


TRANS-2,2,5-TRIMETHYL-3-HEXENE

(gauche) form

The numbering of the atoms is the same as for the (anti) conformer.

1.334 R23 = 1.509 MI23 = 125.89 R12 =


NA NB

1 2

1 2

3 2

2 1

2 1

2 1

3 2

6 1

1 2

2 3

2 3

2 3

2 3

2 3

2 3

1 6

1 6

1 6

1 6

1 6 1 A 6

1 6

1 6 i

1 6 /

1

NC • ND atom (D). RCD THBCD . PH ABCD

• 3 4 C 1.529 114.34 6.74

3 5 C 1.536 109.24 242.C9

1 6 , C 1.514 126.03 180.07

6 7 C 1.540 108.19 238.98

6 8 C 1.540 108.17 120.83

6 9 C 1.533 113.36 359.92

1 10 H 1.090 120.94 359.93

2 11 H 1.089 121.31 0.03

3 18 H 1.107 107.18 126.08

5 12 H 1.106 112.80 183.19

5 13 H 1.106 112.94 62.90

5 14 H 1.106 112.66 302.78

4 15 H 1.106 112.06 176.76

4 , 16 H 1.106 113.07 57.84

4 1 17 H 1.106 113.67 296.39

7% 19 H 1.106 108.19 181.53

q 20 H 1.106 112.68 61.50

7', 21 H 1.106 113.00 301.62

8 22 H 1.106 113.05 181.50

/ 8 823

24

H

H

1.106

1.106

112.68

113.00

. 61.48

301.60

9 25 H 1.106 112.36 .179.99

9 26 H 1.106 113.41 299.35

9 27 H 1.106 113.41 60.63

156


CIS-2,2,5-TRIMETHYL-3-HEXENE

conformation (as)

•

12 r . 2322

11;5. 18 24-8,1 ,19 14 -,3/ 25,90 5 ----k-20 15 .4/ \ 26- / '

*--4 \ 2/ 21 16/ I 2 1

17

R12 = 1.333

1, 2, 3 are carbon atoms

/ \ 11 . 10

R23

=11499 TH123

= 130.22

NA NB • NC • ND atom (D) RCD THBCD g

PHABCD

1 2 . 3 4. C 1.535 109.87 119.16

1 2 .3 5 C 1.535 109.87 240.87

3 2 1 6 C 1.506 .-a..

129.12 0.00

2 1 6 7 C 1.55? 108.09 180.02

2 1 6 8 C 1.534 111.35 62.59

2 1 6 9 C 1.534 111.35, 297.43

3 2 1 10 H 1.091 115.45 181.00

6 1 2 11 H 1.091 115.70 181.00

1 2 3 18 H 1.102 111.83 0.02

2 3 5 12 H 1.106 112.68 179.11

2 3 5 13 H 1.106 112.47 59.63

2 3 5 14 H . 1.106 113:24 299.46

2 3 4 15 H 1.106 112.68 180.89

2 3 4 16 H 1.106 113.24 60.53

2 3 4 17 H 1.106 112.47 300.37

1 6 7 19 H 1.106 112.83 180.00

1 6 7 20 H 1.106 112.92 60.09

1 6 7 21 H 1.106 112.92 299,61

1 6 8 22 H 1.106 112.63 185.27

1 6 8 23 H 1.106 114.56 65.21

1 6 8 24 H 1.106 112.59 304.63

1 6 9 25 H 1.106 112.63 174.72

1 6 9 .26 H 1.106 114.56 294.78

1 6 -9 27 H 1.106 112.59 55.36

157



(aa) form, conformation II

The numbering of the atoms is the same as for the (as) form.

R12 = 1.331


R23 = 1.496 TH.123 = 133.37

NA NB NC ND atom (0) Rco .TH BCD - pH ABCo '

1 2 3 4 C 1.536 109.75 119.37

1 2 3 5 C 1.536 109.75 4' 1240.63

3 2 1 6 C 1.502 133.97 0.00

2 1 6 7 C 1.545 107.71 121.68

2 1 6 8 C 1.527 116.45 0.00 2 1 6 9 C 1.545 107.71 ` 238.32

3 2 1 10 h 1.092 114.05 180.00

6 1 2 11 H 1.091 113.67 180.06

1 2 3 18 H 1.099 113.16 0.00

2 3 5 12 H 1.106 112.66 179.66

2 3 5 13 H 1.106 112.41 60.22

2 3 5 14 H 1.106 113.29 300.03

2 3 4 15 H - 1.106 , 112.66 180.34

2 3 4 16 H 1.106 113.29 59.97

2 3 4 17 H 1.106 112.41 299.77

1 6 7 19 H 1.106 113.06 177.10

1 6 7 20 H 1.106 113.05 57.01

1 6 7 21 H 1.106 112.61 297.10

1 6 8 22 H 1.106 111.79 180.00

1 6 8 23 H 1.106 113.75 61.65

1 6 8 24 H 1.106 113.75 298.35

1 6 9 25 H 1.106 113.06 177.10

- 1 6 9 26 H 1.106 112.61 297.10

1 6 9 27 H 1.106 113.05 57.01

158



Conformation III

The numbering of the atoms is the same as for the (as) conformer.

R12 = 1.331


R23 = 1.494 TH123

= 135.77

NA NB NC ND atom (D) RCD TMBCD PHABCD

1 .2 3 4 C 1.524 115.36 47.91

1 2 3 5 C 1.52.8 112.60 275.57

3 2 1 6 C 1.501 134.12 355.66

2 1 6 7 .0 1.556, 107.22 201.96

2 1 6 ' 8 C 1.535 110.50 85.56

2 1 6 , 9 C 1.530 114.28 318.90

3 2 1 10 H 1:092 112.91 175.31

.6 1 2 11 4V H 1.092 112.48 183.56

1 2 3 18 ii 1.108 104.03 161.79

2 . 3-- 5 12 H 1.106 111.67 188.94

2 3 5 13 H 1.106 112.38 68.41

2 3 5 14 H 1.103 114.71 307.73

2 3 4 15 H 1.106 112.30 166.53

2 3 4 16 H 1.106 112.57 48..42

2 3 4' 17 H 1.101 115.63 286.20

1 6 7 19 H 1.106 112.87 180.36

1 6 7 20 H 1.106 112.70 60.41

1 6 7 21 H 1.106 113.14 300.19

1 6 8 22 H 1.106 112.87 184.41

1 6 8 23 H 1.103 113.96 84.13

1 '6 8 24 H 1.106 112.62 304.07

1 6 9 25 H 1.106 112.18 170.62

1 6 9 26 H 1.100 115.12 289.64

1 6 9 27 H 1.106 112.87 51.77

159


CHAPTER IV

NMR EXPERIMENTAL RESULTS

4.1 EXPERIMENTAL CONDITIONS

Cis- and trans-2,2,5-trimethylS3-hexene were obtaindd by Van

der Heijden (see reference [112]) by reduction of the corresponding

hexyne. The trans isomer was formed by reduction of the hexyne in liquid

ammonia solution of alkali metal; preparative gas chromatography yielded

the final pure product. The second isomer (cis) resulted from a selec-

tive hydrogenation cif, the hexyne over a deactivated palladium catalyst

(palladium on barium sulfate deactivated by pure synthetic quinoline).

The hexene was then purified using the same gas chromatography technique

as for the trans isomer.

The cis-2,5-dimethy1-3-hexene was obtained from Aldrich

Chemical Co. The purity of this sample has beer tested by Rummens et al.

[108]; a presence of a weak band near 960cm-1 in the infrared spectrum

was an indication of the presence of a small amount of trans isomer in

the sample; this was later confirmed by the NMR signals of the methyl

region of the compound. This small impurity never interfered• with the

analysis of the NMR spectra reported in this work.

The cis-4,4-dimethy1-2-pentene was purchased from Chemical

Procurement Laboratories Inc., and was used without any further purifica-

tion.

160


The proton NMR spectra of the three compounds studied (cis- and

trans-2,2,5-trimethyl-3-hexene and cis-2,5-dimethyl-3-hexene) have been

recorded at 90MHz with a Bruker HX90 spectrometer. Additional runs at

100MHz have also been performed using a Varian HA100 spectrometer. As it

turned out, however, the 90MHz spectra show more detail; henceforth only

the results from the 90MHz spectra will be discussed.

The proton spectra were run using a proton lock. The TMS

(tetramethylsilane) single line was used as the internal lock signal. To

the neat sample of cis-2,2,5-trimethy1-3-hexene, 12.5% v/v of TMS were

added; 12% of TMS, 25% of CDC13 and 63% of the trans isomer composed the

other sample. Approximately 5% of the lock compound was mixed with the

cis-2,5-dimethy1-3-hexene and with the cis-4,4-dimethy1-3-pentene. The•

proton spectra were run using the CW mode. A linewidth of 0.1Hz was

achieved with the magnet, as deter Mined from acetaldehyde spectra run as

a reference. Each spectrum is composh of three regions: the olefinic

part at high frequency, the methine part in the medium range and the

methyl part at high field close to the,TMS reference signal. To obtain

the best possible resolution each part was recorded separately. For each

temperature three runs were performed uhder identical conditions:. scan

. rate of 0.03Hz.sec-1 using a display scale of 1Hz.cm-1, the filter was

set in such a way that the signal-to-noise ratio was the best possible-

without distortion of the signals. Each region (olefinic, methine,

methyl) was recorded in small sections--usually 5Hz wide or less. The

calibration was 'made using a HP5216A electronic counter, by determining

the frequency at the beginning and at the end of each section. All line

161


Positions, by this procedure, had an internal precision of ±0.03Hz or

less (when well defined); the exact display scale was calculated to vary

from 0.998Hz.cm 1 to /.009Hz.cm-1.

The temperature variation was accomplished using a Bruker

BST-100/700 temperature control unit. Following the Bruker procedure the

thermocouple is situated immediately below the sample in the heat exchange

gas. At room temperature and above, air is blown around the sample; at

lower temperature nitrogen is used, as the heat exchange gas. The flow

rate,. for either gas, is 3001,he1 in order to reach equilibrium in a

reasonable time. Monitoring and controlling the temperature is done by

the thermocouple sensor, the comparison circuitry of the BST unit in

conjunction with a small heater resistance put in the path of the heat

exchange gai. The exact temperatures were determined using the ethylene

glycol shift for the high temperature measurements and the methanol shift

fop beloW ambient temperature. Van Geet'S equatiqns for the calibration

bf both compounds were used to provide the exact temperature of the

0

sample [113].

Natural abundance carbon-13 experiments were done on the cis-

and trans-2,2,5-trimethyl-3-hexene, using the Bruker HX90 spectrometer in

its FT mode. A Nicolet 1080 computer provided the computing facilities. DBTFE

(1, 2-dibromotetrafluoroethane) was added to both samples to be Used as

a fluorine lock compound. For each temperature two spectra were recorded:

one to give the whole spectrum (4000Hz wide), the other to expand the

region around the methyl carbons (850Hz). A pulse width of 4us was used

in all cases with a trigger time (time between two pulses) of 6s for an

162 •


acquisition time of 2.41s for the 850Hz width spectra; a trigger time of

is we: used when pulsing over 4000Hz. The FID (free induction decay) was

completed after 512 or 1K pulses. Therefore, the data resolution was 4

0.41Hz and 1.95Hz 'for spectral widths of 850 and 4000Hz.respectively.

Fourier transformation was applied to these data points to which 4K

"zeros" were added in order to increase the definition of the spectrum as

stated by Bartholdi and Ernst [114]. In this manner, the accuracy of the

line position was increased to ±0.10Hz and ±0.49Hz respectively for each

spectral width.

All carbon-13 spectra were proton-noise decoupled. As for the

proton spectra, a 5mm probe,was used in every experiment. The temperature

variation was achieved in exactly the same way as for the proton experi-

ment. No correction was applied because of the heating effect caused by

the interaction between molecules and the high radio-frequency fields;' .

the amount of heat developed is supposedly small and the heat transmission

through the sample as well as the cooling capacity of the temperature

regulating 'gas flow are supposedly sigh enough to maintain a temperature,

in the sample, equal to, or slightly higher than the temperature of the

gas flow (the difference should not have exceeded 2K). Such a belief is A

reinforced by a study on the effect of proton-noise decoupling,on the

heat of a sample, made by Led and Petersen [115]. 4

163


4.2 SPECTRAL ANALYSIS OF THE PROTON SPECTRA

4.2.1 Cis- and trans-2,2,5-Trimethy1-3-hexene

For both isomers three characteristic regions can be distin-

guished. The olefinic region between 6 = 4.5 - 5.5ppm, the methine

region between 6 = 2.2 - 2.3ppm and the region of the methyl groups of

thetert-butyl and isopropyl groups 6 = 0.8 - 1.0ppm. In Figure (4.2-1)

the nomenclature for the spin-spin coupling constants !IL] is given

(coupling constants between nuclei separated by n bonds are noted 72.3)

together with that for the chemical shifts.

The nine protons of the tert-butyl group are assumed to be

magnetically equivalent, but they are weakly coupled with all the other

protons of the molecule: an X approximation can be used to describe the

system. The isopropyl group is composed of six equivalent methyl protons

and one methine proton. The two remaining protons of--te moleCule are

'the .olefinic protons. Using the conventional notation (first introduced N

by Bernstein et al. [/16]), the spin system can be begt described as an

ABCD6X9.for both isomers. ThiS system consists of two subsystems, the-

ABCD6 system which has been extensively developed by Van der Heijden in

his thesis [1/2] and the X9 system. The inclusion of the X subsystem

increases the number of transitions from 736 (ABCD6 system) to more than

40 000. This makes the use of an iterative computer program imperative.

Ten coupling constants and five Larmor'frequencies (chemical shifts) are

sufficient to fully describe the ABCD6X9 system.

Throughout the iteration process, the chemical shifts of the

164


471.,

j I2

j 23traJJ fin tiC0.,C;0-"H rrea

Jm= • ..134---r"J (in HC.04.7C:0-1141

23" J ft (in Hi.4 J•C 7H ) 7r

• ' '113' J- •

j 34= -11J. HC0 .1C0./H)

lhquRE 4.2=1 Numbering system and nomenclature used for, the (11,H) coupling constant§ of cis= and trans-2,2,5-trimettly1-3-hexane:..

AIN

•

Reproduced w



ithout permission.

methyl protons composing the isopropyl group were kept constant at a

value equal to the average between the two isopropyl lines. Initially,

all the coupling constants were iterated. Only four of them were of

sizeable magnitude, and in a second step only these were varied during

the iteration, while'the other six coupling constants were put equal to

zero. An example of the difference between the parameters obtained by

the two above techniques is given in Table 4. 1. All the subsequent

--results will only be given for the second techriique (only four non-zero

coupling constants).

The starting parameters for both isomers were taken from Van

der Heijden's thesis [112]; the procedure to find the best set of these

parameters was exactly as outlined in chapter II. The best experimental

spectrum for the trans isomer shows 26 totally resolved lines in the

methine region, to 'vhich 141 transitions were assigned. The 'differences

between observed and final calculated line frequencies never exceeded•

0.05Hz. Figure (4.2-2) shows the kind of agreement reached between the

experimental spectrum and the final theoretical spectrum for the methine

part of the trans isomer. A decrease in line separations- 'resulting in a

smaller number of assigned lines was observed when lowering the tempera-

ture. This change can be seen in Figure (4.2-3). At the lowest tempera-

ture of measurement, the total number of transitions assigned was down to

100. Of the eight lines compoiing the olefinic region (the AB part of

the spin system), seven were well resolved (in the entire range of 41

temperatures); this made possible the assignment of 53 transitions to the

seven experimental frequencies. Chemical shifts and coupling constants

166 •


• TABLE 4.2-1 Comparison between parameters as obtained from the NUMARIT

program,(a) iterating all the coupling constants, (b) itera-ting only the'coupling constants of sizeable magnitude. The examplg is given for the trans-2,2,5-trimethyl-3-hexene at 345.50

a

61 5.38813±7x10-5 5.38817±6x10-5

62 5.27556±5x10-5 5.27557±7x10-5

63 2.20826±3x10_ 5 2.20826±3x10-5

64 0.9545 0.9545

----______A 0.9818±2x10-4 0.9818±2x10-4

J1-2 15.710±0.008 15.710±0.008

J1-3 -1.336±0.01 -1:338±0.02

J1-A 0.005±0.02

J1-5 -0.001±0.004

J2-3 6.787±0.004 6.789±0.004

J2-4 -0.001±0.007

J2-5 0.004±0.007 ---

J3-4 6.744±0.002 6.744±0.002

J3-5 0.000±0.002 ---

J4-5 -0.001±0.02 N ---

RMS* 0.025 0.025

Units: the chemical shifts are in ppm from TMS, the coupling constants in Hz.

The numbering system is given in Figure (4.2-1). *The RMS represents the residual mean-squares of the transitions.

167


4. •

I

210 200 190

Hz from TMS 180

FIGURE 4.2-2 Methine region of observed (upper spectrum) and computer simulated (lower spectrum) 90MHz proton spectra of trans-2,2,5-trimethyl-3-hexene. The observed spectrum was recorded at 298K.

168


a

v

2.3 34 1.1 ppm from TMS

34

FIGURE 4.2-3 Temperature dependence of the methine region of the 90MHz proton spedtrum for trans-2,2,5-trimethyl-3-hexene. The upper spectrum was recorded at 330K, the lower one at 270K.

169


CD

c7i m. o

0

TABLE 4.2-2 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the trans-2,2,5-trimethy1-3-hexene at each investi-gated temperaturet

0 0 -0

T (K) 361 356 345.5 340 324 314 298 279 270 257 251, 246 238

61 5.3917 5.3906 5.3881 5.3857 5.3831 5.3810 5.3771 5.3724 5.3697 5.3679 5.3661 5.3650 5:3043

62

5.2819 5.2799 5.2756 5.2727 5.2680 5.2645 5.2578 5.2501 5.2465 5.2438 5.2408 5:2381 5.2304

63

2.2071 2.2089 2.2083 2.2081 2.2073 2.2079 2.2070 2.2070 2.2076 2.2085 2.208 ,

64

0.9544 0.9555 0.9545 0.9542 0.9533 0.9540 0.9534 0'.9528 0.9532 0.9530 0.9531 .0':6529 0.9528

@ -0 8 a c

-4 c) 65

J1-2

0.9823

15.702

0.9829

15.721

0.9818

15.710

0.9812

15.716

0.9804

15.671

0.9800

15.667

0.9808

15.617

0.9701

' 15.00

0.9777.'0.9776

15.663 15-050

0:074

15.637

0.9773

15.618

0.9768

15.615 0.

J1-3

-1.375 -1.359---1.338 -1.394 -1.353 -1.356 -1.320 -1.354 4..315 -1.375 ,-1.350 -1.382 -1.347

0 3 J2-3 6.775 6.777 6.789 6.836 6.816 6.860 6.824 J5.895 6.890 6.946 6.936 6:981 6.970

m 0_ J3-4 6.744 6.745 . 6.744 6.740 6.744 0,734. 6.741 6.735, 6.745 6.738 6.734 6.762 6.754

*' 78-

----- RMS 0.021 0.023 0:025 0.015 0.014 0":020 0.032 0.017 0.029 0.023 0.021 0.028 0.026

0 c -0

5 a . Cl) 5' z

.+the numbering system is given in Figure (4.2-1).

