Phosphorus Chernical Shift and Indirect 31P-3LP Spin-Spin Coupling Teasors in Compounds Containhg P-P Bonds: A Solid-State '*P NMR

and Theoretical Study

by

Myrlene Gee

Submitted in partial hilfiilrnent of the requirements for the degree of D w o r of Philosophy

Dalhousie University Halifax, Nova Scotia

lune, 2001

@ Copyright by Myrlene Gee, 2001

National Libmy Bibliothèque nationale du Canada

Acquisitions and Acquisitions et Bibliographie Services services bibliographiques

The author has granted a non- exclusive licence allowing the National Library of Canada to reproduce, loan, distri'bute or seii copies of this thesis in microforrn, paper or electronic formats.

The author retains ownership of the copyright in this thesis. Neither the

L'auteur a accordé une licence non exclusive pefmettant à la Bibliothèque nationale du Canada de reproduire, prêter, distribuer ou vendre des copies de cette thèse sous la forme de microfiche/film, de reproduction sur papier ou sur format électronique .

L'auteur conserve la propriété du droit d'auteur qui protège cette thèse.

thesis nor substantial extracts fiom it Ni la thèse ni des extraits substantiels may be p ~ t e d or othenwise de ceiie-ci ne doivent être imprimés reproduced without the author's ou autrement reproduits sans son permission. autorisation.

For M m und Dad

7 went to the wu& because I wished to live deliberately, tofront only the essential facts of life. and see if1 could not learn whm it had to teuch, and not, when I came to die, discover that I had not lived. "

"1 leji the wmds for as g w d a reason as I weni there. Perhaps it seemed to me that I had several more lives to live, and could not spre any more time for thor one. "

Front Waùien. by Henry David nioreau

Table of Contents Page

............................................................................. Table of Figures vïii

.............................................................................. List of Tables.. xi

Abstract ....................................................................................... xii

...................................................... List of Abbreviations aml Symbols xiii

Chapter 1 : Introduction and Scope

................................................................... 1 . 1 Introduction 1

................................................................. 1.2TtiesisOutline 5

Chapter 2: Background Theory

2.1 NMR Interactions

........................................................... 2.1.1 Overview

............................................... 2.1.2 Zeeman Interaction

.................................... 2.1 .3 Radio Frequency interaction

2.1.4 Nuclear Magnetic Shieldhg and Chernical Shift ............ ................................................. 2.1.5 Dipolar Coupling

2.1.6 J Coupling ......................................................... 2.2 NMR Spectra Arising from Isolated Spin Pairs

......................................................... 2.2.1 Overview

2.2.2 The Dipolar Chernical Shi& Method ......................... .................................... 2.2.3 2D Spin-Echo Spectroscopy

2.3 Ab Initio Calculations of NMR Parameters

.......................... 2.3.1 Nuclear Magnetic Shielding Tensors

................................. 2.3.2 Indirect Spinspin (5) Tensors

Chapter 3 : Phosphocus Chernid Shift Teosors for Tetr amethy ldiphosphine Disulphide: A Single-Crystal P NMR, Dipolar-Chernical Shift NMR and A b Initio Molecular Orbital Study

.................................................................. 3.1 Introduction.. 43

................................ 3.2 Experimental and Computational Details 46

3.3 Results and Discussion

..................... 3.3.1Phosphonis31NMRofaSingleCrystal 51

..... 3.3.2 Phospho~s-3 1 NMR of Crystalline Powder Samples 60

... 3.3.3 Ab Initio Calculation of Phosphocus Shielding Tensors 65

3.3.5 Trends in Phosphorus Chernical Shifts for .................................... Al@ ldiphosphine Disulfides 67

Chapter 4: Characterization of Phosphonis Chernical Shift Tensors in a Phosphole Tetramer: A Combiwd Experimental NMR and Theoretical Study

................................................................... 4.1 introduction 70

................................ 4.2 Experimental and Computational Deuils 71

4.3 Results and Discussion

4.3.1 Experimental Determination of Phosphorus Chernical Shift Tensors ......................... .... ......................... 74

4.3.2 Ab Initio Calculations of Phosphorus Shielding Tensors . . 84

4.3.3 Trends in Phosphonis Chemical Shifts for Phospholes .... 87

................................................................. 4.4 Conclusions 90

Chapter 5: lJelP. "P) Coupling Tensors . Conformational Shidies in Mode1 Systems and Structural Characterization of [Ph, P.PPhJ[GaClJ

................................................................... 5.1 Introduction 91

................................ 5.2 Experimental and Computational Details 94

...................................................... 5.3 Results and Discussion 97

5 .3.1 Phosphorus-3 1 NMR Spectra of [Ph, P.PPhJ [GaClJ ...... 97

5.3.2 Dependence of 1J(31P. "P) on conformation: HLP.PH, vs . ................................. ................... HIP-PH2+ .... 105

vii

.......................... ...............*.....-................ Chapter 6: Conclusions .. 117

Chapter 7: Future Research Directions

................................................................... 7.1 Introduction 120

..................................................... 7.2 [Ph2(CI)P-PPhJ [ChCd 120

7.3 Ab Inirio Calculation of Phosphorus Chemicai Shift Tepsors ........ 122

7.5 NMR Spectra Arising from Three Coupled Homonuclear Spin-% ................................................... Nuclei in the Solid State 127

Appendix 1: Performing the 2D Spin-Echo NMR Experiment on the CMX ....................................... 2ûû at the University of Alberta 129

............................... Appendix 2: Handling Air-Sensitive NMR Samples 131

.................................................................................... References 133

List of Figures

Page

Figure 1.1 Structures of the compounds studied this thesis 3

Figure 2.1 Zeeman ewrgy as a function of B, 10

Figure 2.2 Angles d e m g the orientation of $, rK, and the PAS of the nuclear magnetic shielding tensor 13

Figure 2.3 Typical Iine shapes for an isolated spin in a powder crystailine 16 sample

Figure 2.4 Calculated NMR spectra when the Zeeman and dipolar interactions are present 19

Figure 2.5 Calculated NMR spectra illustrating the effect of dipolar and J couplhg 27

Figure 2.6 Calculated NMR spectra iilustrating the effect of dipolar coupling and anisotropic nuctear magnetic shielding 28

Fipre 2.7 Euler angles relating the PAS of the nuclear magnetic shielding tensor to the molecular frame of reference 29

Figure 2.8 The 2D spin-echo pulse sequence 3 1

Figure 3.1 Structure of tetramethyldiphosphine disulfde, TMPS 45

Fi- 3.2 Phosphorus-3 1 NMR specua of a single crystal of TMPS 52

Figure 3.3 Example of a 31P NMR spectrum of the TMPS single crystal 53

Figure 3.4 Phosphorus chernical shift as a huiction of crystal rotation for TMPS 55

Figure 3.5 Dipolar splitthg as a function of crystal rotation angle TMPS 55

Figure 3.6 Orientation of the phosphorus chemical shift tensor for TMPS 58

Figure 3.7 Experimentai and calculated "P NMR spectra of stationary powder samples of TMPS 61

viii

Figure 3.8

F i r e 3.9

F i r e 4.1

Figure 4.2

Figure 4.3

Figure 4.4

Figure 4.5

Figure 4.6

Fipre 4.7

Figure 4.8

Figure 5. 1

Fipre 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Experimental and calculated 3ïP NMR spectra of MAS samples of TMPS