Reproduced w



ithout permission.

I

J I

vU

4)

270 260 Hz from TMS

250 240

0

•

FIGURE 4.2=4 Methine region of computer simulated (lower spectrum) and observed (upper spectrum) 90MHz proton spectra of cis-2,2,5-trimethyl-3-hexene. Tf* observed spectrum was • recorded at 298K.

• 171


-0 8

TABLE 4.2-3 List of proton chemical shifts (in ppm from TM) and of H-H coupling constants (in Hz) which . give the best fit with to experimental spectra for the cis-2,2,5-trimethyl-3-hexene at each'

N0 investigated temperature

05-' m - T (K) 354 345.5 335 - 324 314 299 284 271 257 246 229

co

-Ps s< 61 5.1643 5.1648 5.1646 5.1652 5.1662 5.1680 5.1698 5.1726 5.1741 5.1764 5.1804 m. m-

62 4.9215 4.9212 4.9201 4.9196 4.9188 4.5186 4.9183 4.9184 4.9181 4.9182 4,9191 o

63

2.8459 2.8451 2.8432 2.8422 2:8403 2.8385 2.8352 2.8335 2.8324 2.8309 2.8282

64 0.9382- 0.9378 0.9367 0.9362 0.9352 0.9347 0.9339 0.9328 0.9321 0.9317 0.9305 c a-

65

1.1107 1.1100 1.1090 1.1086 1.1074 1.1067 1.1052 1.1046." 1.1041 1.1037 1:1020 @ IN3

,4 -0 J

1-2 11.989 11.984 11.990 11.960 11.940 11.951 11.942 11.913 11.896 11..884- 11.861

J1-3

-0.711 -0.722 -0.708 -0.702 -0.709 -0.677 -0.667 -0.606 -0.715 -0.625 -0.658 o m0 J2-3 10.506 10.507 10.527 10.531 10.545 10.577 10.584 10.611 10.632 10.653 10.693 8 - I 6- 7 J3-4 6.533 6.557 6.549 6.556 6.546 6.562 6.561 6.565 6.568 6.555 6.563

a .

a RMS 0.017 0.024 0.021 0.018 0.023 0.016 0.019 0.018 0.013 0.018 0.034

74 o +the numbering system is given in Figure (4.2-1).

z

Reproduced w



ithout permission.

for this isomer are listed in Table 4.2-2.

For the,cis isomer, at most 20 lines were resolved in the

methine region. Once again the number of assigned transitions, for this

region, went down with the lowering of temperature (from 74 it 366K to 58

at 229K). Figure (4.2-4) gives an idea of the fitting obtained between

experimental and computed patterns. Forty-seven transitions have been

assigned to the six frequencies of the resolved lines in the olefinic

portion of'the spectra for all the temperatures of measurement. The

final parameters are listed in Table 4.2-3.

4.2.2 cis-2,5-Dimethyl-3-hexene

In this case, full use of the symmetry feature present in the

"NUMARIT" program has been made. A weak coupling has been assumed to

exist between the olefinic protons and all other protons in the molecule.

Similar to.the 2,2,5-trimethy1-3-he isomers, the six methyl protons

of each isopropyl group are chemically and netically equivalent. The

spin system is therefore treated as in AA'XX 1Y6 6 system (following the

notation introduced by Diehl and Pople [217]) involving eight coupling

constants and three chemical shifts. Because of.the symmetry involved,

some of the coupling constants are not obtained independently through fhe

iteration process. They are rather the sum and the difference of two

computed parameters. For example, following the notations given in

Figure (4.2-5), 3vJ(sp2-sp

3) is the sum of two iterated parameters, while

4taJ is their difference.

The analysis was started with a set of parameters obtained by

1,73


1

C

•

j Yelj

• 11

J 12= (7 1 -3'

)

J 21= J

ievi; J22-4 J

y

J23 J (0. -71'')

FIGURE 4.2-5 Numbering system and nomenclature used for 4-11,N) coupling constants of cis-2,5-dimethy1-3-hexene.

s

Reproduced w



ithout permission.

-o 3 a

a

•

CD 0 0

"fi cQ

0

7 CD

,j un

CD

CD -o 3 a C o.

= -E3 3 7

a

FIGURE 4.2-6 Methine region of the observed 9014Hz proton spectrUm of cis-2,5-dimethy1-3-hexene recorded at 354K under the conditions described in Section 4.2.

O

I 250 230 210

Hz from IMS

•

Reproduced w



ithout permission.

4

7J m a -0_C C) m 0_

7'

5 TABLE 4.2-4 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give thg best a.'4*

fit with the experimental spectra for the cis-2,5-dimethyl-3-hexene at each temperature investigated o 0 0

5' m T(K) 354 349 344 333 323.5 .313 297 293 288 280.5 271 260.5 2g0 ' 239 0 0

co 0-o

m

c -n

a-gi0-

0. 0.0

-0 a = a:

a

78-:0 c -0

0--

61 5.0389 5.0387 5.0387 5.0383 5.0381 5.0383 5.0391 5.0393 5.0399 5.0405 5.0418 5.0430 5.0430 5.0480

62 2.6000 2.5999 2.6002 2.6003 2.6007 2.6011 2.6018 2.6023 2.6029 2.6034 2.6047 2.6064 2.6080- 2.6094

63

0.9448 0.9451 0.9437 0.9443' 0.9430 0.9429 0.9409 0.9420 0.9420 0.9418 0.9416 0.9414 0.9426 0.9423

3c J1 _ 1, 10.850 10.843 10.828 10.824 10.824 10.829 10.801 10.787 10.817 10.803 10.805 10.782 10.795 10.769

3ua 1-2 to

9.428 .91445 9.458 9.477 9.498 9.496 9.505 9.539 9.554 9.548 9.575* 9.599 9.619 9.655

---4 Cr4 J2-1 -1.061 -1.061 -1.047 -1.061 -1.058 -1:034 -1.008 -1.036 -1.029 -1.027 -1.007 -1.025 -1.994 -1.021

J1-3

0.186 0.188 0.177 0.203 0.242 0.240 0.269 0.232 0.229 0.240 0.227 0.220 0.210 0.226

J3-1 -0.032 -0.034 -0.033 -0.038 -0.046 -0.046 -0.051 -0.040 -0.041 -0.046 -0.043 -0.042 -0.034 -0.034

5cha j2...2., 0.373 .0.386 0.375 0.392 0.397 0.393 0.408 0.390 0.387 0.403 0.394 0.391 0.358 0.367

J2-3 6.640 6.641 6.640 6.641 6.648 6.646 6.647 6.651 6.643 6.648 6.655 6.650 6.651 6.654

RMS. 0.023 0.020 0.022 0.023 0.018 0.025 0.026 0.021 0.029 0.024 .0.022 0.023 0.024 .

0.027

5 +numbering system: (CH3)2-CH-CH=CH-C1H-(CH,),.

0. 3 2 i 1 2 1 1 i i I,

o

I/

Reproduced w



ithout permission.

Rummens et al. [108]. For the best spectrum recorded at the highest

temperature- achieved (354K), 109 frequencies have been determined with

,248 transitions assigned to these. In a similar fashion as for the

2,2,5-trimethy1-3-hexenes, lines of the methine region are getting closer

together as the temperature is lowered, and the number of frequencies

which can be distinguished drops to 45 at 250K with 191 transitions

assigned. Fifty-nine of these transitions have been assigned to the %ix

frequencies of the olefinic part (the AA' part of the spin system). An.

example of the methine region recorded is displayed/in Figure (4.2-6).

The parameters which give the best fit are reported in Table 4.2-4.

4.2.3 'Cie-4,4-dimethy1-2-pentene

The spectra were analyzed as due to an ABC3 system using the

"NUMAR1T" program, assuming that the coupling between the tert-butyl

group and any other protons is negligible; consequently this coupling has been

dropped from the analysis. The starting parameters were those obtained

by Nicholas et al. [118] (with the 8C coupling positive). A temperature

range of 117K (from 249 to.356K) was investigated. At high temperature

. (where the best spectra are recorded), 22 frequencies were assigned to 22

transitions of the possible 61 transitions. At lower temperatures (below

- 270K) the number of assigned frequencies dropped to 17. The final para-

meters are listed in Table 4.2-5.

177


TABLE 4.2-5 Proton chemical shifts and H-H coupling constants for cis-4,4-dimethy1-2-pentene at various temperature.*

T (K) 249' 265 308 323 344 356

5.2943 5.2920. 5.2905 5.2903 5.2911 5.2917

52 5.2248 5.2244 5.2241 5.2242 5.2246 5.2250

.53 , 1.6864 1.6860 1.6864 1.6865

.1.6872 1.6873

J1-2 11.948 11.949 11.952 11.946 11.953 11.950

J1-3 -1.818 -1.810 -1.843 -1.846 -1.837

J2-3

*

7.280 7.281 7.301, 7.298 7.286 7.303

1114St 0.028 0.031 0.024 0.022 0..020 0.018

*A11 coupling constants are in Hz, all chemical shifts in ppm from TMS. Numbering of the atoms: CH,-CH=CH-C-(CH3)3 0

1

178


4.3 CARBON-13 DATA

Carbon-13 experiments have been performed for the two isomers

of the 2,2,5-frimethyl-3-hexene. The numbering system (similar to the

one for the, proton) is given in Figure (4.3-1) and will be used through;

out. THe assignment of each spectrum is based in part on relative peak

heights for the methyl carbons of the isopropyl and tert-butyl groups.

The assignments for carbons C3 and C6 have been made in such a way that

°the carbon C6 is downfield compared with carbon C3. Such a relative

shift has been obsertied for the 4,4-dimethyl-2-pentene and the 2,2-

dimethy1-3-hexene [119] (i.e., with successive replacement of the iso-

propyl group by a methyl and an ethyl group). This is furthermore

confirmed by the presence of a nuclear Overhauser effect (NOE) which

enhances the signal for carbon C3 as compared to the signal for carbon C6.

• The room temperature carbon-13 NMR spectra for both isomers are

shown in Figures (4.3-2) and (4.3-3). The expansions of the methyl part

are given in Figures (4.3-4) and (4.3-5). As can be seen, there is only

a single resonance for the two olefinic carbons in the cis isomer spectrum

(where the height of the peak is twice that of a single carbon). The

variable temperature measurements show that the coincidence of the two

olefihic "esonances occurs between .290 and 310K. This leads to an

ambiguous assignment for the cis isomer; a discussion of the different

possibilities will be given in the following chapter. A representation

of the temperature dependence of both olefinic resonance frequencies is

shown in Figure (4.3-6). For the trans isomer, the olefinic carbon

179


Reproduced w

ith permission o



ission.

8

C

(*)

(s)

FIGURE 4.3-1 Numbering system used for the carbon atoms of cis- and trans-2,2,5-trimethy1-3-hexene.

f

Reproduced w



ithout permission.

I.

i 1 1 I 1 1 1 1

140 120 100 80 60 40 20 0

ppm from TMS

FIGURE 4.3-2 Natural abundance 22:63MHz proton noise-decoupled carbon-13 spectrum of trans-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.

181


13C

re

son

an

ce

w tr.. 1--co ra

8 g 0 . 1

• • • • • • • • • • II • m • • • • . 1••• • 1.......

co Z )--

. dwe410641411 4,4ra

I 1 i I 1 I I I 140 120 100 80 60 40 20 0

ppm from TMS

FIGURE 4.3-3 Natural abundance 22.63MHz proton noise-decoupied carbon-13 spectrum of cis-2,2,5-trimethyl-3-hexene recorded at 298K under the conditions described in Section 4.3.

182


(CH3 )2 —CH—CH=CH—C—(CH3)3 a b c d

b

C

34 32 30 28

ppm from TMS

26 24 22

FIGURE 4.3-4 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrucof trans-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.

183


8 o. C)o_

a.

0

C)

0

M.

0

7

m

8

8 0_ a

8

74:

o_

0

0 0

d (CH3)2 — CH-- CH=CH—C —( CH3)3

a b c d

I I I I I I I34 32 30 28 26 24-- --- 22

ppm from TMS

FIGURE 4.3-5 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.

Reproduced w



ithout permission.

Reproduced w

ith permission o



ission.

137.9

137.4

0

• •

136 9

200 250 300 350

T [K

FIGURE 4.3-6 Temperature dependence of the olefinic carbons C1 and C2 chemical shifts for cis-2,2,5-trimethyl-3-hexene. 0

Reproduced w



ithout permission.

bearing the text-butyl group is assumed downfield with respect to the

other olefinic carbon following assignments already made for various

trans olefins. For example, Nicholas et aZ. 1118] assigned the carbon

bearing the tert-butyl group to the downfield line in the case of the

trans-4,4-dimethyl-2-pentene. Listed in Tables 4.3-1 and 4.3-2 are the

chemical shifts expressed in ppm downfield from internal tetramethylsilane

(TMS). The shifts are estimated to be accurate to within 0.05ppm for the

methyl region.

,ft

186


TABLE 4.3-1 Carbon-13 chemical shifts (in ppm-from internal TMS) of ' trans-2,2,5-trimethy1-3-hexene as a function of temperature. The numbering of, the atoms is given in Figure (4.3-1).

T (K) 61 62 3 64 165

200 138.36 131.79 3.1.54 22.99 29.81 32.93

220 138.45 131.88 31.54 --„ -2i.99 ,---

29.81 32.84

240 138.53 132.05 --11.53 23.06 29.91 32.78

260 138.66 --112.18 31.52 23.06 29.97 32.75 ..--

280 138.79 132.31 31.50 23.06 30.02 32.75

300 138.92 132.48 31.50 23.07 30.07 32.71

310 139.03 132.60 31.49 21,06 30.14 32.73

320 139.08 132.66 31.49 23.06 30.14 32.73

340 139.22 132.79 31.50 23.07 30.20 32.75

350 139.27 132.87 31.50 23.07 30.24 32.75

p

187


TABLE 4.3-2 Carbon-13 chemical shifts (in ppm from TMS) of cis-2,2,5-trimethyl-3-hexene as a function of temperature. The numbering is given in Figure (4.3-1). The chemical shifts of the olefinic carbons (1 and 2) are given in Figure (4.3-6).

T (K) 63 64 65 66

180 27.89 23.33 31.53 32.78

190 27.88 23.36 31.54 32.80

200 27.88 23.39 31.57 32.86

213 27.86 23.41 31.59 32.91

222 27.86 23.44 31.62 32.96

240 27.83 23.48 31.65 33.07

245 27.84 23.50 31.67 33.10

260 27.83 23.53 31.71 33.18

270 27.84 23.54 31.73 33.22

280 27.83 23.55 31.74 33.25

300 27.85 23.60 31.79 33.37

310 27.87 23.61 31.81 33.40.

320 27.87 23.63 31.84 33.46

`j40 27.88 23.65 31.87 33.55

188


CHAPTER V

INTERPRETATION OF THE NMR DATA

5.1. INTRODUCTION

In the last decade, several studies have been done by proton

and carbon-13 NMR on substituted ethylene molecules. In particular,

geometrical and thermodynamical features have been related to NMR para-

meters. As far as the latter are concerned AG for a conformational change.

can be linked to changes in coupling 'constants (and chemical shifts) with

temperature by equations, of the type (2.5-2) and (2.5-3), Some difficul-

ties with this approach are the inherent (i.e., not conformation-related

temperature) dependence of coupling and shifts and the possible tempera-

ture dependence of AG itself. In addition, this method requires observed

temperature dependencies that are quadratic, since in general three para-

meters need to be derived from it through least-squares fitting, If the

observed temperature dependence is (almost) linear then it is itore prudent

to attempt to estimate one of the parameters of the set from analogous

cases and to, then, calculate the other two from equations (2.5-2) and

(2.5-3).

A recent procedure developed by Rummens et al. [71] has been

found to give reasonable results in the case of 3-methyl-l-butene. In

their approach, each temperature dependent coupling constant has been

189


corrected for non-conformational temperature effects as obtained from

propene. These authors have also used the results of Rummens and

Kaslander's study on the influence of valence angles on coupling constants

[70], and they have introduced consistent Force Field calculations of

optimized geometries. This technique allows.one to extend the knowledge

of conformationally induced geometry changes beyond the simple molecules

for which exact structures are presently known. All the couplings

belonging to anti conformers were derived by4tummens et al. [72] from the

known coupling constants for 4,4-dimethyl-3-tert-butyl-l-pentene. The

AG0's extracted (531 ± 59 J.mo1-1 or 127± 14 cal.mo1-1) using at the same

time a number of independent parameters were consistent thus lending some

credence to the technique. In this chapter, the above-mentiOned procedure

or variations thereof is employed.

Studies on proton and carbon-13 chemical shifts involving

temperature dependence measurements have not been used as often as

studies on coupling constants, mainly because of problems of referencing

and of intermolecular interactions. However, in this study, an attempt

is made to extract some useful structural information from shifts.

Of the molecules described in this chapter trans- and cie-2,2,5-

trimethy1-3-hexene are discussed in the fullest extent, using variable

temperature information on H-H coupling constants and proton and carbon-

13 chemical shifts. cis-2,5-Dimethyl-3-hexene is discussed almost as

fully, except that no carbon-13 study was done. Finally some data for

cis-4,4-dimethy1-2-pentene are discussed, mostly in relation to cis-2,2,5-

trimethy1-3-hexene.

190


5.2 TRANS-2,2,5-TRIMETHYL-3-HEXENE

5.2.1 Analysis of.the temperature dependence of coupling constants

For a single, non-sytmetrical rotor such as an isopropyl

3vj, 3tj, 4ca J couplinggroup, the constants are simple-Boltzmann statis-

tical averages, as has been shown for the 3-methyl-l-butene by Rummens

et al. [71]. If p is the population of a rotamer characterized by the

constant Ja (in the case under study, Ja is the constant when the methine

proton is in anti position), and (1-p) that of the two-fold degenerate

rotamer with J as coupling constant (with methine in gauche position),

one has the relation:

<J> = pJ + (1-p) J9

with

a .g

with -2- = exp (1.-42) 1-p 2 RT

(5.2.1)

where AG is the Gibbs energy difference between both conformations; R and

T have their usual meaning.

Accompanying conformational exchange, several significant geo-

metrical changes'in the "rigid" part (e.i. the part excluding the rotor)

can occur. In this case the coupling constant of this "rigid" part (here

3t0 must also become temperature sensitive, and its variation should be

usable for the determination of the energy separation between the rota-

rners and of the coupling constants belonging to each rotamer.

191


In order to solve the problem of having too many unknowns for

the number of available relations, various, approaches have been considered

as mentioned previously.

As can be seen in Figure (5.2-1) and Table 4.2-3, the tempera-

ture dependence for all the coupling constants is virtually linear; only

two unknown' parameters can be deduced from .each of these variations.