Experimental and calculated Fi projections of the 2D spin-echo "P NMR spectnim of TMPS

Structure of the phosphole tetramer and the mode1 system used for ab inirio calculations

Experimentai and calculated "P NMR spectra of stationary samples of the phosphole tetramer

Experimental and calculaied 31P NMR spectra of MAS samples of the phosphole tetramer at 4.7 T

Experimental and caiculated NMR spectra of MAS samples of the phosphole t e m e r at 9.4 T

The calculated and experimental Fi projections of the 2D spin- echo 3LP NMR spectrum of the phosphole tetramer

The relative orientation of the two phosphorus chemical shifk teosors in the phosphole tetramer

The phosphorus chemical shifi tensor orientations for the phosphoie tetramer determinecl b y ub initio calculat ions

Structures of compound 5, 6, and 7 in table 4.2

Structures of the molecules discussed in chapter 5

Experimental and calculated 31P NMR spectra of MAS samples of [Ph3P-PPhJ[GaCb] at 4.7 T

Experimentai and calculated 'lP NMR spectra of MAS samples of [Ph,P-PPhJ[GaC4] at 9.4 T

Experirnental and calculated FI projections of the 2D spin-echo 31P NMR spectru~~~ of [Ph,P-PPhJ[GaClJ at 4.7 T

Experirnental and calculated 31P NMR spectra of stationary wwder sam~les of IPhtP-PPh711GaCL1

Figure 5.6

Figure 5.7

Figure 5.8

F g u e 5.9

Figure 7.1

Figure 7.2

Calculated orientation of the phosphorus chernical shifi tenson for (CH,),P-P(CH,),+

Plot of the total energy for H2P-PH2 a huiction of 4, The dependence of 1Je1P,31P) in H,P-PH, on +pp

The depenâence of 1Je1P,31P) in H,P-PH2+ on @,+

Phosphonis-3 1 NMR spectra of solid [Ph,(Cl)P-PPhJ [GaCh] (MAS)

Structure of a phosphonis-containing homonuclear three-spin s ystem

Figure A2.1 A Varian-Chemagnetics rotor

List of Tables

Page

Table 3.1 Selected bond lengths and bond angles for TMPS 47

Table 3.2 Direction cosiaes orienting the crystal axes of a single crystal of TMPS to the NMR cube fiame 48

Table 3.3 Linear least-squares coefficients for the phosphocus chemical shifi and spin-spin coupling interactions in TMPS as functions of crystal rotation 56

Table 3.4 Principal components and orientations of the phosphonis chemical shift and dipolar coupling tensors relative to the crystal axes (a*bc) for TMPS 57

Table 3.5 Spin-spin coupling data for TMPS 57

Table 3.6 The isotropic chemical shift, principal components, Q, and K of the phosphorus chernical shift tensors for TMPS 64

Table 3.7 Cornparison of 8, and C-P-C bond angle for &P(S)], 68

Table 4.1 Experimental and calculateci phosphorus chemical shift tensor principal components for the phosphole tetramer 78

Table 4.2 Phosphorus chernical shift tensor principal components for some phospholes 89

Table S. 1 Phosphorus chernical shift tensor principal components and spin-spin coupling parameters for [Ph,P-PPhJ[GaClJ 101

Table 5.2 1J(31P,31P) for H2P-PH, as a function of @,, 110

Table 5.3 1J(3iP,31P) for H,P-PH,+ as a function of @,,+ 112

Table 5.4 Geometry dependence of 'le tP,31P), for H,P-PH, 114

The combination of solid-state NMR and theoretid calculations to characterize

NMR parameters is applied to compounds containiog P-P bonds where phosphorus

participates in a variety of bonding modes. In particular, phosphorus chemical shifi

tensors and one-bond indirect spin-spin or J-coupling temors, 1J("P,31P), have been

investigated experimentally by NMR and complemented by first-prhciples calculations.

The phosphorus chernical shift and spin-spin coupling tensors for

tetramethy ldiphosphine disul fide are characterized by analysis of 31P NMR spectra

obtained at 4.7 T for a single crystal. These results were compared to those obtained

ftom spectra aquired at 4.7 T and 9.4 T for powder samples. The data obtained from

both methods are in exceilent agreement. It was aiso found that the upper limit on the

anisotropy in 1J(31P,nP), hl. is approximately 450 Hz.

The phosphorus chemical shifi tensors for a phosphole tetramer were

characterized by analysis of "P NMR spectra aquired at 4.7 T and 9.4 T for powder

samples . The experimental NMR results are supplemented by f i s t principles

calculations of the chemical shift tensor. The calculatioos are useful for proposing

chemical shift tensor orientations.

The final example presented here is an investigation of the

phosphinophosphonium sali, ph,P-PPhJ[GaClJ. The structure is not available fiom X-

ray diffraction studies, thus characterization by other means, such as solid-state NMR,

is important. To determine the P-P boad length from the effective dipolar coupling

constant, R,, AJ needs to be estimated, in this case by ab initio calculations on a mode1

system, H,P-PH,+. Combination of the calculated AJ value and the measured Re, yields

a P-P bond length of 2.25 A. Further calculations of 1J(31P,31P) for H,P-PH, offers an

opportunity to iavestigate the dependence of this parameter on conformation. First-

principles calculations allows one to map out the detailed orientation dependence as well

as the potential energy surface.

Lis# of Abbreviatbns and Symbols

10)

B

b

Bo

Bn

Brf

B,

Bi,

CASSCF

CC-pVTZ

CSGT

CP '

D

DFT

DSO

E(B, M)

LIE

ground electronic state

a magnetic field vector

applied magnetic field vector

magnitude of Bo

applied radio frequency field vector

magnitude of B,

amplitude of B,

induced magnetic field vector

complete active space selfconsistent field

correlation-consistent polarization valence triple-zeta

coatinuous set of gauge transformations

cross polarization

dipolar coupling tensor

density hinctiooal theory

diamagnetic spin-orbit

the energy of a molecule

the ewrgy separation between the + Yz and -95 nuclear spin States of I in

the presence of Bo

Fermi contact

finite field

xiii

xiv

ûee induction decay

finite perturbation

Fourier tram form

gauge-iiifluding atomic orbitals

Planck's constant divided by 2%

Hamiltonian describing the chernid shift interaction for I

Hamiltonian describing the dipolar couphg between I and S

Hamiltonian describing the DSO contribution to J

Hamiltonian describing the FC contribution to J

Hamiltonian descr ibing the indirect spin-spin coupling (J-coupling )

between I and S

Hamiltonian describing the PSO contribution to J

Hamiltonian describing the interaction of I with 8,

Hamiltonian describing the SD contribution to J

Hamiltonian describing the Zeeman interaction

Hartree Fock

nuclear spin angular momentun operators

ith component of 1 or S

nuclei with spin of 'h

individuai gauge for localized orbitals

intemediate neglect of differential overlap

LORG

indirect spin-spin coupling tensor

tensor describing the anisotropic part of J

the DSO contribution to J

the FC contribution to J

the FC x SD contribution to J

the PSO contribution to J

the SD contribution to J

J coupling over n bonds between 1 and S (Hz)

principal components of J (Hz)

a component of J (Hz)

component of an axially symmetric J which is perpendicular to the bond

component of an axially symmetric J which is pardlel to the bond

isotropic J coupling (Hz)

anisotropy in J (Hz)

reduced J-coupling tensor (N A-I

Boltzmann constant

angular momentum operator for the &th electron (N denotes with respect

to a nucleus)

localized orbital local origin

the set of nuclear magnetic moment vectors in a molecule

the nuclear magnetic moment vector or nucleus I

xvi

me

ml

MAS

Mes'

MCLR

MCSCF

MP

I n)

An1

N

NMR

o. d.

Pi

PAS

PSO

6 s

ris

=k* rkN

%D

9 n

lm

stt,), ~ ( l r )

efectron mass

z-compownt of the nuclear angular momentum of 1

magic angle splliaing

(2,4,6-tri-t-butyi) phenyl

multiconfipratiod liwar respoose

multiconfiprational sel €-consistent field

Msller-Plesset

nth excited electronic state

population difference between the + H and -95 nuclear spin States of I

total number of I nuclei in a sample

nuclear magne tic resomce

outer diameter

intensity of the vi transition for a homonuclear spin pair

principal axis system

paramagnetic spin-or bit

vector between spin I and S of magnitude r,

distance between I and S

position vector for the kth eeleciroa (N denotes with respect to a nucleus)

the dipolar coupling constant (kHz)

the effective dipolar coupling constant (kHz)

rotational resonance

FDs for the 2D spin-echo NMR experiment

xvii

SD

SO

SOS-CI

SOPPA

STO

T

tl

t2

TBPS

TEPS

TMPS

spindipolar

spin-orbit

sum-over-states configuration interaction

second-order polarization propagator approximation

Slater-type orbital

temperature

evolution time in 2D spin-echo experiment

acquisition tirne in 2D spin-echo experiment

tetrabutyldiphosphine disulfide

teuaethyldiphosphine disulfide

te tramethy ldiphosphine disul fide

phase angle for Bd

polar angle defining the position of q, with respect to the PAS of (3

Euler angles

difference between the values of the Euler angle a for chernical shift

teosors of a spin pair

rnagwtogyric ratio of nucleus I (rad T1s")

chernical shifi tensor (ppm)

principal compownts of 8 (ppm)

a component of 6 (ppm)

xviii

isotropic chernid shifi (pprn)

the angle between B, anci r,

asymmetry in J

polar angles defining the position of $ with respect to the PAS of (J

tip angle

skew

the set of parameters that dehe the wavefunction for a molecule

permeability of vacuum

frequency corresponding to the ith (i = 1,2. 3 or 4) transition for a

homonuclear spin pair

Vii resoaance frequency for a sample

V,f resonance frequency for a reference compound

V rf Frequency of an applied radio frequency field

VKN MAS spinning frapuency

VO Larmor frequency

(3 nuclear magnetic shielding tensor

a,, , or, q3 principal cornponents of (f (ppm)

d diamagnetic contribution to a (ppm)

paramagnetic contribution to a (pprn)

uii a component of U (ppm)

0, isotropie ouclear rnagnetic shielduig (ppm)

xix

nuclear magnetic shielding for a ceference cornpourd (ppm)

duratioa of radio f r q u e ~ ~ y irradiation

dihedrai angle for (CH,),P-P(CH,), +

dihedral angle for H2P-PH,

dihedral angle for H3P-PH,+

angle describing the relative orientation of adjacent phosphole rings in the

phosphole tevamer

rotation angle of a single crystal in a goniorneter about its X, Y or Z axis

span m m )

Acknowledgments

1 would like to thaiilr my Ph. D. supervisor. Rod Wasylishen, for his patience

and support. For his constant encouragement anâ guidance, 1 am grateful. The

members of the solid-state NMR group at Dalhousie University and at the University of

Alberta are acknowledged for al1 their help. In particular, 1 would like to thank Klaus

Eichele for help with the spectrometers and suggestions on many projects. 1 would also

like to thank Dave Bryce, Guy Bernard, Shelley Forgeron. Rob Schurko. Mike

Lumsden, and Scott Kroeker for their interest in my research projects. Special thanks

to Dave and Guy for proofreading this thesis.

Neil Bdord and Paul Ragogna at Daihousie University and Edgar Ocando-

Mavarez at IVIC are acknowledged for samples and suggestions. 1 am grateful to Gang

Wu at Queen's University for suggestions on the phosphole tetramer project. Sian T.

Cameron at Dalhousie University is acknowledged for his contribution to the phosphole

tetramer project as well. I am gratefùl to Jim Britten at McMaster University for his

contribution to the TMPS project. 1 would also like CO thank Brian Millier at Dalhousie

University for his help.

I acknowledge the hancial support of the Natural Sciences and Engineering

Research Council (NSERC) of Canada. the Izaak Walton Killam Trust, and the Walter

C. Sumner Foundation for postgraduate scholarships. Al1 NMR spectra were acquired

at the Atlantic Regional Magwtic Resonance Centre (ARMRC) which is also funded by

NSERC.

Starting my Ph. D. degree at Dalhousie University and finishing at the

XX

xxi

University of Alberta means that 1 have twice the number of friends and colleagues to

thank cumpared to the average Ph. D. candidate. To everyow 1 met at both places.

thank you. F W y . 1 would like to th& my family for al1 their support and

encouragement.

Chapter 1: Introduction and Seope

1.1 Introduction

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful

tools avaiiable for characterizing molecular structure and dynamics in chernistry.

However, it is important to recognize ihat some fundamental questions regarding the

relationship between NMR parameters anâ structure remain. An NMR spectnim is

characterized by a number of parameters, for example the chemical shift and the indirect

spin-spin coupling (or J-coupling) constant. The majority of the NMR literature

concentrates on the measurement of the isotropic values of these parameters and the

application of various empirical niles and correlations to exuact information on

structure and dynamics. For example, one of the most important relationships between

an isotropic NMR parameter and molecular structure is the Karplus relationship, which

describes how the indirect spin-spin coupling over three bonds depends on the dihedral

angle.' However, the chernicd shift and J couplhg are tensor propertie~;~~ hence, it is

essential to characterize the anisotropic nature of these interactions to fully understand

the origins of observed trends. For example, considering only the isotropic chemical

shift leads to the observation of trends which often de@ simple explaaations in terms of

local structure, particularly in the case of phosphorus chemicai shifts."

The determination of the chernical shift tensor, ôoth its principal components and

the orientation of its principal anis system (PAS) with respect to the moletule, is

particularly valuabte due to its close relationship with the local structure and electronic

1

2

proprties of the rnole~ule.~ Nuclear magnetic resooance spectroscopy of solids is ideal

for investigating the tensor nature of these parameters since the interactions are not

usually averaged as in the case of solutioa NMR stuciies . The field of solid-state NMR

is curreatly enjoying an expanding popularity, thanks in part to a number of

experimental advances which have led to applications of this technique to a range of

research problerns, from protein structure to materials science. Recent advances in

computatiod chemistry, particularly with regards to ob initio calculation of NMR

para me ter^,^^*^*' bave resulted in the use of calculated results as a complement to

experimental data.

Ideally, NMR studies using single crystals are desirable since, in principle. the

chernical shift tensor as well as dipolar and J-coupling tensors may be determined

unambiguously. Unfortunately, large single crystals are rarely available; hence, powder

samples must be used. If the system of interest contains an isolated spin pair, some

orientation information can be extracted from NMR studies (see section 2.2).