Thus, for each set of coupling constants, one of the unknowns must be

found by another method. As the energy difference AG obtained byrForce

Field calculation does not seem to be accurate enough (see Rummens et al.

[72]), one of the other parameters (one of the coupling constants) has to

be calculated. For this purpose, the method already tested by Rummens

et al. [71] can be applied. Geometrical features of the conformation

under study, combined with the (AJ/A6) data found by the previous authors

[71] should give an adequate result. For 4caJ and 3vJ, the starting

values are taken from the 4,4-dimethyl-3-tert-butyl-l-pentene molecule

reported by Bothner-8y,et al. [107] and corrected for valence angle

differences as well as torsional angle differences., To complete the

calculation, diffirences in electronegativity have to be taken into

account. For 3vJ and 4caJ this effect is deduced from the experimental

differences (corrected for steric cohtr:Ibution differences) obtained for

propene by Rummens et aZ. [71] (3vJ = 6.47Hz, 4caJ = -1.78Hz) and for

trans-4,4-dimethy1-2-pentene by Nicholas et al. [118] (3vJ = 6.37Hz,

4caJ = -1.33Hz).' It is assumed that the electronegativity effect of the

substitution is the same for the averaged coupling constant as for each

individual coupling constant. For the vicinal 3vJ coupling constant,

192


A 6.97

6.871.-

6 77

230

o. a

•

I280

, •

•

330

T [K] ___4 1,..

0 0

NI.

FIGURE 5.2-1 Temperature dependence of the vicinal coupling constant (J23, for notation see Figure (4.2-1)) for trans-2,2,5-tri methyl - 3- hexene , (.) uncorrected values (a) values corrected for temperature dependence of

intrinsic contribution — best fit as obtained from the G8M method us g

corrected values.

193


this effect amounts to 0.07Hz and for the allylic cisoid 4aaj coupling

it amounts to 0.21Hz. These corrections lead to coupling constants for

the.anti conformation equal to 10.07Hz and L0.72Hz for 3°J and 4caJ

respectively.

The third coupling constant, 3tJ, should be more sensitive to

substituent effeEts. Replacement of one olefinic hydrogen by a tert-

butyl group gives a decrease for 3tJ equal to -1.62Hz as can be deduced

from data obtained by Lynden-Bell and N. Sheppard [120] and by Nicholas

et at. [118]. After correcting these values for steric contributions, an

electronegativity effect of -3.28Hz has to be assumed to explain the

total substitution effect. Similarly, for an isopropyl group replacing

an olefinic hydrogen (the data are taken from Rumens et al. [72] for the

3-methyl-l-butene) an electronegativity effect of -3.24Hz is obtained.

Combining these results and correcting for the geometrical changes, 3tJ

for the anti conformation of the trans-2,2,5-trimethyl-3-hexene is calcu-

lated to be equal to 14.91Hz (starting from the ethylene molecule). .

Alternately (and avoiding the estimation of any electronegativity effect),

one may consider that the calculated difference between 3tJ for anti and

for gauche conformations is due entirely to steric effects. The calcula-

tions, following Rummens and Kaslander's [70] procedure, give a difference

3tJ .ft = 1 2Hz an -gauche • •

Rummens et al. [71] have found a temperature effect for

several coupling constants in propene which is not related to population

ratio change between conformations, but rather is the result of intrinsic

effects attributed by these authors to electric reaction field effects as

194


well as to Van der Waals effects or to population chan s i vibrational

states. Rummens et aZ. [71] assume that it is reasonable to attribute a

similar non-conformational temperature dependence to hydrocarbons of the

same type. A correction was applied to the present experimental results

approximating the intrinsic effect dependence by a linear-type of varia-

tion as has been done by the above-mentioned authors, using their data

for the propene molecule.

In the Gutowsky, Belford and MacMahon's [91] method (hereafter

called the GBM method), the three parameters (two coupling constants and

the Gibbs energy difference) are allowed to vary. Instead of taking the •

set of values corresponding to a minimum in 4)2, the selected set of para-

meters must contain the previously calculated coupling constant(s) (in

the case of 3tJ, the second technique consists in selecting the set of

parameters where the difference between anti and gauche coupling constants

is 1.2Hz). These techniques give the results as shown in Table 5.2-1,

when a correction for intrinsic temperature dependence is applied. By

this procedure, a value for AG is obtained; this value is equal to tH in

the approximation that no entropy difference exists between the various

rotamers. The statistical-mechanical calculation described in Section

3.3 proves that this assumption is not always correct. The intrinsic

temperature dependence of AH can be assumed to be small in comparison

with that of the T AS term. Then, to account for the entropy differences

and their temperature dependence, the GBM method can be easily changed

(AG is replaced by AH-T AS). Using the three calculated entropies which

can be found in Table 3.5-3, postulating a quadratic variation with

195


TABLE 5.2-1 Sets of coupling constants and Gibbs energy differences as obtained by the GBM method applied to the. experimental data of trans-2,2,5-trimethyl-3-hexene under the assumption AS = Ot

3vj J*a = 10.07 Jg = 4.70 AG° = 0.795 ± 0.17 (0.190)

3tj** Ja = 14.97 Jg = 16.18 AG° = 1.000 ± 0.21 (0.240)

4caj J*a = -0.72 Jg = -1.77 AG° = 0.670 ± 0.30 (0.160)

Ta° = 0.842 ± 0.091 (0.200 ± 0.022)

4A11 couplings in Hz; AG° in KJ.mo1-1 (Kcal.mo1-1).

*calculated as mentioned in the text.

**the difference between the anti and the gauche coupling is taken equal to 1.2Hz (3tj9

3tja).

196


temperature, values of enthalpy separations between rotamers are obtained

by the application of the GBM method. These values, together with the

corresponding standard Gibbs free energy are listed in Table 5.2-2.

These values, which differ from the previous results by around 300J.mol-1

(70cal.mol-1), can be assumed to be more exact, if one believes that the

entropy calculated through the statistical-mechanical method is reliable.

Using statistical weights proportional to the magnitude of the variation

of each coupling constant, an average value of AG° . 531±89J.mo1-1

(127±21cal.mo1-1) is found.

5.2.2 Coupling constants and conformational structure

A Vicinal coupling constant 3vJ (J23)

The anti coupling constant being the result of the previously

described estimation will not be discussed here. The corresponding

gauche coupling is of the same magnitude as found already by Rummens

et aZ. [71] for the same rotor (the isopropyl group) in the 3-methyl-l-

butene molecule. This coupling increases from 4.32Hz (in the monosub-

stituted ethylene) to 4.89Hz (for the disubstituted ethylene in question).

This increase cannot be entirely explained by valence angle contribution

differences (which account for less than 0.01Hz), but it can be correlated

with a change in torsional angle (124.6° for the 3-methyl-l-butene (see

reference [71]) in gauche position and 126.1° for the studied molecule).

This geometrical change is responsible for an increase of 0.25Hz, which •

is qu'alitatively in concordance with the experimental difference (0.57Hz).

197


TABLE 5.2-Z Sets of coupling constants and energy separations between rotamers as obtained by the GBM method applied to ,the

4 experimental data of trans-2,2,5=trimethy1-3-hexenef

A) With intrinsic temperature dependence correction

3vJ

3tJ **

4taJ

B)

3vJ

3tj**

4taJ

J* = 10.07 J = 4.89 Aff = 1.10 ± 0.15 (0.2e) a g AG° r- 0.53 ± 0.15 (0.13)

Ja = 14.94 J = 16.14 AH = 1.30 ± 0.50 AG° = 0.72 ± 0.50

(0.31) (0.17)

J* = -0.72 J = -1.74 AH = 0.92 ± 0.18 (0.22) AG° '= 0.35 ± 0.18 (0.08)

Without intrinsic temperature dependence correction

Ja = 10.07 Jg = 4.82 AH = 1.18 ± 0.17 (0.28) AG° = 0.61 ± 0.17 (0.15)

Ja = 15.05 Jg = 16.24 AH = 2.05 ± 0.67 AG° = 1.48 ± 0.67

(0.49) (0.35)

Ja* = -0.72 Jg = -1.73 AH = 0.52 ± 0.16 (0:12) AG° = -0.10 ±0.16 (-0.25)

couplings are in Hz. AG°, AH are in KJ.mo1-1 (Kcal .mol -1) and AS in cal .mol -1.K-1 as calculated from AS = aT' + bT + c with a = 0.35 x 10-5, b = -0.28 x 10-2, c = 0.99.

*coupling constant calculated as explained in the text. **difference between anti and gauche ( 3tJg - 3tJa) taken equal to 1.2Hz.

198


The high temperature limit value ((„1 -anti 2Jgauche)I3)'.for

the 3vJ coupling constant is different from that of the 3-methyl-l-butene

(6. z for the molecule under study instead of 6.28Hz for the 3-methyl-

1-butene as given by Rummens et al. [72]). This difference comes mainly

from different HCsp 2-Csp 3H dihedral angles for the gauche rotamers.

B Olefinic coupling constant 3t

J (J12)

It is interesting to note that the GBM-extracted 3t

Janti =

14.94Hz is almost identical to the value 3tJanti = 14.91Hz estimated (in

Section 5.2-1) from that of ethylene with adjustments for electronegativity

and valence angle (steric) effects. The latter estimation technique

having been found rather reliable in many previous cases, th& above

results lend credence to the modified GBM technique employed and to the

other results (for 3t

Jgauche and -M).

A decrease of 1.31Hz is found for the 3t

Jgauche coupling

constant when going from the 3-methyl-l-butene (3t jgauche = 17:45Hz

[71])

to the trans-2,2,5-trimethyl-3-hexene k Jgauche = 16.14Hz). Combining

the INDO-derived (DJAG) data with the Force Field-based a changes, one

obtains an increase of 2.1Hz due to steric effects when going from

3-methyl-l-butene to trans-2,2;5-trimethy1-3-hexene (in their gauche

conformations). An electronegativity effect of /3.40Hz for the replace-

ment of one olefinic proton by a tert-butyl group would explain the total

substitution effect. This value compares relatively well with the

electronegativity effect amounting to -3.28Hz for the same substitution

in the anti conformers (see Section 5.2-1).

199


The high temperature limit value ((Janti 2J )/3) for

3tJ (= 15.74Hz), is 0.75Hz larger than the average value obtained for

trans-2-butene (3.J = 14.99Hz). A valence angle (steric) effect amounting

to an increase of 1.22Hz for the substitution of two methyl groups by a

(tent-butyl, isopropyl) pair is calculated. This would leave an electro-

negativity effect of -0.47Hz for the same substitution.

C Allylic coupling constant 4caJ (J13)

The temperature dependence for this coupling is small (aroLnd

'0.03Hz/100 K). In Section 5.2-1, the analysis was made with an approxi-

mate 4coJa coupling constant. Alternately (and avoiding any assumptions)

the analysis from the GBM method can be made with the enthalpy separation

as the known parameter. This enthalpy separation is taken equal to the

previously determined averaged value (1100J.mo1-1 or 265cal.mo1-1), the

best fit between experimental (corrected for intrinsic contributions) and

anti. calculated temperature dependence is obtained for 4caj -0.90Hz and

= -1.65Hz. An approximate value of 4caJantv . = -0.72Hz is 4caJgauche

obtained starting with the 4caJanti coupling given .by Rummens et aZ. [71]

for the 4,4-dimethyl-3-tert-butyl-1-pentene. The close similarity of

these two results could be taken to mean that the assumptions in the

estimation technique for 4caJanti = - 0.72Hz were close to correct. These

included the assumption of a zero electronegativity effects of the tert-

b.tyl group (confirming a similar conclusion [70]) and the assumption of

a zero electronegativity effect due to the replacement of two methyl

groups by terr-butyl groups on the Ca atom.

200


A rotation of 126.1° of the CH methirie was calculated by the

Force Field method for the anti+gauche transformation. Using Barfield

et al. 's [79] results (with the VB-SOT treatment corrected with EHMO),

'this transformation gives a difference anti-vauche of -1.34Hz for the

propene molecule. An approximate value for this difference in the case

under study can be calculated by comparing the known geometry [122] of

propene with the Force Pi el d geometries of the trans-2,2,5-trimethyl-3-

hexene and by combining this with the IND° calculated (AJ/A8) data and

with the variation of J with the CCCH dihedral angle (from Barfield et aZ.

[79]). A decrease of -1.26Hz is obtained for the anti+gauche transforma-

tion. The experimentally deduced result is only -0.75Hz (if AH = 1100J.mo1-1

or 2.65cal.mo1-1 is used as the basis) or -1.02Hz (if 4ca j = -0.72Hz is

used as the taasis); the agreement is in any case reasonable.

The high temperature limit for this coupling Asonstant is -1.40Hz.

The corresponding limit is -1.78Hz for the propene molecule. In this

latter molecule, the replacement of the trans olefinic hydrogen by a

tart-butyl group increases the average value by 0.15Hz (see Nicholas

et al. [118]), while the replacement of the methyl group by an isopropyl

group increases it by 0.24Hz (see Rummens et al. [71]). Under a strict

addi tivity rule, the coupling constant, 4caJ, for the trans-2,2,5-tri- t

methyl-3-hexene would be -1.39Hz, close to the experimentally found -1.40Hz.

D Vicinal coupling constant in the HCsp 3-C sp3H fragment

This coupling represents the average of the six couplings which

exist in the isopropyl group. No significant temperature dependence can

201


be discerned (see Table*4.2-3). Thus, either there is not any appreciable

increase in strain, in this group, for the anti+gauche transformation or

there is substantial compensation among the six couplings. Furthermore,

this constant is not considerably affected by the substitution of one

olefinic hydrogen by one isopropyl group (a value of 6.80Hz is found by

Rummens et aZ. [108] for the trans-2,5-dimethyl-3-hexene, while the

constant for the 3-methyl-l-butene is 6.77Hz as given by Rummens et aZ.

[71]) or by one tert-butyl group (the value obtained in this study is

6.74Hz). The same observation can be made when comparing the bond lengths

and bond angles calculated by the Force Field method.

5.2.3 Proton chemical shifts and conformations

Because of the presence of a non-negligible and only approxi-

mately known amount of CDC13 in the sample, the tert-butyl resonance,

rather than the TMS line, was chosen as the reference signal for the

temperature dependence of the various proton chemical shifts. This

technique also eliminates the temperature dependence of the TMS resonance.

Knowing the enthalpy difference between the conformations of minimum

energy (taken from the preceding section), the difference in shifts for

the various protons (between the two conformations of minimum energy) can

be calculated using the GBM method. Instead of performing the GBM

analysis wttk.the enthalpy difference and one of the coupling constants

as the two unknowns, the analysis is done with the two chemical shifts as

the unknowns.

202


A Olefinic protons

(i) Relative positions of 112 and R2 resonances in the anti conformer

Application of the OM method assuming AG° = 531J.mo1-1 (127cal.mo1-1)

gives the H1 resonance on the high

frequency side of the H2 resonance

in the anti conformation (with a difference of 0.45ppm), while it is

the reverse in the gauche conformation: H1 resonance is at a lower

frequency than H2 by 0.08ppm.

The contribution from the magnetic anisotropies of the bonds

has been evaluated using the point dipole approximation. Atomic

magnetic anisotropic susceptibilities were taken from Pople [32] for

the C=C double bond (AxC=C = -7.15 x 10-30 cm3.molecule

-1 per atom),

with each sp2 atom assumed to be the'point dipole location. The a-

contributions from the C-C and cr1-1 single bonds were calculated using

ApSimon et al.'s [28] Ax values (respectively 11.2 x 10-30 and 7.5 x

10-30cm3.molecule-1). The centre of each considered bond was taken as

the point dipole location.

For the anti conformation, the magnetic bond anisotropy effect,

qualitatively accounts for the di-ó? difference. A separation of

0.26ppm-is calculated for this effect with the Hi resonance on the

high frequency side. If one includes the steric 1,4-interaction, the

calculated separation incregps to 0.38ppm. The linear electric field

effect is negligible, while the (E2> term (see Equation 2.3-6) brings

the difference to 1 .38ppm.

Another contribution may come from a difference in electron

density at the olefinic carbon atoms. The charge distribution over

203


the molecule (and particularly on the C=C fragment) is sensitive.to

the electronegativity of the substituents. The inductive effects of

alkyl groups have long been appreciated. The electron donating or

withdrawing ability of such groups has been studied by Huheey [88],

who has shown the dependency of this property upon differential

effects. In the oversimplified case of complete equalization of

charge, the tert-butyl group is calculated to have a higher electron

withdrawing ability on an HC=CH-CH(CH3)2 fragment than has an b

isopropyl. group on an HC=CH-C(CH3)3 fragment (the net positive charge

induced by the tert-butyl grouptis calculated to be 0.01esu). This

tert-butyl group is driving electrons away from the carbon to which it

is attached, and the net effect is a general redistribution of the

electrons in the olefinic fragment, as has been already suggested by

Pople and Beveridge [222] for a propene molecule. The difference in

charge at the olefinic carbon atoms causes a difference in shielding

between their nearest proton neighbours. This difference can be

calculated using the relation suggested by Rummens [29] (Au = -8.1 Aec,

where,Aec is the differenc.. io charge density at the nearest carbon

atom). The electron density being smaller in C1 than in C2 (see

Figure (4.3-1) for notation), H1 resonance is calculated to be 0.08ppm

higher (on the frequency scale) than the H2 resonance. The charge

difference obtained above between C1 and C2 is corroborated by the

difference in frequency resonance obtained by carbon-13 NMR (see

Table 4.3-1). This difference in shielding has been shown by Seidman

and Maciel [65] to be linearly related to the difference in electron

204.


density at the carbon atoms (with (S(C1)-6(C2) = -300 (e(C1)-e(C2));

e(C) is the electron density on C). The experimental difference in

carbon-13 shift varies (with temperature) between 6.4 and 6.6ppm (with

C1 resonance in high frequency position relative to C2 resonance).

This would indicate a smaller electron density on C1 than on C2 (with

a difference round 0.02esu); this results in a frequency resonance

for H1 0.16ppm higher than that for H2.

(ii) Temperature dependence of the olefinic proton shifts

The application of the GBM method, assuming tiG° = 531J.mo1-1 (127ca1.

mol-1) gives increases in frequency resonance for both olefinic

protons, H1 (0.7ppm) and H2 (1.2ppm) for the antivauche transforma-

tion.

The contribution from the magnetic bond anisotropy of the

double bond is calculated to decrease the frequency resonance for H1

(-0.16ppm) and to increase it for H2 (by 0.12ppm). For both protons,

the major a-contributions come from the methine C-H and the C sp 3-Csp 3

single bonds of the isopropyl group. The combined contribution of all

bonds leads to a down frequency shift for Hi (-0.12ppm) for the anti-}

gauche transformation (in contradiction with the experimental results),

while H2 would have its resonance at higher frequency in the gauche

conformation (with a 0.02ppm difference).

The shielding mechanism by a steric perturbation as proposed by

Grant and Cheney (49], relating the shift of the proton to the effect

of a force created by a neighbouring H atom on the C-H bond, does not

205


0

improve the agreement with the experiment: both olefinic protons are

calculated to have their lower resonahce frequency in the gauche con-

formation. Respective decreases of -0.1ppm and -0.02ppm (thus rather

small)"are obtained for H1 and H2 for the anti-gauche-"transformation.