One objective of my Ph.D. research was to use solid-state I1P NMR combineci

with first-principles calculatioos to characterize the NMR parameters for systems

containhg P-P bonds. The three examples illustrated in figure 1.1 have been selected

for discussion in ihis thesis. For one of these systems, tetramethyldiphosphine

disulfide, 1, abbreviated as TMPS, a singlecrystai "P NMR investigation was carried

out. For another compound, a phosphole tetramer, 2, the NMR parameters were

characterized experimentally using a crystalline powder sample and by theoretical

Figure 1.1 Molecular ssllctures of the compoumls studied by solid-state NMR in this thesis. 1 : tetramethy ldiphosphhe disulfide, TMPS . 2: a phosphole tetraxner. 3: pentapheny lphosphinopho~honium tetrachlorogallate.

4

calculations. In addition, the X-ray crystai structure was redetermined in the course of

this study. For a third compound, pentaphenylphosphinophosphonium

tetrachlorogallate, [Ph,P-PPhJ[GaCb], 3, the X-ray structure was unavailable aad NMR

investigations of solid samples have provided valuable structural information.

There are three themes running through the examples presented in this thesis.

The fist theme concems the orientation of the phosphorus chemical shift teasor as a

reflection of molecular structure. It has been shown that for compounds such as

tetraethy ldiphosphine disuifide, (CH3CH3,P(S)P(S)(CHZCH3)Z , abbreviated as TEPS.

the most shielded component of the phosphonis chemical shift tensor is duected dong

the P = S bond. 1°*11 This observation has also been made in (CH3),PS. l2 Investigation of

the phosphonis chemical shift tensor orientations in TMPS may aid in establishing this

observation as a general phenornenon. On a related note, one assumption about

chemical shift tensor orientations is that the direction of greatest shielding corresponds

to the direction of greatest electron density." Studies of phosphonis shielding in a

phosphole tetramer and a phosphinophosphonium cation, where there are formal lone

pairs on the phosphorus nuclei, affords an opportunity to investigate these trends

m e r .

A second theme concems the indirect spin-spin couplhg tensor between

phosphonis nuclei that are bonded to each other, 1J(31P,31P), and in particular its

aaisotropy, Aï. The investigation of hl in TMPS is relevant here, as is explained in

fiirther detail in section 1.2. Ab initio dculations of 1J(31P,3'P) in mode1 compounds,

H,P-PH, and H3P-PH,+, are potentially usehl for exploring the dependence of

1Je1P,31P) on conformatioa.

The third theme concems the value of ob initio calculations of NMR parameters

as a cornpiement to experimental &ta. The accuracy of calculated chernid shift tensor

orientations is explored in the chapter on TMPS (chapter 3) and calculations of J on a

mode1 system, H,P-PH,+, are applied to the determination of the dipolar coupling

constant, R,, between the phosphorus nuclei in [Ph,P-PPhJ[GaClJ, and hence estimate

the P-P bond length (chapter 5). The contents of each chapter are discussed in more

detail in the following section.

1.2 Thesis Outline

Following a chapter detailing the relevant background theory (chapter 2). the

work on TMPS is describeci in chapter 3. There have been a few NMR studies of

alkyldiphosphine disulfides in the literature. Many solution studies stem from an

interest in the relationship between conformation and indirect spin-spin coupling

between phosphorus nuclei that are directly bonded to each other, 1J~1P,xP).14*15

TEPS1o*ll and tetrabutyldiphosphine disulfidei6 (TBPS) have beeo testing grounds for the

determination of anisotrop y in indirect spin-spin coupling teasors. Ear 1 y sing leîry stal

NMR studies reporteci large anisotropies for 1J(3 LP,31 P) in TEPS and TBPS of 2.2 kHz1

and 1.9 kHz,'6 respectively. The phosphorus chemicai shift and spin-spin coupling

tenson for TMPS (figure 1 .l, structure 1) are characterized by a single-crystal jlP

NMR study and by an iodependent anaiysis of jlP NMR spectra obtained from

crystaliine powdered samples combined with ub inirio calculations. As so much

6

information is available about this system. it also serves as a benchmark for evaluating

experimentai NMR methods as well as ub initio approaches for the characterization of

NMR parameters. Since accurate P-P bond lengths are required for a reliable

determination of AJ, the X-ray crystal structure was redetermined. Data available in the

literature for related compounds provide an opportunity to consider some trends in

phosphonis magnetic shielding.

Chapter 4 summarizes the results for a phosphole tetramer, figure 1.1, structure

2. This compound contains two phosphonis spin pairs, each one consisting of two

three-coordinate phosphorus nuclei directîy bonded to each other ; characterization of

phosphorus chernical shift tensors and spin-spin coupling parameters in such

environments are relatively rare.13*17*18*1920 Ab initio calculations prove to be an

extremely valuable addition to the experimental "P NMR data for a complete

characterization of the two phosphorus chernical shift tensors since single crystals large

enough for an NMR investigation were unavailable for this compound. It was found

that the relative orientation of the two chernical shift tensors reflects the local structure.

Inconsistencies between the NMR data and the published X-ray crystal structurefi

prompted a redetermiaation of the structure.

The structural characterization of pentapheny lphosphinophosphonium

tetrachlorogailate, [Ph,P-PPhJ [GaCL] (figure 1.1, structure 3), by solid-state NMR is

detailed in chapter 5. Phosphinophosphonium saltsa represent a new class of

compounds and are thus important to characterize. X-ray crystal structures are not

avaiiable in the Literanire; hence, characterization by other means is vital. For the

7

example presented in this chapter, ~h3P-PF%J[GaQ]. some structural information is

avaiiable from analysis of "P NMR spectra of solid samples combined with ab initio

caiculation of 1Jc1P,31P). Trends in 1Jc1P,31P) are explored by ab initio caiculatioas on

mode1 systems, H2P-PH2 and H3P-PH2+. in particular. the effect of the conformation is

considered.

Finally, extensions of the research projects describeci here are proposeci in

chapter 7 of this thesis.

Chapter 2: Background Theory

2.1 NMR Interactions

2.1.1 O v e ~ e w

The systems of interest in this thesis consist of homonuclear spin pairs, IS,

where 1 and S refer to spin-% nuclei. To d y z e the NMR spectra for such a spin pair,

the following Hamihonian needs to be considered:

where Nz(l) and MZ(S) are the Harniltonian operators that describe the interaction of 1

and S respectively with the applied external magnetic field, $, termed the Zeeman

interaction. WC) and W S ) describe the interaction of each spin with an applied radio

frequency field, B,. and G ( S ) are the nuclear magnetic shielding (or chernical

shift) Hamiltonians, %,(I,S) describes the dipolar interaction between I and S, and

H,(I,S) is the indirect spin-spin or J-couplhg interaction between the two nuclei. Hz

and 9& are under the control of the spectroscopist, hence they are termeà exzenuzl

Hamiltonians; the remaining ternis are dependent on the Panire of the system anci are

hence referred to as intemal Hamiltonians.

2.1.2 The Zeeman Interaction

The huidamental phenornenon upon which NMR is based involves the interaction

of the nuclear magnetic moment with B, as described by the following Hamiltonian:

where y, is the magnetogyric ratio (in rad T' s'l) of nucleus I and 1 is the nuclear spin

angular momenturn operator. For NMR studies of spin-% nuclei, this is the largest of

the interactions described in equation 2.1. The spin states for I are described by the

quantum number m, which gives the z-component of angular momentum. For a spin-%

nucleus, ml = + '/i or -%. In the presence of Bo, these two states are separated by an

energy, Al?, that is dependent on the magnitude of the applied magnetic field, Bo, as

illustratecl in figure 2.1. The corresponding frequency ,

is called the Larmor frequency.

2.1.3 Radio-Frequency Interaction

To obtain an NMR spectrum, it is necessary to induce transitions between the

allowed nuclear spin states. This is achieved by applying electromagnetic radiation at or

near the Larmor frequency d usually in a direction that is perpendicular to $.

Figure 2.1 The Zeeman enetgy as a fuoction of the magnitude of the applied magnetic field, Bo, for a spin-% nucleus with y, > 0.

Typically , vo fdls in the radio frequency region of the electromagnetic spectrum. The

Hamihonian describing the interaction between I and an applied radio frequency field,

B,, is identical to the Zeeman Harnilionian (equation 2.2) except that the magnetic field

is not static. The magnitude of Bd in a direction perpendicular to B, is B,:

where B, is the amplitude of the applied radio frequency field, v, is its frequency (at or

near vo), and a is its phase. Under the influence of B , the net magnebtion resulting

11

from the nuclear magnetic moments are tipped away from their equiiibrium positions by

an angle 0, = y,B,r, where r, is the duration of the radio fiequency irradiation.

NMR is an inherently insensitive technique, as AE is much less than the thermal

ewrgy, kBT. As a result, the population difference between the m, = + 'A and m, = -!h

States, An,, is very small. Under the high-temperature approximation,

where N, is the total nurnber of nuclei, I , in the sample. Typically , An, / N, is on the

order of 1 O-5 ?

2.1.4 Nuclear Magneâic Shieldhg and Chernieal SWt

The nuclear rnagnetic shielding interaction, described by a second-rank tensor,

0, arises from the interaction of electrons around the nucleus with B, to produce a local

induced rnagnetic field at the nucleus, Bi,:

The auclear rnagnetic shielding Hamiltonkm is:

&-i3c,(~ = y,1*0*B~

in general, O can be expressed as the sum of symmetric and antisymmetric parts

The symmetric tensor, which has compownts such that oi,=oji, influences the line shape

in NMR of solids, whereas the antisymmetric part does not to tint order.*l in

principle, the antisymmetric part can play a role in the relaxation of the nu cl eu^.^ In

this thesis, the symbol O refers exclusively to the symmetric put:

in which there are six independent components. It rnay be transformeci, as with any

symmetric second-rank tensor, to a frarne of reference known as the principal mis

system (PAS), in which the tensor is diagonal:

where a,, , a,, and a, are the principal compownts (in units of ppm) of the nuclear

magwtic shielding tensor. The PAS is related to the molecular frame of reference by

Euler angles, a, P. and y ." There are still six parameters to determine (three principal

components and three Euler angles) to fdly characterize the tensor. In the soiid state,

Figure 2.2 Illustration of the angles which define the orientation of the applied magnetic field, &, and the dipolar vector, rû, with respect to each other and to the principal axis system of the nuclear magnetic shielding tensor for I .

the observed frequency is dependent on the orientation of the crystallite with respect to

B, if the shielding is anisotropic; thus equation 2.3 must be modified to include both the

Zeeman and nuclear magnetic shielding interactions :

i - (a,, sin20 cos2 4 + a, sin29 sin2 4 + a,, cos20) 1 where 0 and 4 are polar angles definhg the position of B, in the PAS of the shielding

tensor, as shown in figure 2.2.

By convention, a,, a a, s a,,, therefore a, corresponds to the direction of

greatest shieldirig. Experimentally, the chemicai shift teasor, 6, is measured rather than

the nuclear shielding tensor, the difference king thai (3 is referenced to the bare nucleus

while 6 is referenced to a prllnary standard:

V.. - oü = u 'Ef 106

h m ) "Ri

where Vii and v, refer to the resonance frequencies of the sample and the reference

respectively. The chemical shift and nuclear magnetic shielding are related as follows:

Since 1 - o, = 1 .O, equation 2.12 simplifies to:

The largest component of the chemical shift teosor, &,,, corresponds to the srnailest

component of the nuclear magnetic shielding tensor, a, ,, in accordance with equation

2.13. Hence 6,, 2 42 2 &33. The isotropie nuclear magnetic shieldiag is '1, the trace of

(3:

with an analogous expression for the isotropic chemid shift, 6,. One can also define

two parameters, the span, Q, and the skew, K. which describe the breadth and sbape of

the powder pattern:27

Span = Q = a,,- a,, = o,*- il3,

3 ( 0 ~ - 0 , ) 3(6,-hu0) skew = n = - -

Q Q

Altematively, the anisotropy and asymrnetry are ofien used; however they have k e n

defined in various ways by different au th or^?^ For a powder sample, in which al1

possible orientations of crystallites are preseat, the NMR spectrum of an isolateci spin

cm have one of several line shapes as shown in figure 2.3, depending on the nature of

the chernical shift teosor. In one case, 6, , = 6, = 6 , (isotropic), in the second case

6, , = 6n or 6 , = b3 (axially symmetric) and in the third case none of the components

are equivalent (non-axially symmetric) .

2.1.5 DipIar Coupüng

Dipolar or direct spin-spin coupling is an interaction between auclear magnetic

moments separated by a vector r, where the subscript indicates nuclei I and S

re~pectively.~ '~ This interaction is anaiogous to the classical interaction between two

Figure 2.3 Typical line shapes for an isolated spin in a powder crystalline sample where a) al1 the principal components of the chernical shift tensor are equal, b) two compownts are equal and c) ww of the components are the same. b) illustrates the difference between the two extreme values for K, +l and-1.

bar magnets.

The dipolar H d t o n i a n is:

where S is the nuclear spin angular momentum operator for nucleus S and D is the

dipolar coupling tensor which is diagonal in its PAS:

if I and S are not magneticaily equivalent, e.g . , a heteronuclear spin pair and:

if I and S are magnetically equivalent, e.g., a homonuclear spin pair. Different types of

homonuclear spin pairs are discussed in further detail in section 2.2. Udike 0, D is

traceless; hence, dipolar interactions are not observed d k t l y in NMR studies of

isotropie fluids. The unique axis of D is dong r, uniess there is anisotropic motion.