Electric dipole contributions are expected to,play an important

role in determining the magnitude of the proton chemical shifts. To

evaluate'such contributions, use of Equation (2.3-3) was made, where

Ez is the field component along the bond produced at the proton by a

point dipole placed at the centre of any polar bond in the molecule.

The estimation of the linear electric field contributions (first term

of Equation (2.3-3)) was made using Equation (2.3-7) relating this

field to charge separation at the centre of the bond. The change in

charge gives a shielding variation at the atom, which can be calculated

with the Lamb formula (Aa = -17.8AqH). The acting charges were taken

from Seidman and Vlaciel's [55] calculations for trans-2-butene. Only

small differences in shifts were obtained, for both protons, for the

anti-►gauche transformation. For example, the methine C-H dipole

accounts for an upfrequency shift of 0.012ppm for H1 and of less than

O.Olppm for H2, for the anti-►gauche conversion. Similarly, the contri-

bution to the shielding constant at the olefinic protons from the

quadratic term is negligible (second term of Equation (2.3-3)). It

amounts to less than 0.001ppm. Another contribution to the shielding

constant comes from the effect of time-dependent dipole moments in

neighbouring electron groups, giving rise to a non-zero averaged value

'E2> (thus a contribution to E2). This effect is described by

206


0 Equation (2.3-6) for distances larger than 3.5A. Despite its lack of

solid support for short distances, Feeney et aZ. [123] have found a

linear relation between this contribution (where the electron .group is

at the centre of the dipolar bond) and the experimental proton shifts

in a series of alkanes (a B value of -1.02 x 10-18esu is deduced from

the work). Ir the trans-2,2,5-trimethy1-3-hexene, for both olefinic

protons, this effect gives sizeable contributions to the shift for the

anti-vauche transformation. From Equation (2.3-6) it was calculated

that, due to the effect of the isopropyl group, 1 would have a

frequency resonance 0.05ppm higher in the gauche conformation (to be

compared with the experimental 0.-70ppm). The contribution from. the

tert-butyl group was calculated to be 0.17ppm for the anti-gauche

transformation. The <E2> term contributes also to give )12 a higher

frequency resonance in the gauche conformation. For this latter pro-

ton, the calculated shift is 0.87ppm, which has to be compared with

the experimental 1.2ppm. Despite its relative agreement with the

experiment, the <E2> contributions have to be taken with caution;

firstly because Equation (2.3-6) is applied outside its range of vali-

dity, which may give absolute shift of far too large magnitude;

secondly, because small changes in distances correspond to relativel, 0

large variations in shielding constants (for example a change of 0.01A 0 0

in a distance of 1.76A gives a variation of 0.4ppm in the contribution)

which implies the need of a high accuracy in the knowledge of

structural conformations. '

207


Methine proton

The analysis of the temperature dependence of the chemical

shift of the methine proton by the application of the GBM method

(assuming AGo 531J.mol-1 (127cal.mol-1)) indicates a low frequency

resonance in the gauche conformation (with a shielding difference

of.0.2ppm). Such a shielding change is not a general feature of anti

-►gauche transformation involving an isopropyl group: Rummens et al. [71]

have found a high frequency resonance for the same proton in the gauche

conformation (relative to the anti conformation) of 3-methyl-l-butene.

For the trans-2,2,5-trimethyl-3-hexene, the difference in shielding

between the two positions of the methine (anti and gauche) is qualita-

tively explained by the anisotropic effects of the c and it bonds. A

decrease of 0.75ppm in frequency is calculated for the anti+gauche con-

version, when using the point dipole approximation. Of these -0.75ppm,

-0.5ppm is caused by the C=C double bond.

The charge separation induced by the linear electric field

created by a point charge located at the various atoms (making use of

Equation (2.3-7)) does not contribute significantly to the shift change

of the anti+gauche transformation. A difference of less than 0.01ppm was

calC\ulated. The quadratic electric field effects of the time-dependent

dipoL moments in neighbouring electron groups give rise to substantial

variations however; a further decrease of -0.61ppm in frequency for the

anti-gauche conversion comes from this effect. As for the olefinic

protons, this latter contribution is to be taken with great caution, the

smallest distance involved being 2.11A as compared with the validity limit

208


of R > 3.5 A of Equation (2.3-6).


A Olefinic carbons

(i) Chemical shifts and electron density

Table 5.2-3 displays a list of carbon-13 shifts for various alkyl

trans substitutions on a tert-butyl ethylene. The largest variation

obtained occurs amongst ethylenic carbon atoms. The C1 carbon

(olefinic carbon that the tert-butyl is attached to) has always its

resonance line on the high frequency side of C2 (see Figure (4.3-1)

for notation) resonance. Both shifts reflect the distribution of

electrons surrounding the observed nucleus; Seidman and Maciel [65]

have obtained a linear relation between the difference in computed carbon-

13 chemical shifts for two olefinic carbons (doubly-bonded together)

and the corresponding difference in the computed total valence-shell

electron densities for those atoms. Applying this result to the

trans-2,45-trimethy1-3-hexene would indicate an electropositive

charge on C1 as compared to C2. The induced charge calculated using

Huheey's method [88] is in concordance with the above property. A

tert-butyl group is calculated to have a larger electron withdrawing

ability on a CHX=CH fragment (X standing for a hydrogen atom, a

methyl, ethyl or isopropyl group) than either'a hydrogen atom or a

methyl, ethyl, isopropyl group would have on a (CH3)3-CH=CH fragment.

Using Huheey's method, the induced charge difference between C1 and C2

209


TABLE 5.2-3 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm upfrequency from TMS.

C1 C2 C3 C4 C5 C6 jr,ef.

1 135.6 135.6 (31.7) (29.6) 31.7 29.6 • a

2 138.92 132.50 31.50 23.06 30.07 32.75 b

3 140.90 126.77 26.14 14.38 30.34 33.02

4 142.0 118., 16.97 29.1 32.0 a

5 148.6 108.2 28.4 32.8 a

aData taken from reference [118]; neat samples were used. bbata taken from this thesis. °Data taken from reference [119]; neat samples were used.

C c cs 1; I

1 C— C—C=C— C — c 2 C= C — C— C— C —C I

5 6 1 2 3 4

C C C 5

C C I I

3 C— C— C=C —C— C 4 C— C- C=C— C I

CI

C

5 C—C—C=C--- C

C

210


is calculated to gradually decrease from 7.4 x 10-2 to 1.0 x 10-2esu

when going from a hydrogen atom to an isopropyl group; this decrease

correlates approximately linearly with the decrease in shift difference

between the two olefinic carbons for the molecules given in Table

5.2-3. A shift of around 550ppm/e is obtained, twice the value gi'ven

by Seidman and Maciel [65] and three times that suggested by Lauterbur

[124]. This factor difference can be caused by the approximate nature

of the electron density calculated using Huheey's technique. This can

be seen from data on propene, for which CNDO calculation by Pople and

Gordon [125] gives a difference in electron density between the two

olefinic carbons of 7.4 x 10-2esu instead of 3.8 x 10-2esu as calcu-

lated using Huheey's method in the oversimplified assumption of

complete equalization of charge.

(ii) Temperature dependence

As can be seen from their temperature dependences (Table 4.3-1), the

resonance frequencies of both olefinic carbons increase virtually

linearly for the anti+gauche conversion. For both carbons, the steric

1,4-interaction described by Grant and Cheney [49] cannot explain the

trend. Using chemical shifts relative to TMS, the GBM method (under

the assumption AGo = 531J.mol-1 (or 127cal.mol-1)) gives increases of

18.lppm and of 21.4ppm for C1 and C2 respectively for the anti-*gauche

transformation. On the other hand, the calculated steric 1,4-inter-

action contributes to increases of only 2.07ppm (for C1) and 0.30ppm

(for C2) for the same anti-*gauche transformation. The linear field

211


.,.

effect is not an important factoi' either; variations of less than

0.01ppm are calculated assuming a 200ppm/e variation. As in the case

of the proton shifts, the carbon-13 shifts are dependent upon the

square of the field created by time-dependent dipole moments in

neighbouring groups. Following experimental findings by Rummens and

Mourits [226] for alkanes, the constant B for carbon-13 of Equation

(2.3-3) varies between -17 x 10-18 and-88 x 10-18esu, depending on the

number of alkyl substituents. For the olefinic carbons in question an

estimate of B = -40 x 10-18esu will be used. This Van der Waals shift

effect accounts to an increase of 3.7ppm for C2 due to the anti-gauche

rotation of the isopropyl group. The same structural change gives an

increase of 2.6ppm for Cl. Addition of all these effects gives the

right direction of variation of the shifts of both carbons, but the

calculated values are too small. .

B Methine carbon

) The lack of sensitivity (which could be caused by two antagonis-

tic effects) of the shielding of this carbon upon 1,4-substitution can be

seen in Table 5.2-4, where a list of carbon-13 shifts for substituted

isopropyl ethylenes is given. All the C3 shifts are within 0.2ppm except i

when there is no substitution (molecule 5).

The shift for this carbon in trans-2,2,5-trimethy1-3-hexene

does not display any temperature dependence (see Table 4.3-1). The

application of Grant and Cheney's technique is not possible because of

the absence of any relevant steric 1,4-interaction between hydrogen

212


TABLE 5.2-4 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is an isopropyl group, in ppm from TMS.

C1 C2 C3 C4 C5 C6 ref.

1 138.92 132.5 31.49 23.06 30.19 32.75 a

2 134.91 134.91 31.64 23.24 (23.24) (31.64) b

3 129.16 136.96 31.41 22.87 14.14 25.89 c

4 121.61 139.04 31.49 21.70 ,17.59 c

5 111.41 145.94 32.70 22.30 d

aData taken from this thesis. bData taken from L. F. Johnson and W. C. Jankowski, 13C NMR spectra, spectrum n315, Wiley and Sons Inc. (1972); CDC13 was used as solvent.

cData taken from reference [119]; the samples were neat. K dData taken from J. W. de Haan, L. J. M. van de Ven, A. R. N. Wilson, A. E. van der Hout-Lodder, C. Altona and D. H. Faber, Org. Magn. Res. 8, 477 (1976).

C4

C .5 1 • 1 1

1 C5 C -6 C= C-2 C3 C4 2 C — C— C=C— C —C

1

C5

4 C-C=C- 0T-C 3 C— C— C=C — C3— C

C

5 C=C— C3 C

213


atoms; however, other steric interaction: (for example 1,5-interactions)

could be not negligible and their change for an anti-gauche conversion

could give shift differences. Whereas linear electric field effects

turned out to be not effective for the conversion, the Vander Weals

shift (<E2> factor) was calculated to be substantially different between

the two conformations. A shift of -1.0ppm (thus toward lower frequencies)

was evaluated using Equation (2.3-7) for the anti+gauche transformation.

If this difference is real (the smallest distance affecting <E2> is 0

2.366A), another unknown cn-ltribution has to account for the balance of

an upfrequency shift of 1.0ppm for the conversion. The intrinsic varier

tion of the TMS line reference with temperature, as indicated by

Sc)neider et al. [127], should not be the cause of this shift. At

temperature below 300K, the shift of the TMS resonance is toward higher

frequency (when increasing the temperature) at a rate of about 0.012ppm/K,

meaning that a line in fixed position relative to the TMS reference

would actually be going toward high frequency.

5.2.5 Conclusion

The approach taken.for this molecule in the coupling constant

study seems most valuable. The consistency found for the Gibbs energy

difference results gives some credence to the technique used; it indicates

also the importance of the entropy variation. It is found that the

Force-Field based AG° is much too high (by 4.07KJ.mo1-1 or 0.973Kcal.mol-1 );

this difference is due to an overestimation of the steric energy

(5.15KJ.mo1-1 or 1.23Kcal.mo1-1). This overestimation was noticed first

214


by Rummens et al. [71] for the 3-methyl-l-butene, tey suggested that the

cause of the discrepancy was the overestimation of the non-bonded strain

energy in the 1.8-2.2A region. For the trans-2,2,5-trimethyl-3-hexene,

the difference between calculated and experimentally deduced values is

caused by the angle bending energy (2.64Klmol-1 or 0.63Kcal.mo1-1) as

well as by the non-bonded energy (2.68KJ.mo1-1 or 0.64Kcal.mo1-1).

The experimental value AG° = 531±89J.mo1-1 (127cal.mo1-1) 74=-

happens to be the same number as found for 3-methyl-l-butene (5311:60 Jmol-1

or 127cal.mol-1). In the latter case AS was, assumed zero, meaning that

the result is really a FI° value rather a AG° datun; this distinction is

unimportant, mostly because 3-methyl-l-butene is a small molecule. Of

course it is natural to expect that the AG° data for the two molecules

should be equal: there cannot be any direct steric hindrance by the

tert-butyl group and the electronic effeCt of the tert-butyl group

through the C=C double bond causes only minor electronic changes in the

isopropyl group. That virtually equal AG° values are indeed found forms

a strong support for the methodology employed.

The geometrical features, obtained from the Force Field calcula-

tion, combined with the INDO-derived (AJ/60) data have a relative success

in explaining the variations of each coupling constant for the anti-gauche

conversion. However, Rummens et a/. [71] have noticed that the systematic

errors in the (1J/A6) data and in the valence angles (as calculated ty

the Force Field calculation) have a tendency to cahcel out.

The chemical shift study (for proton and carbon-13) was not as

successful as the coupling constant study. The various effects suggested

215


to be involved in the conversion (anti to gauche) failed to explain, in

most cases, the variations (particularly their magnitude) of the chemical

shifts. The absence of an appropriate referencing (for proton as well as

carbon-13 spectra) should be one of the major causes of the failure.

Analysis of the results shows that, of all calculated effects, only the

intramolecular Van der Waals effect gives close to the correct magnitude

and always the correct sign of the various trends, thoth for proton and i

carbon-13 data. Another important contribution/for the proton shifts

involves the magnetic anisotropy of the bonds, while for carbon-13 shifts

the steric 1,4-interaction appears to play a non-negligible role for the

anti+gauche transformation.

5.3 cis-2,2,5-TRIMETHYL-3-HEXENE

5.3.1 Introduction ,

In view of the investigations made with the Force Field method

and of the resulting criticisms in the case of the trans isomer, three

possible transformations were foreseen for the cis isomer in the tempera-

ture range of the experiment. These are shown in Figure (5.3-1). The

Force Field method gives transformation(Das the most likely to occur:

starting from the (as) state (rotamer I) a 60° rotation of the tert-butyl

.group leads to the (aa) state (rotamer II), while the major features of

the isopropyl group remain unchanged. In the study of the trans isomer

(see preceding section) the energy difference calculated using the Force

Field procedure was shown to be overestimated by 4.2KJ.mo1-1 (1Kcal.mo1-1)

216


aJ

It ad

/ \ / aJ

f

"I

In

FIGURE 5.3-1 Schematic representation of the transformations considered in the discussion of the NMR results for cis-2,2,5-trimethy1-3-hexene

217


for an antivauche conversion. Transformation ®for the cis isomer is

calculated to involve a steric energy separation of 2.7KJ.mol-1

(0.65Kcal.mol-1), an amount which is smaller than the above-mentioned

overestimation, thus making transformation(!)(inverse of transformation

®) a possibility. A 160° rotation of the isopropyl group around the

C sp 2-C sp3 single bond defines transformation ©(it involves also profound

changes in the tert-butyl group). Thistis the closest to the anti-gauche

conversion foreseen by Van der Heijden in his thesis [112]. For trans-

formation®, it is assumed that the (as) and (aa) states are true minima

with negligible energy separation. It is also assumed that the energy

change for the conversion is relatively high (the steric energy difference

calculated by using the Force Field method amounts to 28.2KJ.mo1-1

(6.74Kcal.mol-1) when going from the conformation I to conformation III).

5.3.2 Analysis of the temperature dependence of several coupling

constants

If the temperature dependence of the coupling constants is a

reflection of transformation(Dor®, involving states of equal

degeneracy, Equation (5.2,44) used for the anti4gauche conversion has to'

be replaced by the following expression:

<J>T = p J1 + (1-p)J2

with 1-p -2— = exp RT

218

(5.3-1)


where p is the population of the more stable of the two conformations and

AG is the Gibbs energy difference between them; R and T have their usual

meaning.

'To make transformation manageable, one has to assume that the

energy difference between the (as) and (aa) states is exactly zero, and

that the entropy difference is also zero; then relation (5.3-1) can also

be used, p being the population of the (as) and (aa) pair of states.

Each 'of the coupling constants would be the average coupling of both

conformations.

For this isomer, two coupling constants (3vJ and 3cJ) show an

appreciable temperature dependence. Figure (5.3-2) indicates also a non-

negligible curvature in this dependence, which allows one to directly

extract three parameters. The direct application of the GBM method

should, in this case, give reliable answers, without having to estimate

one of the unknowns through another procedure. As for the trans isomer,

an intrinsic temperature dependence, deduced from the results from

propene given by Rummens et al. [71], has been removed. Given in Table

5.3-1 are the results obtained with AS = 0 as well as with AS = f(T)

(deduced from the data of Table 3.5-4 in a similar fashion as that used

for the trans isomer and described in the preceding section). This table

shows the results for each transformation. First of all these results

indicate the major importance of the entropy factor AS, both for the

Gibbs energy separation and for the coupling constants for each conforma-

tion. If one accepts that the Force Field employed results in reasonably

accurate vibrational frequencies, then, as the results of Table 5.3-1 show,

219


f

10.7

1$

10.5

10.5

10.4

e

220 270 320

T[K]

FIGURE 5.3-2 Temperature dependence of tie vici,nal coupling constant (J23, see Figure (4.2-1) fo notation) for the cia-2,2,5-trirnethy1-3-hexene (values .0 corrected for temperature dependence of the intrinsic ntribution). (---) represents the best-fit s obtained from the GBM method.

220 POI


TABLE 5.3-1 Sets of coupling constants and energy separations between rotamers obtained by the GBM metnod for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-tri-methyl-3-hexenef

transformation C) transformation() transformation @

3vJ

3cJ

11H

TG0

AS

Jl =15.047 Jas=11.270

J2 = 5.266 Jaa = 8.502

AN = 0.418±0.38 AH = 3.347±0.25

AG°. 0.418±0.38 AG°= 2.699±0.25

J1 =11.303

J2 =13.204

AH = 1.67±0.33

( AG°= 1.6710.33

0.902±0.36 (0.216)

0.902±0.36 (0.216)

0.0

Jas=11.339

J aa =13.286

AH = 2.678±0.5

AG°. 2.03±0.5

3.096±0.33 (0.74)

2.448±0.33 (0.585)

Jaa=11.362

Jas= 9.388

AH = 0.377±0.35

1.025±0.35

0.11 10-4 T2

-0.001 1+2.81

J aa=11.550

Jas=12.521

AH = 0.418±C.I

AG°= 1.067±0.4

0.39310.37 (0.094)

1.04210.37 (0.249)

-0.11 10-4 T2

+0.011 T-2.81

J/ =11.757

J2 = 4.803

AH = 1.3810.29

AG°= 3.924±0.29

JI =10.741

J2 =16.765

AH = 0.92±0.67

iG°= 3.464±0.67

1.192±0.42 10.285)

3.73610.42 (0.893)

0.25 10-5 T2

-0.0027 T-1.445

The coupling constants are in Hz, AH and AG° in KJ.mol-1 (Kcal.mol-1); AS in cal.mo1-1.0 as calculated by the relations listed.

221


it is not allowed to assume that AS is not a function of temperature, let

alone to assume that its value would be equal to zero. Thus the results

from the AS = 0 assumption will henceforth be eliminated from further

discussion. As before, it will be assumed that AH is temperature

independent. All three possibilities (0,(1q),(D) give results that are

internally consistent within the estimated limits_ of error.

Using statistical weights proportional to the magnitude of the

variation of each coupling constant, average values for each transforma-

tion have been calculated as also shown in Table 5.3-1. None of the

other coupling constants (in particular 4 1J) has large enough variations

in the temperature domain investigated to be useful for the determination

of the energy separation between the rotamers. In view of the magnitude

of the Gibbs energy separation deduced from the experiment for transfor-

mation(70(3.74KJ.mol (0.89Kcal.mol-1 )) as compared to the calculated

(by Force Field) value (33.14KJ.mo1-1 (7.93Kcal.mo1-1)), this transforma-

tion will not be given a prime consideratiOn in the following discussions.

5.3.3 Coupling constants and conformations

A Vicinal coupling constant 3vJ (J23)

An alternate estimate for the values of this coupling constant,

for both rotamers, can be given following the procedure used for the

trans isomer (see Section 5.2.1). The value obtained by ,othner-By et al.

[107] for the 4,4-dimethyl-3-tert-butyl-l-pentene is t::,%en as the

starting quantity. A combination of the geometrical features of each

conformation with the (AJ/Ae) data found by Rummens et al. [71] allows

222


.,for the steric effect correction. A value of 11.88Hz is thus obtained

for the (as) state (conformation I)? while the same coupling constant for

the (aa) state (conformation II) is similarly calculated to be 0.75Hz

higher, TninsformationOgives the qualitative trend; however, the

experimentally deduced difference between the two conformations• for this

coupling constant exceeds the calculated difference value (1.97Hz instead

of 0.75Hz). For transformations@and®, the calculated values lead to

an overestimation in all cases: in transformation for example, the

experimentally deduced coupling constant for the (-as) conformation is

9.388Hz while the calculation through geometrical structure gives 11.88Hz.

The discussion on the reliability of the geometrical features

of cis isomers given in Chapter III led to question the accuracy of the

valence angles obt.ined through the Fqrce Field method. Following the

• discussion in Section 3.2.1, an estimate of the errors for the cis-2,2,5-

trimethyl-3-hexene in the (aa) state was given. Correction for these

errors leads to a decrease of 0.65Hz for the 3vJaa coupling constant

(thus equal to 11.90Hz, closer to the experimentally deduced 11.36Hz).

At the present time, the inaccuracy of the valence angles for the (as)

state cannot be estimated, because of a lack of experimentally known

structures of olefinic molecules displaying the studied structure. A

correction of more than 2.Hz would have to come from the inaccuracy of

the valence angles to fit the experimental finding (for a® transforma-

tion), meaning an overestimation of the C=C-C valence angles of about 10°

which appears unlikely. A

According to the values deduced experimentally for transformation

223


(D, the vicinal coupling constant 3vJ for conformation III is 4.803Hz.

The use of the propene value calculated by Maciel et al. [73] for a 20°

HCCH dihedral angle (this value is 7.5Hz) and its correction for valence

angle differences between propene and the cis-2,2,5-trimethyl-3-hexene

(using the (AJ/iO) calculated by Rummens et al. [72] one calculates

AJ = 0.7Hz) leads to an estimate of 8.2Hz.

On the basis of the results for 3vJ, it appears that transfonma-

tionOgives the wrong relative magnitude'for 3vJaa and 3vJas. Also, as

for the ©transformation, it appears that one of the coupling (this time

3vJaa) as deduced from the experiment is much too low. Such low values

for an anti 3vJ can only be understood if the HCCH dihedral angle is

considerably different from 180°. Such a possibility exists if a slight

modification of conformation III could be considered. A dihedral angle

of 50°, instead of the calculated 20° of conformation III, would give an

adequate fit for.ihe data Of 3vJ (3vJaa,

= 11.757Hz, 3vJIII = 4' 803Hz). '

B Olefinic coupling constant 3cJ (j12)

This coupling is experimentally found to bt larger for the

second minimum (which is the (aa) state if one considers transformation®

and the (as) state if one considers transformation (E)). The steric effect

through valence angle changes and (AJ/Ae) data gives the largest value

for the coupling belonging to conformation (aa), which would favour

transformationOas the correct interpretation. While the GBM method

gives a difference of 1.9Hz for the two couplings of the@transformation,

the calculated difference due to geometrical structure is 2.55Hz, which

224


ti

is a reasonable agreement.

As for the trans isomer, this coupling is sensitive to

electronegativity effects. Replacement of an hydrogen atom in the

ethylene molecule by-a tert-butyl group gives a decrease of 0.91Hz (the

data are obtained from Lynden-Bell and Sheppard [120] for the ethylene

molecule, and from Nicholas et al. [118] for the 3,3-dimethyl-l-butene).

After correcting these values for steric contributions, an electronegati-

vity effect of -3.00Hz is calculated. Using the values obtained by

Rummens et aZ. [72], the same procedure leads to an electronegativity

sect of -2.75Hz whey replacing an hydrogen atom by an isopropyl group

(these numbers could be compared with contributioiis of -3.28 and -3.24Hz

respectively calculated for the electronegativity effect on 3tJ, as

discussed in Section 5.2.2). Combining these effects with the steric

contribution present in the cis-2,2,5-trimethyl-3-hexene, a coupling

constant of 10.04Hz is predicted for the (as)`state (starting with the

propene molecule, instead of the ethylene molecule a value of 10.28Hz is

calculated), while 12.59Hz is the value obtained for the (aa) state. The

suggested errors given in Section 3.2.2 for the valence angles of the (aa)

state would decrease the latter value to 11.88Hz, 1.52Hz lower than the

value deduced through the use of the GBM method assuming an transforma-

tion; for a(Dtransformation this value of 11.88Hz is closer to the GBM

result (difference of 0.33Hz) and well within the uncertainty of the

calculation. But the (as) state would still have a lower 3ctl value. An

arbitrary decrease of 10° in-the C=C-C angle as would be required to fit

3vJ (see preceding paragraph) would worsen the situation ((AJ/66) data

225


being positive in this case, an overestimation of e leads to an over-

estimation of J). However, one must remember at the electronegativity

effects have been evaluated without taking account of possible errors in

valence angle calculations.

It is interesting to note that a transformation of the type

(as) 4- (aa) has been obtained through the Force Field method for the cis-

4,4-dimethy)-2-pentene (whee the isopropyl group is replaced by a methyl

group) by Ermer and Lifson [3]. For this molecule,.a temperature

dependence study of the NMR spectra (see Table 4.2-5) shows that 3cJ

(corrected or not for intrinsic temperature dependence) is virtually

constant between 250K and 350K'(the variation is less than 10-2Hz). The

standard Gibbs energy separation, resulting from the Force Field calcu-

lation, is 2.9KJ.mo1-1 (0.7Kcal.mo1-1) with a steric contribution -of

1.76KJ.mol-1 (0.42Kcal.mol-1). The expected difference (calculated'

through the geometrical structure given by Ermer and Lifson [3] and using

the (AJ/A8) data) for 3cJ between the two rotamers is 2.21Hz, a value

which is close to the 2.55Hz calculated for the corresponding difference

for either the(Dor(Dtransformation of cis-2,2,5-trimethyl-3-hexene.

The overall experimental temperature independence combined with the

predicted sizeable difference in the two 3cJ couplings, means that

(i) either the calculated AO values are wildly exaggerated

(ii) or AG° for tert-butyl group transformation is very close to zero

(smaller than 0.1KJ.mo1-1 (0.03Kcal.mo1-1))

(iii) or AG° for tert-butyl group transformation is fairly large

(larger than 6.3KJ.mo1-1 (1.5Kcal.mo1-1)).

226

14


In view of the AO data shown in Table 3.2 c, (i)'is not likely

to be correct.

If one assumes transformation QA to be the correct one for the cis-2,2,5-trimethyl-3-hexene, the calculated (using the Force Field

procedure) standard GibtA energy separation is overestimated by 2.8KJ.mo1-1

(0.68Kcal.mo1-1) as can be calculated from Tables 3.5-4 and 5.3-1. This

"correction" is likely to be a good approximation for the cis-4,4-dimethyl-

2-pentene because of the identical cisoid steric interaction in the two

molecules compared. The Force Field derived AG° for cis-4,4-dimethyl-2-

pentene is equal to 2.93KJ.mo1-1 (0.700Kcal.mo1-1). After "correction",

in the case of the latter molecule for the overestimation, the Gibbs

energy separation drops to 0.65KJ.mo1-1 (0.015Kcal.mo1-1) making (ii) the

most likely explanation for the temperature independence of the k J

coupling constant.

If transformation(Dis assumed to be the correct one, the

difference between calculated (with the Force Field method) and experi-

mentally deduced (using the GBM method) Gibbs energy is 6.28KJ.mo1-1

(1.5Kcal.mol-1). Correction for this difference leads to'a Gibbs energy

separation between the two rotamers of the cis-4,4-dimethyl-2-pentene

amounting to 3.35KJ.mol-1 (0.8Kcal.mol-1 ); this value is smaller than the

suggested value (6.28KJ.mol .) for the (iii) condition to apply and is

larger than the required difference for condition (ii) to be true.

Assuming a coupling constant difference of 2.21Hz between the rotamers,

an increase of 0.18Hz between 240K and 350K should be observed for a

Gibbs energy separation of 3.35KJ.mol (0.8Kcal.mol-1 ). This would

227


indicate that transformationOis not the correct transformation.

It may be noted that the experimental 3°J couplings at 298K are

almost the same for both molecules. While a value of 11.95Hz is found

for the cis-40-dimethy1-2-pentene, 11.94Hz is the coupling reported for

the cis-2,2,5-trimethyl-3-hexene. If AG° = 0 is assumed for the former,

and if one takes 2.21Hz as the difference in 3°J between the two rotamers

of the cis-4,4-dimethyl-2-pentene, values of 3cjas = 10.84Hz and

13.05Hz are obtained (the high temperature limit for the coupling 3cjaa =

being equal to (jaa Jas(2)) for the two rotamers. Neglecting the

differential electronegativity effect between methyl and isopropyl groups

(as suggested by Rummens and Kaslander [70]), values of 10.99Hz and

13.29Hz are then expected for the 3°J coupling constants in the (as) and

(aa) forms of the cis-2,2,5-trimethyl-3-hexene after correction for

steric effect contributions.

As was shown in the beginning of this section, transformation®

gives the wrong relative magnitude for 3cJas and 3cJaa in the case of

cis-2,2,5-trimethy1-3-hexene. It was also shown that transformation®,

if true, leads to a AG° value for cis-4,4-dimethy1-2-pentene which is

irreconcilable with the observed temperature independence. of.3cJ of the

latter molecule. On the other hand, transformation (A the correct

relative magnitude for 3cJas

and 3cJaa (although both are numerically

smaller than those derived from experiment), while in addition transfor-

mation(Dleads to a prediction o G° = 0 for cis-4,4-dimethy1-2-pentene,

which explains the temperat independence for 3cJ of the latter

molecule.

228


As for transformationG, transformation(Dgives the right

relative magnitude for 3aJas,aa

and 3cJIII' The predicted value for

3cJIII obtained through steric and electronegativity contributions from

ethylene is too small; a value of 13.51Hz is calculated instead of the

experimentally deduced value of 16.765Hz. The predicted (11.32Hz) and

the experimentally deduced (10.74Hz) values for 3cJas,aa are in fair

agreement.

C Allylic coupling constant 4taJ (J13)

The temperature dependence for this coupling is small (0.1Hz/

100K) with a scatter of about 0.05Hz/100K; as is to be expected, the

extraction of three parameters from this variation, in this case, does

not lead to any reasonable values. Taking for each transformation the

average Gibbs energy difference obtained from the 3cJ and 3vJ temperature

dependence, one deduces from the experimental data (corrected for

intrinsic temperature dependence), using the GBM method, the values

displayed in Table 5.3-2.

For the (as) form, the difference in steric contribution with

the 3-methyl-l-butene (where 4taJ (anti form) = 0.00Hz, see Rummens et al.

[71]) leads to an expected value of 4taJ = -0.42Hz. Similarly, CIS

4tczt)aa = -0.56Hz was calculated. These estimated 4taJ values are in

total variance however, with the GBM-deduced results as given in Table

5.3-2; the magnitude of the (AJ/M) data for this coupling constant (of

the order of 10-2Hz per degree) excludes the errors in valence angles as

the unique explanation; inaccuracy of the experimental data (the scatter

229


TABLE 5.3-2 Sets of 4taJ coupling constants as obtained by the GBM

method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethyl-3-hexene, witenergy separations as taken from the 3v3 and 3cJ resultsT

DH

transformation() transformation® transformation ©

x 3.096 0.393 1.192

(0.74) (0.094) (0.285)

4taj Jas

= -0.231 J.aa = -0.243 Jas,as = -0.46

J aa

= -1.927 Jas = -1.364 JIII = -1.17

#A11 couplings are in Hz, AN are in KJ.mol-1 (Kcal.mol-1 ). AS in cal.mo1-1.K-1 as calculated by the relations given in Table 5.3-1.

230


is as large as one half of the variation) is the likely explanation.

Using the coupling dependence on dihedral angles as calculated

by Barfield et a7. [79] for propene, and after correction for steric

contribution differences, a positive coupling constant is predicted for

conformation III (the approximate value is 0.2Hz). This result excludes

transformation ©from the possibilities (the variation of 4taJ with

temperature is small, but the tendency is, nevertheless, toward a more

negative value for the second minimum). However, if a slight variation

of conformation III could be considered, to the extent of having a CCCH

dihedral angle of 130° rathqf than 160°, an exact fit for the data of

4taJ would be possible (4 tajQS, aa

= -0,5Hz and 4taJIII = -1.2Hz).


A Analysis of the temperature dependence of proton chemical

shifts

The values given in Table 4.2-3 are referenced to the TMS line.

A study of the temperature dependence of the resonance frequencies of the

various protons should be made preferably without the unwanted intrinsic

temperature variation of the TMS line. Jn the discussion of the coupling

constants (see 5.3.3),At was suggested that either the cia-4,4-dimethyl-,,

2-pentene is subject to an equal-population equilibrium of theOtype

(meaning AG° smaller than 100J.mo1-1 or 25cal.mo1-1) in the temperature

range of the investigation for the cis-2,2,5-trimethyl-3-hexene or, in

the same range studied, only one conformation of the cia-4,4,dimethy1-2-

pentene is present (meaning that AG° is larger than 6.27KJ.mo1-1

231


(1.5Kcal.mol-1)). In either case the proton chemical shift variation of

the cis-4,4-dimethy1-2-pentene should not be caused by population changes,

but rather by the differential solvent effets. The temperature depen-

dence for the olefinic protons are shown in Figure (5.3-3) and Figure

(5.3-4). Due to the similarity of the surroundings for H1 and H2 in cis-

2,2,5-trimethy1-3.7hexene and in cis-4,4-dimethyl-2-pentene, the tempera-

ture dependence resulting from differential solvent effects should be

almost the same. A correction for these unwanted contributions can thus

be made by simple subtraction as shown in Figures (5.3-3) and (5.3-4)

(where do is the chemical shift of cis-4,4-dimethy1-2-pentene assumed to,

be free of unwanted contributions). Despite the fact that the methine

proton in the cis-2,2,5-trimethy1-3-hexene has no direct equivalent in

the cis-4,4-dimethyl-2-pentene, a similar correction was made by subtrac-

ting the temperature dependence of the methyl group of the latter

molecule (see Figure (5.3-5)).

For the three suggested transformations (G),(Dand(D) the

direct GBM method was applied. The results are shown in Table 5.3-3 for

the uncorrected shifts and in Table 5.3-4 for the results based on the

corrected shifts. The inconsistency of the AG° values for each assumed

transformation, as well as their poor correspondence with the AGo yalues

obtained from.the coupling constants, indicates that the corrections

applied were inadequate. Furthermore, due to these corrections, the

individual chemical shifts found are not the true ones; only the

differeice aa -(5as for(D, 6as-(5as for(D, III-(5as,aa for (D) for each

proton considerea has a quantitrtive meaning. Assuming that the mean

232


5.30 -

5.29

.0"

5.18

5.16 5.16

'C

220 270

T [pq ________. 320

FIGURE 5.3-3 Olefinic proton (H1) chemical shift dependence on tempera-ture for: A - cis-4,4-dimethy1-2-pentene referenced to TMS B - cis-2,2,5-trimethyl-3-hexene referenced to TMS C - cis-2,2,5-trimethy1-3-hexene referenced to TMS and

corrected for temperature dependence of intrinsic contribution (using curve A).

233


5.226

5.224

4.921

I 4.919

0

4.917 4

220 i „.07' 270

[K]

320

FIGURE 5.3-4 Olefinic proton (H2) chemical shift dependence'on tempera-ture for: A -as-4,4-dimethy1-2-pentene referenced to TMS B - cis-2,2,5-trimethy1-3-hexene referenced to IIMS C cis-2,2,5-trimethyl-3-hexene referenced to TMS and

corrected for the temperature dependence of intrinsic contribution (using curve A).

($) represents values obtained using correction extra-polated from the dash part of curve A.

234


2.843

2.835

2.825

co

1.690

• a A

1.685 22C 270 320

[K]

FIGURE 5.3-5 Proton chemical shift dependence on temperate for: A - methyl proton of cis-4,4-dimethy1-2-pentene referenced

to TMS B methine proton of cis-2,12,5-trimethyl-3-hexene

referenced td TMS C methine protbn of cis-22,5-trimethy1-3-hexene

referenced to TMS, corr cted for the temperatLre dependence of the intrinsic contribution (using curve A).

235


TABLE 5.3-3 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3-hexene. The GBM method i$$ applied to uncorrected chemical shifts in ppm from TMSf

transformation() transformation® transformation

6as=5.274 6aa=5.2475 , 6aa,as

=5.664

H1

6 aa =4.911

AH =2.84± .50(0.63)

bas =5.052

AH =0.33±0.50(0.08)'

'III tH

.-3.3"

=0.67±0.50(0.16)

AG°=2.20±0.50(0.53) AG°=0.98±0.50(0.23) AG° =3.21±0.50(0.77)

6as=2.745 6 =2.780 as . 6 aa,as

=2.641

6 =3.033 aa H

6as=2.928 6III =3.599

methineAN =2.55±0.30(0.61) Ali =0.54±0.30(0.13) AH =0.84±0.30(0.20)

AG°=1.90±0.30(0.45) AG°=1.19±0.30(0.28) AG° =3.38±0.30(0.81)

4Energies are in KJ.mol-1 (Kcal.mol-1 ); AS in cal .mol-1.K-1 as calculated using the relations given in Table 5.3-1.