The dipolar coupling constant, RD,, in frequency wits (Hz) is defined as follows:

where CI, is the permeability of vacuum and kW-') refers to the vibrationai average of the

cubed intemuclear distauce. Since RDD depends only on (r,-3). the remaining factors

king constants, the dipolar coupling constant is a valuable parameter for structurai

determination by NMR of solids, as will be discussed in greater detail in section 2.1.6

and chapter 5 . The specvum for I coupled to a spin-% nucleus, S, in the absence of any

other interaction except the Zeeman interaction. consists of a doublet centred at the

Larmor frequency of I with a splitting given by RD, (3 cos2 C - 1) if I aod S are not

magnetically equivalent (figure 2.4(a)) and by '1, RD, (3 cos2 C - 1) if I and S are

rnagnetically equivaient (figure 2.4(b)), where C is the angle between Bo and r,. In a

powdered crystalline sample, al1 possible values of C are present, hence a characteristic

powder pattern with a Pake doublet3' is observed. Figure 2.4(c) shows the Pake doublet

for a heteronuclear spin pair while the specuum arising fiom a pair of magnetically

equivalent nuclei is shown in figure 2.4(d). The two subspectra, shown by dotted lines,

illustrate the fact that the dipolar line shape arises from two transitions conesponding to

%,- two spin States of S.

w - . - . - - - - - = - - - - - - - - - = - ~ - = - - - - - - -

1800 1400 1OOO 600 200 -200 -600 -1000 -1400 -1800

Hz Figure 2.4 Calculated NMR spectra for the I nucleus of a spin pair where 1 and S are

a) not magnetidly equivalent aod b) where they are magnetidy equivalent. Bo and r, are perpendicular in this case, i .e., F =!JO0. The corresponding line shapes for powder crystalline sample, where al1 values of C are present, are shown in c) for noomagneticaiiy equivalence and d) for magnetic equivalence. The subspectra shown by doned lines in c) correspond to the two spin States of S. These spectra were calculateci using RD, = 700 Hz.

2.1.6 J Coupüng

Another interaction between two nuclei that may be measured in NMR

experiments is the indirect spin-spin or J-mupling interaction. This is an interaction

whereby a nucleus pemirbs the surrounding electrons. This perturbation is

subsequently transmitted to a second nucleus through the electron network of the

molecule. The streogth of the coupling depends on the nature of the electron network,

hence J coupling is an extremely useful parameter for characterizhg systems where

nuclei are separated by one or more covalent The Hamiltonian for J couphg

between two nuclei is:29S0

where J is a second-rank tensor. Like the nuclear magnetic shielding tensor, J can be

represented by a symmetric and antisymmetric part;' however the antisymmetric part

does not perturb the NMR line shape to first order? In its PAS, the symmetric part of

J is given by :

The isotropie J coupling is:

While J coupling is measured experimentally in units of Hz. cornparison of indirect

spin-spin couplings for different spin pairs is facilitated by using the reduced coupling

teosor, K. which is independent of the magnetogyric ratios of the coupled nuclei:

where K is in units of N A" m-3 or equivalently in TL J? The ensuing defultions also

apply to K.

The features of J may be described by the anisotropy, hl, and the asymmetry,

:2935."

and

where the p ~ c i p a l compownts are assigned accordhg to 1 J, - J., 1 r 1 JI, - J,1 2

22

1 J - J . If J is axially symmetric, then hl = J, - J , where J, is the component dong

the intemuclear axis while J , is perpendicular to it. The indirect spin-spin couplhg

Hamiltonian (equation (2.21)) can be expressed in terms involving only J , and an

anisotropic term which is identical in form to the dipolar Hamiltonian (equation

2. 17):"j2

where

Consequently, it is impossible to experimentally distinguish between the dipolar

coupling and anisotropy in J. Experimentally, one measures an effective dipolar

coupling constant:

In practice, RD, can be calculated fiom equation 2.20 if the intemuclear distance is

known. If RDD differs sipnificantly from the experimental value of R,, then one can

estimate AJ. R& is available from solid-state NMR experiments or, for simple diatomic

molecules, from hyperfine constants measured in molecular beam or high-resolution

microwave spectroûcopy experiment~.~' Since RH and RD, c m have the same or

opposite signs, two possible values of hl result €rom equation 2.29, one of which is

usualiy discardeci since it is much larger than J.,. For coupling involviag lighter nuclei,

hl is often assumed to be negligible; for heavier nuclei, hl can be quite large.33*u For

example, in thallium fluoride, A J ~ T 1 , l ~ = -13.3 * 0.7 While reliable

experimental determinations of A J are scarce,m-3739flA1-42 theoretical calculations of J

otfer an avenue for examiniag the relationship between indirect spin-spin coupling and

structure. Calculations of I from fust pruiciples will be discussed in section 2.3.2.

2.2 NMR Spectra Arising from isolatcd Spin Pairs

2.2.1 Overview

For a system consisting of an isolated spin where the chemical shift is the only

internai interaction present, analysis of NMR spectra arishg from single crystals an, in

principle, yield the orientation of the chemical shift tensor with respect to the molecule.

Unfortunately, single crystals of sufficient size for NMR studies are rarely available.

NMR spectra of powder sampies yield the three principal components of the chemical

shifi tensor; however there is no means of determinhg the tensor orientation relative to

the molecular frame of reference unless the chernical shift tensor is axially symmeuic.

If a dipolar interaction is also present, as in the case of systems containhg isolated spin

pairs, then the spectra of powder samples become sensitive to the relative orientation of

the chernical shîft tensors with respect to r, which of course is in the mlecular frame

of reference .43

Systems where an isolated spin pair is present have been extensively

investigated in the solid state."" As mentioned previously, if two nuclei have the same

magnetogyric ratio, the system is referred to as a homonuclear spin pair; otherwise they

form a heteronuclear spin pair. For a homonuclear spin pair, a further distinction can

be made between magnetic equivdence where the two nuclei are relaied by a centre of

inversion and crystallographic equivalence where the two nuclei are related typically by

a C, axis or a &or plane.2 in the case of magnetic quivalence, the two spins have

identical chetnical shift tensor components and orientations. For nuclei that are

crystallographically equivalent but magnetically non-equivalent, the chemicai shift

tensor components are the same but their orientations differ. The most general case is

observed when the two nuclei are neither magnetically nor crystallographically

equivalent. Spin pairs are often classified as A,, AB, or AX spin systerns. If the two

nuciei are magneticall y equivalent, the y have identical resonance frequencies for any

orientation of the spin pair in $, hence they form an A, spin system. On the other

hand, if the difference between their resomce frequencies is much greater than the

magnitude of the spin-spin couplings (dipolar and indirect), then the spin system is

designateci as an AX spin system. The AB spin system lies between these two extremes.

It should be wted that such a iabelling system is not entirely suitable in solid-state NMR

since the difference in the resonance frequencies as well as the magnitudes of the spin-

spin couplings are orientation dependent. It is possible to have a spin pair that is A, at

one crystallite orientation but AB or AX at another.

In general, homouuclear spin pairs give rise to four iramitions in the solid state

hteWities, pi: lOM45.4W7

where v, and v, depend on v,, a,, , a,, and a,,, and the orientation of PAS of the

shielding tensor with respect to $, given by the polar angles 0 and (figure 2.2). for

each nucleus, accordhg to equation 2.10. The terms A, B, and D are:

1

D = [ (v, - v,)' + BZ]'

For an AX spin system, (v, - v a w B; hence, D = v, - v,. Four peaks are observed, two

26

in the region of the I nucleus and two in the region of the S nucleus. In both cases, the

splitting of the I and S peaks is ) J , - &(3 cos2C - 1) 1 . For an A, spin system, v, = v,,

hence D = B, thus the intemities of v, and v, are zero and the remaining two peaks are

split by 1 J , - ' J , ReH (3 cos2 C - 1)l. An interesthg situation a r k s in NMR spectra of

solids containhg isolated AB spin systems. It is possible for the two outer peaks to be

more intense than the hvo inner peaks." An example of this is presented in chapter 3.