236


TABLE 5.3-4 Sets of proton chemical shifts and energy separation between rotamers as obtained from the GBM method applied to shifts corrected for unwanted contributions for the three considered transformations (see Figure (5.3-1)) of cites-2,2,5-trimethy1-3- hexeneT

transformation® transformation® transformation°

H1

H2

H3 (methine)

AH =0:544±0.25(0.13) AH =-0.544±0.25(-0.13) AH = 0.460±0.30(0.11)

AG°=-0.1040.25(-0.045) AG°= 0.104±0.25(0.025) AG° = 3.00± 0.30(0.72)

das= 5.0359 6 aa= 5.2939 as,aa= 4.1512

aa= 5.2939 bas= 5.0359 ( III = 8.5845

AN = 1.423±0.50(0.34) AH =-1.423±0.50(-0.34) AH =15.06±0.60(3.60)

AG°= 0.774±0.50(0.185) AG°=-0.774±0.50(-0.78) AG° =17.6±0.60(4.21)

(5as= 5.1425 d

aa= 4.6127 aa,as= 4.9170

6 = 4.6127 aa

as= 5.1425 ISIII

= 6.8027

AH = 1.213±0.65(0.29) AH = 3.93±0.65(0.94) AH = 0.251±0.71(0.06)

AG°= 0.565±0.65(0.135) AG°- 4.58±0.65(1.09) iG° = 2.7919.71(0.67)

6 as = 3.3036 8 aa= 2.8165 daa,as= 3.4589

6aa= 2.2-527 Bas= 2'9741. 6111 = 0.9193

tAH and AG° are in KJ.mo1-1 (Kcal.mo1-1); chemical shifts in ppm from TMS. AS in cal.mo1-1.K is taken from Table 5.3-1.

Reproduced w



ithout permission.

enthalpy obtained by the application of the GBM method on the coupling 0

constants is accurate, the corresponding chemical shifts together with

their differences can be found; these results are given in Table 5.3-5.

These latter results seem to be the only rationale basis for further

discussion of the chemical shifts and their temperature dependence as

will be detailed below.

c B Olefinic proton H1

The H1 resonance is found at higher frequency in the

conforma-

tion of lowest energy. Differences in short range anisotropic,effect

were calculated by application of Equation (2.3-1) using the same Ax

parameters as for the trans isomer (see Section 5.2-3) and result in a

0.03ppm frequency decrease for transformation0(the reverse is true for

transformation(D). The differential contribution from the double bond

(0.11ppm) is countered by that from the three' C-C single bonds of the

tert-butyl group (-0.07ppm). If one introduces the quadratic effect from

the time-dependent electric dipoles, a further increase in frequency of

1.42ppm is obtained for transformation®, which disagrees both, in sign

and magnitude, with the experimental difference of -0.24ppm. For trans-

formation®, the direction agrees (of course), but the magnitude of the

discrepancy is far too large (-0.14ppm vs -1.42ppm). However, as for the

trans isomer, Equation (2.3-6) is applied outside the range of its tested

validity. The invariance of the isopropyl group conformation during the

transformation0(or(D) implies a negligible contribution difference for

that transformatiOn caused by the stevic 1,4-interaction.

238


x m -0 8 0. c C) m 0.

74: 7'

"0 m TABLE 5.3-5 Sets of proton chemical shifts and their difference as obtained by thq, GBM method g applied to shifts corrected for unwanted contributions; the enthalpy separations for4a' the three considered transformations (see Figure 5.3-1)) are as given in Table 5.3-1T (4. o m 0

m C) 0

. c0

o

transformation® transformation° transformation°

AH 3.096 (0.74)

oas= 5.2320

0.393 (0.094)

&aa= 5.2246

1.234 (0.295)

daa,as= 5.2906

m H1

&aa= 4.9942 dab= 5.0808 (5/// = 4.6018

-n c a-

6as-6aa=0.2378 6aa-6as=0.1438 oaa,as-6///=0.6888

gi m) ca

6 = 4.8980 as S = 4.8998 aa daa,as

= 4.8785

-08 UD H2 6 6aa= 4.9753 bas= 4.9480 d/// = 5.1048

0_ c das-6aa=-0.0773 daa-das=-0.0482 oaa,as-SIII=-0.2263

0.0

-0 (5 = 2.7465 as daa= 2.7547 6aa,as= 2.6802 8 methine H3 6

aa= 3.0856 Sas= 2.9654 d/// = 3.5660

Ei

a S -d =-0.3391 as as • daa-das=-0.1907 Saa,as-6///=-0.8858

74: tAH in KJ.mo1-1 (Kc41.mo1-1); chemical shifts in ppm from TMS.

°c AS AS in cal.mo1-1.K-1 as calculated by the relations given in Table 5.3-1.

Reproduced w



ithout permission.

For transformation ©the sum of linear electric field effects

(-0.002ppm), of quadratic field effects due to time-dependent electric

dipoles (0.77ppm) and of the magnetic anisotropy effects (0.14ppm) cannot

explain the experimental trend (-0.69ppm for transformation (0).

C Olefinic proton H2

The non-monotonic temperature variation of the chemical shift

of this proton (see Figure (5.3-4)) has at least two possible explanations:

(i) the population ratio variation (between the states of minimum

energy) is not entirely responsible for the temperature dependence.

(ii) two successive transformations take place: for example, transfor-

mation(D(or(D) occurs at low temperature, while at higher temperature,

the population of conformation III starts to increase.

Up to this point, no other parameters (coupling constants or

chemical shifts) have given any indication that hypothesis (ii) may be

correct. Furthermore, after a correction is applied, using the tempera-

ture dependence of the H2 proton chemical shift of the cis-4,4-dimethyl-

2-pentene, the (corrected) temperature dependence becomes monotonic. The

magnetic bond anisotropy, as well as the <E2> term (which is the largest

contribution) gives an increased resonance frequency for transformation()

and for transformation (D; this could explain the experimentally found

minimum, if there are two successive transformations, first. transformation

©and then transformation (D. The largest magnetic anisotropy contribution

difference comes from the double bond, giving a high frequency shift for

transformation ®(amounting to 0.14ppm) as well as for(D(amounting to

240


0.18ppm). Similarly, the time-averaged square of the electric field,

<E2>, due to fluctuating dipoles increases the frequency for transforma-

tionG)(0.83ppm) as well as for transformation(D(1.09ppm). Both values

a'•a larger than the experimentally deduced shift increases; one obtains

0.077ppm and 0.23ppm for transformation( )and ©respectively.

D Methine proton

For the three transformations, Table 5.3-5 shows that the

methine proton of the lowest minimum energy has its resonance at low

frequency. While linear electric field effect (accounting for less than

0.001ppm for transformation 0) and steric 1,4-interactions (no such

H....H interaction) are not a factor, magnetic anisotropy of bonds

(accounting for -0.64ppm for transformation 0) and quadratic electric

field effects caused by fluctuating bond dipoles (-0.42ppm for transfor-

mationT) seem to favour transformation(i)(the experimentally deduced

shift for this transformation is 0.19ppm to be compared with the calculated

1.06ppm).

For transformation(Dthe bond magnetic anisotropy differences

(a shift of -1.2ppm is calculated, half coming from the double bond) and

quadratic electric field effects due to fluctuating dipoles (a shift of

-0.28ppm is calculated) would rule out transformation ©from the possi-

bilities (a shift of 0.88ppm is experimentally deduced).

241



A Temperature dependence

As was the case for the proton shifts, the use of the carbon-13

resonance of TMS as a reference does not guarantee that the remaining

variations are exclusively caused by changes in population ratio of

various conformers. The choice of the C5 (for notation see Figure (4.3-1))

frequency line of the cis-2,2,5-trimethy1-3-hexene as a reference was

made, on the basis that, despite large differences between structures and

between population changes of cis and trans isomers, this carbon, in both

isomers, displays a similar increase in resonance frequency for the

temperature range investigated (variations of 0.33ppm and of 0.43ppm are

•observed for the C28 and trans isomers respectively). Also, because of

the symthetry of the tert-butyl group, any effect of conformational change

on C5 resonance will Itend to be minimized. The chemical shift values as

referenced against t ae tert-butyl methyl carbons are given in Table 5.3-6.

Direct application of the GBM method furnished the results as given in

Table 5.3-7. InconsiStency in the energies as derived from the various

carbon-13 shifts can i)e obsemied, and many of the shifts deduced for each

conformation are implausible. As for the proton shifts, the enthalpy

values obtained from the coupling constant study were then used with the

variable temperature carbon-13 shift data to calculate individual confor-

mational shifts. The results are given in Table 5.3-8.

The C5 resonance being taken as reference, was assumed to be not

varying; C4 displaying the same type of variation as C5 (see Table 4.3-2)

242


TABLE 5.3-6 Carbon-13 chemical shift (ppm) dependence on temperature for the cis-2,2,5-trimethyl-3-hexene referenced to the methyl tert-butyl carbon C5.

A)

T (K)

Olefinic carbons

Cl and C2

230 136.95 137.42

245 136.99 137.32

261 137.05 137.34

271 137.10 137.26

281 137.09 137.20

303 137.18 137.18

310 137.18 137.18

320 137.25 137.15

330 137.28 137.13

340 137.38 137.12

B) Saturated carbons

T (K) C3 C4 C6

180 27.89 23.33 32.78

190 27.87 23.35 32.79

200 27.84 23.35 32.82

213 27.80 23.35 32.85

222 27.77 23.35 32.87

240 27.71 23.36 32.95

245 27.70 23.36 32.96

260 27.65 23.35 33.00

270 27.64 23.34 33.02

280 27.62 23.34 33.04

300 27.59 23.34 33.11

310 27.59 23.33 33.12

320 27.56 23.32 33.15

340 27.54 23.31 33.21

243


x m -0 8 0. c C) 0 a • * .,,,....,

= TABLE 5.3-7 Sets of carbon-13 shifts and energy separations obtained from the GBt4 method for the -0

1 three transformations considered (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3- hexene. The shifts are references to C5.

a' m o m o transformation® transformation® transformation (D

AH = 6.40±0.96 (1.53) AH = 3.05±2.47 (0.73) AH = 4.81±2.26 (1.15)

AGO- 5.75±0.96 (1.37) AG°= 3.70±2.47 (0.89) AG° = 7.35±2.26 (1.76) C6 6as- 32.64 6aa= 32.58

6as,aa= 32.61 6 = 37.71 aa 6as= 35.40 6III

= 42.58

.., AH = 1.26±1.05 (0.30) AH = 9.62±3.14 (2.30) AH = 0.293±0.20 (0.07)

C* 1/2

AG°= 0.65±1.05

6 as=151.15

(0.14) AG°= 10.3±3.14

6 =136.90 aa

(2.45) AG° = 2.84±0.20

6 as,

aa=159.36

(6.68)

6aa=119.32 6as=153.77 6III = 67.44

AH = 2.47±1.8 (0.59) AH = +0.5±1.84 (+0.12) AH = 0.795±0.53 (0.19)

C* AGO= 1.82±1.8 (0.43) AG°= 0.15±1.84 (0.04) AG° = 3.34±0.53 (0.80)

2/1 6 =140.00 as - 6as=138.79 6as,aa

=145.76

6aa =131.35 6as=134.67 6111 =104.91

, AH = 3.89±0.90 (0.93) AH = 0.88±0.86 (0.21) AH = 1.80±0.94 (0.43)

AG°= 3.24±0.90 (0.77) AG°= 1.53±0.86 (0.37) AG° = 4.34±0.94 (1.04) a' C

3 m. 5

6as= 28.27 6aa= 28.51

,1 6as,aa= 28.76

m 6 = 25.07 aa 6as= 25.92 6III = 20.99

C4 Negligibly small variation

tAG° and AH are in KJ.mo1-1(Kcal.mol-1); the chemical shifts are in ppm. AS is taken as shown in Table 5.3-1.

Reproduced w



ithout permission.

m 77

a 0_ c 0 00_ P: 7' -0 5 TABLE 5.3-8. Sets of carbon-13 chemical shifts and 'their difference as obtained from the GBM a. method with the enthalpy separations as given in Table 5.3-1 for the three . o considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene+ 0 0

5-' m transformation OA transformation transformation° C) . 0 -0 . AH 3.096 (0.74) 0.393 (0.094) 1.234 (0.295)

c0 0-0 6aa

= 28.56 6aa 6aa,as

= 28.83 = 29.63

C3 6 6as

= 25.74 6,II m = 24.98 aa = 18.43

m 6as-6aa= 3.58 6aa-6as= 3.09 6aa,as-6///= 11.20

a-c

' _/) m-gi 6 6 as as

=138.85 6 =138.91 =140.48 IV aa,as

'0 cri C2 or C1

6aa =134.60 . ofII =121.73 a

=132.75 bas _ c o .

bas-6aa= 6.10 6aa-bas= 4.31 6aa,as-6///= 18.75

0 0

0bas tsaa =135.12 =135.19 =133.68 a - 6aa,as

C1 or C2 6aa =142.76 bas =140.23 s,II. =153.34

it a_ 6aa-6aa= -7.64 6

aa-,6as=.-5.04 6aa,as-6///=-19.7

0c 6as = 31.90 csaa = 31.71 = 30.75

C6 6aa = 36.29 6as = 35.21 :III

aa,as = 43.84

1' 6as-6aa= -4.39 a 6aa-6as= -3.50

u). 6aa,as-6///=-13.09

o -1 0 the chemical shifts are in ppm (referenced to C5); AH are in KJ.mol (Kcal.mol-1).

Reproduced w



ithout permission.

is then, as a consequence, also temperature independent.

B Quaternary tert-butyl carbons (C6)

For C6, the application of the GBM method gives the results

displayed in Table 5.3-7 (direct application of the method) and in Table

5.3-8 (with use of the enthalpy values previously determined). None of

the shifts for the second minimum (6aa

for transformation®, óas

for

transformation ©and 6111 for transformation (D) are reasonable. The

reason for this total failure is probably related to the fact that

carbon-13 solvent effects for quaternary carbons are very much smaller

than that for methyl carbonS (see for'example Rummens and Mourits [126]),

so that the C5 referencing is most inappropriate in this case.

C Olefinic carbons

Examination of Table 5.3-9 shows that an increase in bulkiness

(and therefore also in induced charge on C2) of the second substituent

(the first substituent being a tert-butyl group) correlates with an

increase in resonance frequency for C2 (olefinic carbon atom that the

second substituent is attached to) and with a decrease in resonance

frequency for the'Cl olefinic carbon. The difference in electronic

density at both carbons was invoked to explain the shift separation between

C1 and C2 for the trans molecules (see Table 5.2-1). It can be noted,

however, that this separation is smaller for cis isomers than for the

corresponding trans isomers. From Table 5.3-9, it appears that an

increase in C2 resonance frequency is the main cause of the smaller

246


U

TABLE 5.3-9 Carbon-13 chemical shifts of some cis disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm from IMS.

Cl C2 C3 C4 C5 C6 ref.

1 138.7 138.7 32.1 32.0 32.0 32.1

2 137.4 137.4 27.85 23.60 31.79 33.37 b

3 139.48 131.00 22.13 15.02 31.62 33.53

4 141.02 122.47 14.27 31.26. 51.44 a

5 148.6 108.2 • 28.4 32.8 a

aData taken from reference [118]; neat samples were used; bData taken from this thesis.

°Data taken from reference [119]; neat samples were used.

I • I 141 C C — C=C— C C 2 C— C — C=C— C C

5 6 1 2 3 4

C C C5

C C I

3 C — C — C=iC— C — C a C --C --C=C---C

C ' I

C

• 1

5 C— C — C

C

247

•


separtion for the cis isomers. The C1 resonance shift for the cie."2,2,5-

trimethyl-3-hexene listed in Table 5.3-9 does not follow the general

trend observed above. This fact probably reflects a conformational

equilibrium with unequal populations.

The assignment of the resonance lines of the olefiniC part,

which cross over at around 300K, is ambiguous. One is tempted to assign

the largest value at high temperature to Cl, in order to maintain the

predominance of the induced charge effect, but large structural differences

could upset this predominance. The results from the application of the

GBM method Are given in Tables 5.3-7 and 5.3-8. For transformation®,

one would have high temperature limit averages ((Sas + daa)/2) of 135.80

and 138.94ppm for the C2/C1 pair. Comparison with the data of Table

5.3-9, particularly with molecules 1 and 4, would then lead to good

agreement, provided the assignment <C1> = 138.94 and <C2> = 135.80ppm i§'

made.

For transformation®, no such satisfactory, assignment can be

made. Transformation(Dappears excluded on the basis of excess1'ely

large (6III-6.0ta,as values.)

For transformation®, the steric 1,4-interaction effect on

(6a:das) (less th40..lppm) and the linear electric field effect (around

0.1ppm) are not important. The second order electric field effect due to

fluctuating electric dipoles gives (6aa-

bas) values of 18.9ppm and

27.4ppm for C1 and C2 olefinic carbons respectively, when using Equation

(2.3-6) (the B value of Equation (2.3-3) was taken as-40. x 10-18). Only

one of these results is consistent with the experimentally liduced

248


differences since the latter have opposite sign (7.6ppm for one, -6.lppm

for the other). Transformation®, similarly has experimental (6as-6aa)

values which have different signs for C1 and C2.

Methine carbon

Using thl same C5 reference as for the olefinic carbons,

results as given in Table 5.3-7 were obtained after direct application of

the GBM method. With de help of the enthalpies deduced from coupling

constant study, the differences in shift between conformers were calcu-

lated as shpwn in Table 5.3-8.

ITtre absence of steric 1,4-interaction. between polarizable C-H

bonds, the small difference in linear electric field effects and the

small contribution from quadratic electric field caused by molecular

dipoles (high frequency shift of 0.65ppm for transformati,on0) cannot

explain to difference deduced from the experiment (3.584m for transfor-

mation O, 3.09ppm for transormation(E)). In fact, the 6as

and 6aa

values for.either(Dor(Dappear reasonable. , On the other hand, the

6111 = 18.43ppm for ©i4 implausible.

r

9

5.3,6 Rotational barriers and line intensities

In his thesis, Van der Heiiden [/12] has suggested that the

rotational barrier for the tert-butyl group in the cis-2,2,5-trimethy1-3-

• -1 hexene can be as nigh es 62.8KJ.mol (15Kcal.mol-1). Such a barrier was

estimated following a rapid and clear change, around room temperature, in

the ratio of the tere-butyl line intensity to the isopropyl doublet

249


intensity. A careful reproduction of this result was attempted. The

proton spectra were recorded using a scanning rate of 0.03Hz per sec.

for a scale of 1Hz.cm-1 for a temperature range of 120K (between 240 and

360K). One of the olefinic lines of the cis-2,2,5-trimethyl-3-hexene

was taken as the lock signal. By this technique the TMS line could be

used as the intensity reference.

The results are given in Table 5.3-10. Intensity changes were

studied for the tert-butyl signal as well as for the isopropyl signals.

None of the quantities indicates a drastic change in intensity ratio at

any temperature. The fluctuations observed in the data of Table 5.3-10

are also present in the half line width of the reference. Variation of

the experimental conditions (most likely in homogeneity) are thought to

be the cause of these variations.

The carbon-13 spectra (recorded under the conditions described

in Section 4.1) likewise show only one signal for the methyl carbons of

the tert-butyl group at a1,1 temperatures between 180K and 340K. There is

no observable broadening and the peak intensity ratio with the TMS signal

(see Table 5.3-11) shows no systematic ..hanger.

The absence of any evidence of a drastic change in intensity

ratio for the tert-butyl group (both for proton and carbon-13) seems to

indicate that the rotational barrier for transformation(Dor&is small

(smaller than 24.0KJ:mo1-1 or 6Kcal.mo1-1) or that the Gibbs energy

difference between the (as) and (aa) conformers is large (i.e., larger

than 8.0KJ.mol-1 or 2.0Kcal.mol-1 ). The Force Field calculation agrees

with the former (AGT = 10.5KJ.mol or 2.5Kcal.mol-1 ) but not entirely

250


TABLE 5.3-10 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene (protonNMR).

T (K) R*t-butyl Rt isopropyl AvIITMS (Hz)

360 .57 .50 .36

350 .59 .53 .43

34C .575 .52 .42

330 .55 .52 .40.

320 .58 .53 .43

310 .53 .51 .40

300 .55 .50 .30

280 .59 .46 .22

270 .595 .47 .22

260 .61 .46 .28

250 .58 .47 .30

240 .57 .

.46 .35

210 .57 .41 .40

*Ra = E Id(ITmc0

E ); a represents either the tert-butyl group or the .l opropyT grai lines.

251


TABLE 5.3-11 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene for ' carbon-13 NMR.

T(K) R*. • tert-butyl 11*,isopropyl

300 0.82 0.75

280 0.81 0.74

260 0.77 0.69

240 0.78 0.70

220 0.77 0.69

210 0.77 0.69

200 0.75 0.66

180 0.74 , 0.65

*Ra = E Ia/(ITMS+E Ia); a represents either the tert-butyl signal or the a a isopropyl signal.

252


with the latter (AG° = 5.31KJ.mo1-1 or 1.27Kcal.mo1-1).

Similarly, the constancy of the intensity ratio for the

______i5opropyl group would suggest that either the rotational barrier for

transformation ©is small or the AG° difference between the rotamers of

lowest minimum energy is large. The Force Field would, in this case,

favour the second hypothesis. A rotational barrier AG1 of 49..2KJ.mo1-1

(11.8Kcal.mo1-1) is obtained between the (as, aa) fOrms and conformation

III, while an average Gibbs energy separation AG° of 36.4KJ.mo1:1

(8.7Kcal.mo1-1) is calculated_ between the same'rotamers.

5.3.7 Conclusion

Contradictory results are obtained from the combined investiga-

tion of NMR measurements and of Force Field calculations for the cis-

2,2,5-trimethy1-3-heene.

While transformation(Dis supported by the 3vJ coupling constant

data, transformatiohOis equally favoured by the 3cJ coupling constant

data. This latter transformation leads to a AG° which has the same sign

as that predicted' by the Force Field calculation; this transformation,

gives also a pradiction of AG° = 0 for cis-4,4-dimethyl-2-pentene, which

explains the temperature independence of 3cJ for this latter molecule.

On the other hand, transformation ©leads, for cis-4,4-dimethyl-2-pentene,

to a 40 inco4atible with the temperature independence of 3cJ. On the

basis of the/allylic coupling constant data 4taJ for the cis-2,2,5-

trimethy1-3-ihexene, both transformations (Oand(i)) appear unlikely.

Transformation(Dis relatively successful in explaining the

253


(3vJ and

3cJ) coupling constant data and their temperature dependence,

provided oneintroduces an extra 30° (from a CCCH dihedral angle 4, = 160°

to 130°) rotation of the isopropyl group for conformation III (which

would bring the methine proton virtually to a gauche position). Neverthe-

less, this transformation has to be rejected on the basis of the large

discrepancy between the Gibbs energy separations obtained from the GBM

-method and from the Force Field calculation. An energy separation of

3.74KJ.mo1-1 (0.89Kcal.Mo1-1) seems implausible for an (as)-'-(gs) trans-

formation in the case of cis-,2,2,5-trimethy1-3-hexene. This transforma-

tion can be compared with the cis/trans conversion of 2,2,5,5-tetramethyl-

3-hexene (in the cis conformation of this molecule a strong interaction

exists between the two tert-butyl groups, as should4xist for a (gs)

conformation of cis-2,2,5,trimethy1-3-hexene) which has been found

experimentally by Turner et at. [128] to involve an energy of 38.9KJ.mo1-1

(9.3Kcal.mo1-1).

The information gathered from the (proton and carbon-13)

chemical shift study leads, as much as the coupling constant study, to

irreconcilable results. It can be said, however, that the existence of a

kinetic process, involving rearrangement of the substituent group(s) has

been proven and that this process relates to a Gibbs energy separation in

the order of 2.0 to 4.0KJ.mol-1 (0.5-0.8Kcal.mol-1). Such given AGo

values were used to analyze the temperature dependence of the chemical

shifts. None of the foreseen (from the Force Field calculation) trans-

formations gives satisfactory explanations for all the chemical shift

data. While the olefinic proton Hl and the methine proton H3 favour

254


transformation®, the temperature variation of the olefinic proton H2

chemical shift is in concordance with transformation(Dor®.

In view of the above-mentioned results, the calculated geometri-

cal minima for the cis-2,2,5-trimethyl-3-hexene obtained using the Force

Field method are unsatisfactory. A adequate interconversion could

involve a 30° rotation of the isopropyl group from the anti position (thus

the double-degenerate second minimum would be in a skew form). The

correctness of this suggestion would mean that the Force Field method is

not well suited for interconversion of crowded molecules. The study of

'the cis-2,5-dimethy1-3thexene, which will be described in the next

section, was started in the hope of a clear outcome allowing'vne to

further test the Force Field method used.

5.4 C119-2,5-0IMETHYL-3-HEXENE

5.4.1 Temperature dependence of coupling constants

to

A Introduction

Following the results of the Force Field calculations, one of

the isopropyl groups is in anti position for the two minima of lowest

energy. As the other isopropyl group has its methine CH either in anti

((aa) state) or in syn ((as) state) position, the initial equilibrium in

question here will be of the (aa)4--).(as) type. If p is the population of

the (aa) state, the population of the (as) state, which is two-fold

degenerate (as and sa), will be (1-p)/2. The observed,(avvaged) vicinal

255


and allylic coupling constants (3'J and4ta J respectively) must follow

Equation (5.4-1):

<J>T = pJ + (1=2-) (Jaas

+ Jas) )

au 2 (5.4-1)

Jaa and Jaas are the coupling constants with the methine CH in anti posi-

tion for the (aa) and (as) states respectively. J8as is 'the coupling

constant when the methine.CH of the isopropyl group, is in en position

(HCsp 2-C sp3H dihedral angle = 0°). Application of the GBM method, using

Equation (5.4-1) will give Jam, (Jas + Jas) and the difference in

enthalpy between the conformers. if one uses the second form of Equation

(2.5-2), with the Calculated entropy differences as given in Table 3.5-2.

To calculate the inctividual coupling constants Jas a

and J8s' an estimate

of Jaa has to be given. An approximate difference between J and Jas

can be calculated using the geometries as per Force Field calculations,

plus the (a/o6) data of Rummens et al, [71], if one assumes that only

the steric contributions are involved. Knowing Jas, eas is then,calcu-

lated from the (Jas Jas

) results obtained from the GBM method.

For the homoallylic and olefinic coupling constants (Schaj and

3cJ respectively) one has to replace Equation (5.4-1) by Equation (5.4-2):

<j> = Jaa

+ (1-p) Jas

(5.4-2)

256


where p is the population of the (aa) state; Jaa and Jas are the coupling

constants for the (aa) anti (as) rotamers respectively.

B Vicinal coupling constant 3vJ and olefinic coupling constant 3cii

The temperature dependence for 3vJ is given in Figure (5.4-1).

An inflection point is observed at about 300K. Two successive rate

processes have to be invoked to explain such a change in curvature. To

avoid having to solve too complex a problem, it was assumed that below

the inflection point, 'the temperature dependence of the 3',1 coupling

constant follows Equation (5.4-1). Direct application of the GBM method

was made using Equation (2.5-2); the entropy differences and their

variations with temperature were taken from Table 3.5-2. Three parameters

could be obtained from the 3vJ temperature dependence which displays a

small curvature below 300K. The same procedure, using Equation (5.4-2)

was also applied to the olefinic coupling constant 3'J (as for 3vJ, only

the values below 300K were taken into account). The results for both

coupling constants are given in Table 5,4-1. The consistency of the

enthalpy and Gibbs energy differences is not a certain guarantee of the

correctness of the assumption (that only one transformation occurs below

300K). The weighted average Gibbs energy separation between the two

rotamers is calculated to be equal to 1.13±0.04KJ.mo1-1 (0.27±0.01Kcal

mo1-1), while the enthalpy difference is 0.732±0.04amo1-1 (0.175±0.01

Kcal.mol-1). The difference between Force Field ,calculated and experi-

mentally deduced energy separation is far larger than that found for the

trans- and cis-2,2,5-trimethyl-3-hexene (in the hypothesis of transformation

257


d • '

9.6

9.5

6

9.4

;so 260 290 320

T {K}

350

FIGURE 5.4-1 Temperatui.e dependence of the vicinal coupling constant (J12, see Figure (4.2-5).for notation) for r:8-2,5-dimethy1-3-hexene (not corrected for intrinsic contribution).

258

•


TABLE 5.4-1 Sets of coupling constants and energy separation between rotamers as obtained by the G8M method applied to the experimental data of cis-2,5-dimethyl-3-hexene up to a temperature of 3000

3uj

3cj

J = 11.807 aa (Jas + Jas)/2 = 5.961 AH . 0.711±0.08 (0170)

AG' = 1.11±0.08 (0.265)

Jaa = 10.482 Jas = 11.330 AN, = 0.837±0.08 (0.200)

AG° = 1.23±0.08 (0.295)

TR = 0.732±0.042 (0.175±0.010) 7° = 1.13±0.042 (0.270±0.010)

4A11 J couplings in Hz; AG', AR in KJ.mo1:1(Kcal.mol-1) and AS in cal.mo1-1.K-1,,as calculated from AS . al-4 + bT + c; a . -0.5 10-6, b = 0.748 10-J, c = -0%498.

t

259

1


(A or it would amount to 13.22KJ.mo1-1 (3.16Kcal.mo1-1) if one

assumes an (aa)+-0-(as) equilibrium.

All other coupling, constants showed a variation with tempera-

ture barely different from the random scatter; therefore, these could not

be used to determine AG°.

5.4.2 Coupling constant and structure

A Vicinal coupling constant 3vJ

The combined use of the Force Field derived geometries and of

the (AJ/Ae) data as given by Rummens et al. [71], allows one to evaluate

the anti coupling constant, 3v,.1aa, without relying on the experimental

data. The 3vJa

value given -by Rummens et al. [71] for the 3-methyl-l-

butene is the starting value of the calculation. Neglecting the electr:o-

negativity effect of the second isopropyl group (supposedly small, see

Rummens and Kaslander Pop, the steric contribution (calculated with the

Force Field-based geometry combined with the (AJ/Ae) data given by Rumens

et al. [72]) increases the 3vJa value from 10.21Hz (3-methyl-l-butene) to

11.50Hz. This value is close enough to the experimentally deduced

3vJaa = 11.807Hz, to assume that the major geometrical features of the

(aa) state are well described by the Force Field calculation. The

estimated difference (3v

Jaa 3vs - J

aa) calculated by the same procedure is

s 0.18Hz. From the sum (3v Jaa 3v

s Jas) obtained by the applicatio.; of the

s GBM method, one then deduces a value of -0.07Hz for 3v Jas. This value

seems to rule out the Assumed (aa)+4.(as) transformation. Indeed, in,syn

•

26a


1

position, an FPT-INDO-derived 39J coupling constant of 8.48Hz has been

calculated by Maciel et al. [73] for propene. Neither the steric, nor

the electronegativity contributions would lower this value to reach a

negative coupling. The smallest ' 79J coupling constant obtained by Maciel

et al. [73] is with an HC sp 3-C sp2H dihedral angle of 80° (while the syn

position corresponds to a zero dihedral angle), which gives 39J z 2.3Hz;

this latter value is still too high and correction for steric contribu-

tion would certainly increase this value; the steric hindrance increases

the C=C-C angles and decreases the C=C-H angles while the corresponding

(AJ/A6) data are positive and negative respectively. One possibility is

that, for the second rotamer, none of the methine CH is in anti position.

With a two-fold degenerate state, the sum of the 39J coupling constants

for this rotamer should be 11.92Hz. Postulating equivalent isopropyl

groups, with identical coupling constants, this value of 11.92Hz can be

obtained for HC sp 2-C sp3H dihedral angles of either 40°:T .e., close to

gauche) or 120° (i.e., skew), if one follows the calculatiOns by Maciel

et al. [73] for propene. Of these two the former is least likely because

in this rotamer the four methyl 'groups would be involved in a strong

cisoid interaction. However, neither conformational structure corres-

ponds to an energy minimum according to the Force Field method. ,

Olefinic coupling constant 3eJ

The (aa)-0.(as) transformation explains the observed increase of

3cJ with temperature (see Table 4.2-4). The calculated change due to

steric contributions (0.69Hz)-for this transformation is in good agreement

261


with the experimentally deduced increase (0.85Hz). The 3cJaa coupling

constant can be calculated from the 3-methyl-i-butene value (3cJa =

9.63Hz) obtained by 'Rumens et al. [71]. The change in steric contribd-„

tion 4+3.56Hz) and in the electronegativity effect (-2.75Hz) between the

3-methyl-l-butene and the cis-2,5-dimethY1-3-hpxene gives a calculated

3cJaa' for the -latter molecule, equal to 10.44Hz, in ,guod agreement with

0

the experimentally deduced value of 10.48Hz. The indlusion of anticipated

errors in valence angle calculation by the Fqrce Field method would lower

the theoretically calculated 3cJaa down to 9.87Hz (a 1.4°,overestimation

of the C=C-C valence angles and a 2.6° underestimation of the C=C-H

valence angles,have been estimated for the (aa) state, according -to the

discussion in Section 3.2.1).

On the basis of the fair agreement between the results obtained

by the two above procedures, it can be concluded that the calculated ('by

Force Field) geometry of the "rigid" part,(e.i. not including the rotors)

of the molecule is probably accurate.

C LongLrange H-H coupling constants

Acdording to thrfield et a/. [79], the FPT-INDO-derived 4t2J

coupling constant has its minimum value when the mett,ir.le protein eclipses

the 2p atomic orbital of the olefinic carbon (to which the isopropyl

group is attached). Maximum values are obtained foi/Lanti (0.00Hz'

according to.Barffeld et al. [79]) and for syn positions (a theoretical

value of 1.01Hz was calculated by Barfield et al. [79] for propene).

Wowing fOr the steric contribution differences between propene and

262

;

'


cis72,5-dimethy1-3-hexene, a 4taJ:s coupling constant of about 0.64Hz is

estimated. The low experimental value (-1.04Hz) and its temperature

dependence (toward more negative values for increasing temperatbre) would

render an (aa)4-+(as) transformation implausible. For this transformation,

Rummens et al. [71] estimated that (averaged) values of between -0.5Hz

and 2.0Himust be expected.

From the application of the GBM method 'assuming AG° = 1.13KJ.

mol 6r-0--,2.7Xcal.moI-1), one obtains values equal to -0..944Hz and

-1.14Hz for 4taJaa and for the sum taa J4-S a-4-1 s_l_cepectively. If

Q

ore postulates that the 4taJaa and 4taJaas couplings are equal, a ,syn

coupling constant 4t2J:s = -1.34Hz results..

The calculated rehybridization effect, for 4taJ, in going from

3-methyl-l-butene to cis-2,5-dimethy1-3-hexene is equal to -0.20Hz. The

4ta Ja'given by Rummens et al. [71]

the former molecule being equal to.

0.0Hz, the above result leaves-,the remaining -0.74Hz unexplained. This

is to be compared with a similar unexplained -0.52hz for the cis-2-butene?-

which is, according to Rummens and Kaslander [70],, not due to a differen-

tial electronegativity effect. No reason can yet be giV•en for either of

these discrepancies.

The homoallylic coupling constant, 5c haj, is difficult to inter-

pret. According to calculations performed by Barfield and Sternhell

[80], both 5chaJ and 5c Jas are negative (equal to -0.75Hz and -0.40Hz aa

respectively) so that any (aa)-.+(as) equilibrium would have a negative °' 4!

<5chaLl>. Since the experimental 5chaJ couplings are all positive (see

Table 4.2-4), once more the above-mentioned transformation seems to be

263


ruled out. From Barfield and Sternhell's work [80], it may be seen that

one obtains a positive (and relatively large) 5c haj, when none of the CH

methines is in anti position (a maximum value of 4.99Hz is'reached when

.the and 0' angles are equal to 90° (see Section 2.423 for notations)).


A Methine proton

The'results shown in Table 4.2-4 and in Figure (5.4-2) indicate

a dect:ease of the methine proton chemical shift. The variation observed

1-siii*--enaigh-not-to-be-uniquely due_ to intrinsic effects. For the _

i;raw and cis-2,2,5-trimethy1-3-hexene the' corrections due to these

effects were much less than the variation observed for the cis-2,5-

dimethyl-3-hexene. This would indicate that the methine proton resonance

frequency decreases for the (aa)++(as) transformation. The GBM method •

(Equation (5.4-2)) was applied to uncorrected (referenced to the TMS

line) and to corrected (of the intrinsic variation of the methyl'protons .

of the propene molecule as given by Rummens et al.,[71]) chemical shifts

(both- are_displayed in Figure (5.4-2)). In both cases, the application

of-

of the GBM method appl-ied up to a temprature of 300K as for the

coupling constants) gives a free 'Gibbs energy separation between the

rotamers close to that obtained,frdm the coupling constant study (AG° =

1.276KJ.mo1-1 or 305ca1.mo1-1). The deduced frequency resonance shift ,

for the (aa)4.4-(as) transformation is equal to -0.32 or -0.41p;m depending

on the values employed (the results are given in Table 5.4-2).

264


• 2.610

2.606

ct.

et) 2. •

e<cs.4. 2.602

2.398 220 .270

k T

[K]

320

FIGURE 5.4-2 Temperature.dependence of the methin 'Pr to (H2) chemical shift for cis-2,5-dimethy1-3-hexene. A - referenced to TMS B - referenced to TMS and corrected for the intrinsic

temperature variation found for th-e methyl protons of propene (obtained from reference [71]).