Such spectra are not observed for isotropie fiuids. For a powder crystalline sarnple, the

addition of J coupling modifies the splittiags shown in figure 2.4, as illustrated in figure

2.5. The observed l k shape is dependent on the relative signs of Re, and J,.

2.2.2 The Dipoiar-Chemical Shift Methoà

The combination of anisotropic chernid shifi and dipolar coupling interactions

results in a specirum where each component of the chernical shift tensor is split

according to (in units of freq~ency):~~

for an AX spin pair, where a and P are the polar angles defining the position of r, with

respect to the PAS of in figure 2.2. The expected line shape is illustrated in figure

2.6(a). Although one cannot masure the sign of Av,, the sum of the three splittings

Figure 2.5 Calculatecl NMR spectra for the A nucleus of an AX spin pair illustrating the effect of dipolar and J coupling . For a) J , = +200 Hz, while J , = O Hz for b). J , = -200 Hz for c). Al1 spectra were calculated ushg &fi = 700 Hz and in the absence of anisotropic magnetic shielding.

mut be zero since the dipolar coupling tensor is traceless. One of the subspectra

shown in figure 2.4(c) is stretched out while the other is compressed, as shown in

figures 2.6(b) and (c). For an AB spin system, the overlap of the subspectra due to both

nuclei leads to complex h e shapes, examples of whifh will be discussed in this thesis.

As i.: evident from equations 2.37 to 2.39, the spectnun is sensitive to the

relative orientation of the chernid shift teosor and r,, which is coincident with the

unique component of the dipolar couplhg tensor. Thus sorne information regardhg the

Figure 2.6 Calculated NMR spectrum for the A nucleus of an AX spin pair illustrating the e ffect of dipolar coupling and anisotropic nuclear magnetic s hielding on the line shape . The to ta1 line shape (a) is the sum of the two subspectra, (b) and (c). For this simulation, v, = 81 .O33 MHz, R, = 1.6 kHz, Q = 2 0 ppm, K = 0.0 and r, is coincident with (Le., a= P = O").

chemicaf shift tensor orientation in the molecular frame of ceference is available. This

method of relating the chernical shift tensor to the dipolar coupling is temed the

dipolar-chernical shifi method for characterizing chernical shift tensors. However, since

the dipolar tensor is axially symmetric, there will be an ambiguity as to the orientation

of the shift tensors with respect to rotation about r,. The orientation of each shin

Figure 2.7 Euler angles relating the PAS of the nuclear magnetic shielding tensor to the molecular ftame of reference for nucleus I of a spin pair, IS, where aZ0Q is the original position of a,.

tensor relative to re can be described by a set of Euler angles, a , P. and y,26 as

illustrateci in figure 2.7. The angle P positions r, relative to o, while y determines

whether r, is closer to a,, or a=. The angle a describes the rotation of the chernid

shift tensors about r,; since the dipolar tensor is axiaiiy symmetric, a carmot be

measured relative to an axis fixed in the molecular frame of refereace, hence its value is

arbitrary. However, the difference between the values of a for the two chernical shift

teusors (which wiU be denoted by ha in this thesis) may be determined. Aa defmes the

angle between the projections of the a,, coniponents for I and S on to the same plane. It

should be notai that the angles above are dEerent from those defiaed in figure 2.2.

The analysis of spectra depenàent on as many as six chemical shifi tensor

components, two sets of Euler angles and two spin-spin coupling parameters may seem

difficult if not impossible; however, computer pro gram^^^^-" are available for

caiculating spectra based on the Hamiltonian presented in section 2.1. allow ing a

cornparison with the experimental results. The dipolar coupling constant, RD,, cm be

estimated using bond lengths from diffraction structures if avaiiable. From magic angle

spinning (MAS) NMR spectra, J.,, 6,, and, in some cases. the principal components of

V2 for I and S may be detennined. As well, techniques like 2D spin-echo spectroscopy

are available for homonuclear spin pairs to separate the effect of dipolar and J coupling

from the chemical shift interaction (see section 2.2.3). Acquirhg spectra at two or

more applied magnetic fields is essential as the various spin interactions described in

section 2.1 scale differently with B,,. In practice, al1 the NMR spectra are simulated

until one obtains a set of NMR parameters which gives a satisfactory reproduction of al1

experirnental spectra. In addition, reliable ab Niitio calculations can provide uiformation

concerning the orientations of chernical shift tensors and spin-spin coupling tensors with

respect to the molecular frarne of reference. Ab initio calculations of these two NMR

parameters are discussed in section 2.3.

2.2.3 2D Spin-Echo NMR Spectroscopy

The 2D spin-echo NMR experiment is extremely useful in the characterization of

spin-spin coupihg parameters in systems consisting of isolated homonuclear spin pairs.

CP- spin-echo - i acquisition

contact

Figure 2.8 The 2D spinecho pulse sequence which consists of a CP sequence followeâ by a spin-echo pulse and then the acquisition of an FID.

The spin-spin coupling interactions are separated fiom the chernical shift, allowing for

an independent measurement of R,, and determination of the relative sigm of R, and

I,. The basic 2D pulse seqwnce consists of a preparation period, an evolution time of

duration t , followed by an acquisition tirne, t2.53 The evolution t h e is incremented to

produce a 2D &ta set. The 2D spin-echo pulse sequence,I3 shown in figure 2.8,

consists of the standard cross polarizationM (CP) experiment, under the Hartmann-Hahn

match condition," for the preparation period followed by the evolution time during

which the x spin-echo pulse is applied. The spin-echo pulse has the effect of refocusing

inhomogeneities due to nuclear magnetic shielding, leaving the rnagnetization to evolve

32

exclusively under the influence of spin-spin coupling. In the resulting 2D spectnim, the

Fi projection contains the spin-spin coupling data while the R projection is the normal

ID powder pattern of a stationary sample. Nalcai and McDowellnM have derived

expressions for the fkee induction decays (FïDs). s(tJ and s(ta, of the 2D spin-echo

NMR expriment:

where cos 26 = (v, - v,)ID. sin 26 = BID and the V i s (i = I to 4) are given by

equations 2.30 to 2.33. For an A, or AX spin system in the absence of J coupling , the

dipolar splittings at the 'bonis' of the Pake doublet in the Fl projection will be R, or

R, respectively; however, the d y s i s of 2D spin-echo spectra is complicated by the

possibility of the spin system king A,, AB or AX at different orientations, as

mentioned previously (section 2.2.1). If J , is also present then the splitting in the R

projection is modifieci, sunilar to the case illustrated in figure 2.5. A centre artifact is

ofien observed which has been attributed to imperfect rf pulses.13 Fortunately , the Fl

projection can stüi be caiculated and compareci to the experimental results to extract the

coupling constants. Twodimemional spin-echo spectroscopy has b e n used extensively

to investigate homonuclear spin pairs in the solid, especially in molecules containing

P-P bonds, for example, Mes'P = PMeso (Mes' =(2,4,6-tri-t-butyl) phenyl),17

Wes'NP-PPh3] [S03CF3] 7 Ph2PPPh2, l3 the pymphosphate anion in Ni4P2O7- 10H20,

and Lawesson's reagent. (C,J14ûCH3PS&.59 Specific details regarding performance of

this experiment on the CMX Infinity 200 spectrometer at the University of Alberta are

given in Appedix 1.