265


TABLE 5.4-2 Sets of proton chemical shifts and energy separations as obtained by the GBM method applied to experimental data of cis-2,5-dimethy1-3-hexene up to a temperature of 3000.

•

B

C

From 6H (olefinic). From 6H (methine)

AH° = 83711004200) AH° = 879±250 (210)

AG° = 1234±300 (295) AG° = 1276±250 (305) A

6aa = 5.1782 bas= 4.8092 6 = 2.7210 bas = 2.4025 :aa..6

= -0.318 6as-6aa = -0.369 as aa

AH° = 837±300 (200)

AG° = 1234±300 (295)

AH° = 879±250 (210)

AG° = 1276±250 (305)

6 = 5.2503 6 = 4.6857 D 6 • = 2.7536 6 = 2.3455 aa as aa as

6 -6 = -0.565 6 -6 -0.408 • 'as aa • as as

•AH° = 1137i300 (200).

AG° = 1234306 (298)

6aa = 5.1107 bas = 4.9248

• 6as-6aa -0.186

energie; in J.mol-1 (cal.mol-1) chemical shifts in ppm relative to TMS.

A the reference is uncorrected B reference corrected by subtracting the temperature dependence

of tfie H3 proton in propene C reference corrected by subtracting the average temperature

dependence of the three olefinic protons of propene D corrected,0 subtracting the temperature dependence of the

methyl signal in propene.

266

• a


The sum of the magnetic anisotropy effect (-0.74ppm), the ,

steric 1,4-interaction (-0.12ppm) and the <E2> term (0.68ppm) gives a

total expected shift of -0.18ppm for the transformation, in fair agree-

ment with the above-given experimentally deduced shifts. The agreement

may be fortuitous because of the Oconsistency in the success of the

above-mentioned contributions for the other molecules studied (see

.Sections 5.2 and 5.3).

B Olefinic protons

As can be observed in Table 4.2-4 and in Figure (5.4-3), an

increase in the temperature up to 300K is correlated with a deCrease in

resonance frequency of the olefinic protons. Above 3F IC (the inflection

point for the <3vJ> F(T)) the temperature increase is accompanied with

a shift increase. Despite the absence of adequate referencing, the

experimental variation is large enough so that the GBM procedure is not

necessarily upset by the lack of any good correction. Application of the

GBM method on three different sets of values (each set is the result of

various corrections applied to the experimental values, see,Table 5.4-2)

gives, like for the methine protonoareasonable Gibbs energy separation

between the rotamerg of 1.234KJ.mo1.1 (295ca1.mo1-1), which can

be compared with AG° = 1.13KJ,mo1-1 (270cal.mo1-1) obtained froOhe

coupling constant study. Depending on the correction applied, the ,\

resonance frequency shift obtained for the (aa)+-(as) transformation,

varies between -0.19 and -0'.57ppm (see Table 5.4-2).

The magnetic anisotropy of the bonds gives a shift of -0.30ppm,,

267

• Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

4-

5.047_

E a. a.

C

(r) 5.042

x

5.037

230 230 280

T [K]

330

FIGURE 5.4-3 Temperature dependence of the olefinic protons chemical shift for cis-2,5-dimethyl-3-hexene. A - referenced to TMS B - referenced to TMS and Arrected for the temperature

dependence of the intrinsic contribution found for the H3 proton of Oropene(taken from reference [72])

C referenced to TMS and corrected for the mean tempera-ture dependence of the intrinsic contribution found for the three olefinic protons of propene (from reference [72]).

268


for this transformation, mainly coming from the CH methine bond effect.

The steric 1,4-interaction does not Iplay any important role in the shift.

The quadratic electric field contribUtion due to the time-dependent

dipoles is calculated to account to a shift of +0.09ppm for this trans-

formation. The sum of the three contributions (-0.21ppm) is in good

agreement with the experimentally deduced shift (see Table 5.4-2). How-

ever, as for the methine proton, the agreement could be fortuitous.

•

5.4.4 Conclusion

Although the study of this molecule leaves some unexplained

facts, some obvious conclusions can be drawn. As for the cis-2,2,5-

trimethyl-3-hexene, the cis-2,5-dimedly1-3-hexene is subject to a kinetic

process involving relatively small Gibbs energy difference of about AG° =

1.13amol-1 (0.27Kcal.mol-1). While the Force Field calculation

indicates the possibility of such a process for the former molecule, the

calculation for the latter rules out the observation of any transformation

for the temperature range investigated.

The belief that the Force Field calculation simply overestimates

Gibbs energy differences between rotamers is not supported by the

analysis of the 31)J, "aJ and 6aha J coupling constant data. The study

gives credence to the idea that the employed Force Field technique over-

looks a low-lying minimum For cis-2,5-dimethyl-3-hexene. An acceptable

fit between experimental data and the calculated (by Force Field)

structure of the molecule cannot be obtained on the assumption of an

(aa)+(as) (or even an (aa)4.(ag)) conversion. •

269


However, the 3vJ and 3cJ coupling constant data are compatible

with the Force Field-derived geometry of ,the minimum of lowest energy

(the (aa) state). As well, the "rigid" HC=CH fragment of the second

minimum is adequately reproduced by the Force Field technique (this frav

ment is -only indirectly perturbed by the increase in crowdiness).

The proton chemical shift study does not provide any further

support to the above-mentioned conclusions. Both the olefinic and

methine proton shift data are well explained by the Force Field calculated

geometry of the two minima of lowest energy. The discussion of the trans-

2,2,5-trimethy1-3-hexene data (fOr which the Force Field calculated

geometry is reasonably v.curate) has, however, shown that one cannot rely

too heavily on chemical shift data.

270


CHAPTER VI

EPILOGUE

In this thesis several experimental and calculational techniques

have been employed in various combinations, all in search of new Wnowledge

regarding molecular structure. Because of the conflicting eviden/e that r emerged in several cases, this work also became a testing ground for the

techniques and methodologies employed. This requires• a great Oal of

care in every instance of reasoning, of identifying what the particular

premises are and of keeping track of these premises from one case to the

next. In spite of this interweaving of methodology and results, and

perhaps also because of it, an attempt will be made in this final chapter

to distill some overall conclusions and to indicate what future work is

needea.to resolve the outstanding problems.

•

A Experimental NMR at variable temperature and the extraction of

NMR parameters

This study shows that careful experimental work, coupled with

• powerful spectral analysis techniques, such as the NUMARIT computer

program, can give parameters with a precision at or near ±0.005Hz. Such

low error estimates were found before in the variance-covariance treat-

ment of the data, but they were generally considered suspect. The

scatter of the data around the general trend of temperature dependence of

271


coupling constants, as shown in this thesis, is also .often less than

±0.005Hz, thereby giving additional evidence for the basic precision as

quoted above. Some sources of systematic error still remain, but these

cannot be much greater than the observed scatter; it follows that most

parameters have an accuracy of better than 0..01Hz.

In terms of sensitivity of NMR temperature effects,it is

believed that this thesis has set a new standard.

B Conformational equilibria as studied by temperature variation

of NMR parameters

If there exists at leatt one non-zero Gibbs free energy

difference AG°.between two states, and if the molecular parameters

observed are population averages and if, additionally,'the'parameters

belonging to the individual states have different values, then,the

observed parameters will be temperature dependent. In the reverse

application of this phenomenon, the observed temperature dependence must

be at least quadratic, because three parameters need to be extracted viz.

the AG° and the parameter values in the two states. The extraction itself

is done by lept squares fit, utilizing an over-determined set of para-

meter values (i.e., determined at more than three temperatures). Because

of the high precision of the parameter data, small temperature effects,

some as small as 0.1Hz/100K, could be successfuily employed. If a

larger effect is observed, greater accuracy for AG° results.

As the results in this thesis indicate, provided the individual

parameter values-differ by 2 to 5Hz, the detection limit for AG° can be

272


set at about 0.12KJ.mol (0.03Kcal.mol-1 ) (there exists an upper limit

too for AG , which is probably around 6.3KJ.mol-1 or 1.5Kcal.mol-1 , but

the present study did not involve any such case).

In a number of cases though, the total observed temperature

variation did not exhibit sufficient quadratic character; this thesis

shows some examples of how to cope with such.a situation. Essentially,

either the AG° or one of the individual parameter values, or the

difference of the two of them, must be obtained fr.= another source, so

that the analysis then reduces either to a linear fit, or, as was mostly

done in this thesis, a quadratic fit with one fixed parameter.

.In view of the smallness of all observed temperature effects,

'no attempt was made--or could be made--tcy.test for three-site possibili-

ties, involving two AG° and three parameter values. The molecular

systems were chosen so that the possibility of a thitd low-lying state •

was considered rather minimal. As an extra safeguard against this and

several other possible systematic errors, every molecule Studied had at

least two parameters with a sufficiently large temperature dependence.

One of the more useful conclusions of this thesis is that consistency of

AG° values obtained for one molecule is not only useful, but virtually a.

must. It through this criterion, that it could be established that

coupling constants are much more reliable parameters than chemical shifts

are and also that certain external data (strain energies, conformational a

structure) could be ruled as being in error. Consistency in AGo is

necessary, but not sufficient. To be completely satisfactory, the

process must yield individual parameters which in themselves must be

273


reasonable and at least iii semi-quantitative agreement with the proposed

structure as indicated through additional structure-parameter relation-

ships. As again this study shows, it is possible to obtain consistency

in AG°, together with totally unacceptable individual parameter values.

Such results mean that indeed a kinetic process was observed, with a AG°

as calculated (except when the actual degeneracy is diffdrent from the

assumed one), but these results mean also that at least one of the

individual structures is quite different from the anticipated one.

•

C Structure-parameter relations

The general approach of this thesis has been to start with

certain proposed structures for the rotamers in question and to then see

whether the (two) sets of deduced parameters are in concordance with that

hypothesis. The strong dependence on dihedral angle(s) of vicinal,

allylic and homoallylic couplings has long been known and has been used

extensively in the past (and in this thesis). A new dimension was added

by the realization that, with a rotameric transition, the entire molecule - •

changes, particularly in its valence angles e (bond distance may also .

change, but this effect was found negligibly small for the systems

studied in this thesis): Because of this, parameters belonging to the

so-called rigid part Of the moledule are different in the two rotamers

and their observed 4yerageF are therefore temperature dependent.

A key.role in the discussion of these effects are the (AJ/AB)

data calculated earlier by Rumens and Kaslander. Starting with two

proposed structures and the AA (and,U) differences between them, as

274


calculated.by Force Field techniques (vide infra), the differences AJ.'

belonging to a rotameric transition could be calculated, independently

from the experimental tJ (as determined from the temperature dependence).

This technique had been used only once.before, but proved to be reliable

several times over in this thesis. Because of these repeated successes,

failure of(this technique is now concluded to meadthat'the'workihg hypothe-

sis has been wrong.

An extensive effort was made to find a 'similarly useful

structure-parameter stratagem for the interpretation of chemical shifts.

The nearly complete failure of this attempt has two basid reasons.

Firstly, chemical shifts are susceptible to solvent effects. Even though

the molecules in question were almost non-polar (and dissolved in non-

polar solvent) and even though 44MS was added as an internal reference,

the remaining differential Van der Waals solvent effect is not zero and

is different for each observed nucleus; this differential solvent effect

has also a temperature dependence which may well obscure the sought-after

intramolecular effects. Not only is there a site-effect operative both

for protons and carbon-13, but the basic Van der Waals equation

(aw -B E2) has different B values for carbons of different substitution

character. This latter point is brought out in the thesis: whatever

little could be said about the proton shift data, the carbon-13 shift

data proved virtually useless.

The second set of reasons derives from the various mechanisms

that can be invoked to explain (proton) shift differences between related

molecules. One such mechanism is that due to magnetic anisotropies (ax)

275

0


of chemical bonds. The present study with its pair of rotamers (each

rt,g,with its set of chemical shifts) is particularly useful in testi g \ this

mechanism. Surprisingly (in view of the many publications extoll and

using this mechanisOlt was found systematically that the Ax effect * . .)

falls short by, close to one.order of magnitude in explaining the shift

differences between rotamers. Linear and quadratic electric field

effects (due to the polarity of C-H bonds mainly) were found to be even

smaller in magnitude. The remaining possibility, an intramolecular Van

' sometimes even quantitatively) explaining rotampric shift differences.

This- result is surprising, as such effect has'rarely been invoked as a

significant factor in intramolecular shifts. Consequently, the theory is

only rudimentary; it would seem worthwhile, however, to further pursue

this in any future studies,

der Waals shift effect, turned out to be capable of qualitatively (and

D Force Field calculation

The introduction of Force Field calculations had, as a main

purpose, to give rough.estimation of energy differences'between various

proposed rotameric structures in order to see that the smallest AG° would

be in the observable range and to ensure that any further AG°'s would,be

high enough so as not to interfere. A second objective was to obtain the

basic structural information (usually a dihedral angle) corresponding to

the'-minima in steric energy. The Ermer-Lifson Force Field was chosen for

several reasons: firstly it was based on spectroscopic, thermodynamic and

structural information; secondly it was available in a fully iterative

276


r-, calculation gives 4KJ (1Kcal) more. The error can be traced back to the

input data for-the optimization of the force constants. The only rota-

meric energy irfput relates to (correct) AG° = 0 values for cis- and

trans-2-butene, propene and isobutylene, plus a AG° = 0..63KJ.mo1-1

(0.15Kcal.mol-1) for 1-butene. This sole non-zero AG° input data ts. not

well reproduced by the Force Field calculation. This latter method i1

version (the only one at the time) and lastly, but not least, .it was

the only Force Field that correctly predicted the C=C double bond eclip-

sing stricture for the C-H bonds in cisj-2-butene.

It became clear that this Force Field still has its short-

comings; For example, both for 3-methyl-l-butene and trp/s-2,2,5-tri-

methy1-3-hexene, the experimental NMR based) Gibbs free energy

difference is AG° = 531j:mol-1 (127cal.mo1-1) while the Force Field,

'indicates that the gauche isomer is more stable thanmde s-cis isomer

by 4.9 KJ.mol-1

(1.2 Kcal.mol ). Unfortunately one does nat•know which

force constants got particularly thrown off, but they are likely to

• include the torsional modes and the non-bonded interaction. From

the limited experien.ce available, it appears thatthis error is

almost a constant and therefore not too seriou , in the mono-

alkyl-and trans-dialkyl-substituted ethylene In parti r it is

tentatively concluded that the 0 and (and a d A(1)) d a

pertaining to the calculated structures of minimum energy are

substantially correct for the molecules mentioned. Serious problems were

encountered with the interpretation of the data on cis-2,2,5-trimethy1-3-

hexene and cis-2,5-dimethyl-3-hexene. It was concluded in both cases

• 277


that the calculated structure of the-llowest (or one of the two lowest for

the former molecule), energy is basically correct but that the calcUlated.

second (and third) minimum are totally wrong, both in the sense of -

predicting a too high AG° and in the sense of- putting the energy minimum

at the wrong place (i.e., the wrong dihedral e angle) or, even worse,

possibly overlooking an entire minimum.

The conclusion is that the Force Field requires recalibration;

four reasonably reliable AG° values are now available, in two cases

thereof with rather complete knowledge of the structures involved (in the

other two cases only the ground state structure is adequately known).

The Force Field calculations provide two more bits of informa-,Y

tion, which initially were thouyht rather unimportant, but turned

out to be highly interesting. One of these, the'precise a and Ae infor-

mation together with its use for calculation of J and AJ values has

already been detailed. It appears that no longer one has to rely

exclusively on rotational spectroscopy and electron diffraction to obtain

suc structural data, data which are only availa e experimentally for

small olecules.

More or less as a by-product, the calClations also provide a

list of all the vibrational frequencies and their degeneracies. These

data are essential, however, once entropies have to be calculated. In

earlier studies on conformational equilibria in olefins, it was generally

assumed that AS = 0, that therefore AG = AH and that AG = AE, where AE is

the steric energy differerice of the equilibria minima. As is shown in

this study, AS is rather different from zero and strongly temperature

278


-' dependent and 'even AG° can be quite different from AE. -This means that

even the "sorting out" of energy minima and maxima is hazardous if based

only on Force Field energy calculations, unless supplemented by entropy

calculations. A second ,consequence is that in the least squares fitting

for AG and two. special parameters (the GBM method), one has to correct at

each temperature for the -T AS term: in essence one then data-fits the

experimental values in search for a AH (assumedly temperature independent).

E s. Molecular conformational structure

Trans-2,2,5ztrimethy1-3-hexene was shown to have a conforma-

tional equilibrium with AG° = 531J.mol ( 27cal.mo171), which could be

assigned to an anti4gaicche transition (fo the methine proton) in the

isopropyl group, in complete agreement wig arlie esults on 3-methyl-

1-butene. One consequence of this result i that, apparently, the trans-,

tert-butyl substituent has little or no eff• t on the AG° of the isopropyl

group'. It may well be though that there is such an effect but that it is

so small (smaller than 120J.mo1-1 or 30cal.mo1-1) as.to be hidden in the

error margins of the AG°'s obtained. For this molecule no indication was

found for any conformational process within the tert-butyl group. It is

believed, however, that the Force Field result of pred4pting the most

stable conformation to be with one methyl CH3 group of the tert-butyl

group eclipsing the double bond is basically correct. The finding that a

trans substituent does not noticeably influence the energetics of the

conformational equilibria of the other substituent is important, particu-

larly in application on trans disubstituted ethylenes where both AG°'s

279


I

are non-zero (for example the trans-2,5-dimethy1-3-hexene):

In cis-2,2,5-trimethyl-3-hexene it could be concluded that in

the ground state both substituents have an anti conformation. In addi-

tiori. it seems clear that there exists• ,Inother low-lying minimum (with

AG° = 2.1KJ.mo1-1 or 0.5Kcal.mo1-1), but it has been found impo&siblao

determine the structure:of such a second conformer. It is not even

known whether the conformational change involves primarily the isopropyl

group, the tert-butyl group or both,(concerted rotation). From ,a limited

study of cis-4,4-dimetby1-2-pentene, it appears that there exists no

conformational equilibrium corresponding to a small AG° (i.e., below

6.3KJ.mo1-1 or 1.5Kcal.mo1-1) in this molecule. That would mean that in

cis-2,2,5-trimethyl-3-hexene the possibility of the tert-butyl being

primarily involved in the conformational process can be eliminated.

The results on cis-2,5-dimethyl-3-hexene are similar. There

exists a low energy second conformer, with AG° = 1.13KJ.mo1-1 (0.27Kcal.

mol-1); the ground state is most definitely the anti-anti conformation,

but the structure of the second state could not be determined. The Force

Field prediction of this second conformation being the anti-syn structure

is definitely disproved by the NMR results. The latter are not unequivo-

cal, however, but point as a likely structure to a skew-skew structure as

the second structure.

F Overall conclusion

This study has been an exercise in developing a combination of

variable temperature NMR with Force Field calculation as an independent

280


0.

technique for studying conformational equilibria and the rotamer Struc-

tures involved. It is concluded that the potential of this approach has

been established, but that the full fruition can only ,be expected after

apparent errors in the Force Field calcylations have been removed.

•

281


vok

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