2.3 Ab Initio Calculations of NMR Parameters

2.3.1 Nuclear Magnetic Shielding Teiwrs

The theoretical basis for understanding nuclear magnetic properties in ternis of

modem quantum chemistry was established by Ramsey in a series of papers published

between 1950 and 1953.461*62 A commentary on the significauce of these papers was

publis hed in 2ûûû.63 In this section, Ramsey ' s formulation for uuclear magnetic

shielding and modern approaches to the calculaiion of this parameter wül be discussed.

Rarnsey's perturbation approach separates nuclear magnetic shielding into a

diamagnetic, d, and paramagnetic, d , contribution:"

This partitioning is analogous to the separation of magnetic susceptibility into

diamagnetic and paramagnetic parts? For shieldiag, the lull expressions for ad and op

are:60*65

where r, is the position vector for electron k and L, is its angular momentum operator,

both with respect to a chosen origia. The position vector and angular momentum

operator of electron k with respect to the nucleus of interest are denoted by r, and k,

respectively. One Unportant conclusion from the above equations is that d depends

only on the ground electronic state, IO), hence it is a fust-order property and easiiy

caiculated by ab initio methods. However, op is a second-order property , involving

mixing between ground and excited electronic States, 1 d, and is thus more challenging

to calculate.

Nuclear magnetic shielding is very sensitive to the molecular electroaic

structure, hence very accurate electronic wavefunctioos are required for ab initio

calculations at any level of t h e ~ r y . ~ ~ - ~ " - " The development and implementation of

methods to overcorne the gauge origin problem (vide infia) bas lead to hirther progress

in calculations of shielding tensors. Ab initio calculation of nuclear magnetic shielding

tensors may be usefui to resolve the ambiguity involved in assigning tensor orientations

obtained from a diplatchernical shift analysis (section 2 -2.2) The present statu

of theoreticai methods has been swnmarized in a number of ment r e v i e ~ s ~ * ~ * ~ * ~ - ~ ~ * ~ ~ and

wiii be discussed ody briefly in this thesis.

Rather than ushg Ramsey's formulation for nuclear magnetic shieldiag directly,

most modern ab initio computational approaches use an quivalent expression for the

shielding for I in terms of a second derivative of the total electronic energy, E, which is

dependent on a magnetic field, B, and the set of al1 nuclear magnetic moments, M, for a

mole~ule:~

where M, is the nuclear magnetic moment of I . The calculation of a thus reduces to

evaluating derivatives of molecular electronic energies. Methods in which the

derivatives are evaluated numerically are termed f ~ t e perturbation (FP) or fmite field

(FF). In general, though. quantum chernical programs evaluate the derivatives

analytically , which is more computationaily efficient than numerical analys is . In an

analytical evaluation. it is necessary to determine how the wavefunction respoods to the

perturbation arising from the presence of B andor M. Below, equation 2.45 is stated

more explicitly to show the dependence on the wavefûnction:

where 1 is the set of parameters that define the wavefunction. For a given molecule, it

is necessary to determine the response of the wavefunction with respect to the magnetic

field. via the factor allaB, to calculate the shielding for al1 the nuclei.

With the introduction of a magnetic field, a problem arises due to the need to

describe B using a vector potential.Md-mJ1*R It was recognized early on that calculated

nuclear magnetic sbielding varied dependhg on where one placed the origin of the

vector potential, tenned the gauge origin problem. While the choice of gauge does not

affect the results of an exact quantum mechanical treabnent, this type of calculatioa is

generaily irnpractical; hence, the gauge origin wül be a factor in the quality of the

results when one uses approximate wavehinctions constnicted from standard basis sets

included in quanhim chemistry programs. Several methods are used to overcome this

difficulty , including GIAOn and IGLO ." The GiAO (gauge-including atomic orb itals)

method places the gauge origin for the atomic orbitals at the nucleus on which the

orbitais are centred. The GXAOs are also referred to as London orbitaka The IGLO

(individual gauge for localized orbitals) method uses the origin of the molecular orbital

as the gauge origin. Other meihods include LORG (localized orbital local origin

rneth~d)'~ and CSGT (continuous set of gauge transformations rneth~d).'~

The Hartree-Fock (HF) approach, a common model for shielding calculations,

describes the electronic wavehinction by a single electronic configuration and the

influence of the other electrons is introduced as an effective, static field. This

approximation obviously does not account for the effect arising from the motion of

electrons. Electron correlation is the term used to describe the difference between the

HF model anci an exact description of the system. The neglect of elecaon correlation

can cause severe erron in the calculated nuclear magnetic shielding for systems with

37

multiple bonds or formal lone Ab initio methods which allow for electron

correlation, such as Meller-Plesset (MP) perturbation theoryn or multiconfigurational

selfconsistent field (MCSCF) theory,78-79 ofien give better results that HF in such

situations. ql though not strictly an ub initio method, density frinctional theory (DFT)

has aiso been applied to the calculation of nuclear magnetic ~hielding.~*" Recently,

relativistic effects have been considered in conjunction with DFT.= While the Gaussian

suite of pro gram^"*^ hcludes DFT methods, the currently available functionals do not

include a dependence on the magnetic field. hence it is not an improvement on HF

methods in this case?

To assess the quaiity of an ub initio calculation of nuclear magnetic shielding, it

is necessary to compare calculated results with experiment. However, it is the chemical

shift, 8, and wt the nuclear magnetic shielding, o. which is measured experimentally .

Conversion from one sale to the other requires an absolute shielding scale? If the

shielding for the nucleus of interest is known for a reference compound, then

measurement of the chemical shift relative to this compound can be converted to

shielding according to equation 2.13. Absolute shieMing scales have been established

for a nurnber of elements. including carbon," ~ x y g e n , ~ fluorine," and pbosphorus.~

Recently, we proposed a revised absolute shielding d e for chlo~ine.~'

W ith advances in computational techniques and faster cornputers, the quality of

the caîculations is certain to improve. Signifiant progress has been made in the last

few years and ab initio calculations of nuclear magnetic shielding are becoming

integrated into the rnethodology for aaalyzing NMR ~pectra ."*~*~

2.3.2 Indirect SpinSpin Coupiing (4 Teiisors

For reasons outlined below, reliable ab initio calculations of J couplhg are

challenging. Thus, reports have been relatively scarce compared to calculations of

nuclear magnetic shielding tensors. However, the introduction of some new

computational approaches has prompted interest in the ab initio dculation of J. In

addition. the cecent observation of J couplhg across hydrogen bonds95 has resulted in a

number of papers focussing on the caiculation of J coupling in such s y ~ t e m s . % ~ * ~ ~ The

current state of J-coupling calculations has been recently re~iewed.~~"

In Ramsey's thcory of J c ~ u p l i n g , ~ ~ ~ ' ~ several mechanisms for the interaction

between the auclei and electrons are identified. One rnechanism invoives the coupling

between the nuclear spin and the orbital motions of the electron, temed the spin-orbit

(SO) mechanism. A formai distinction is usually made between a diamagnetic (DSO)

and paramagnetic (PSO) contribution. Another mefhanism is the dipolar interaction

between the nuclear and electron magnetic moments, called the spindipolor (SD)

mechanism. The Femi contact (FC) mechanism describes the interaction between a

nucleus and elecuons that have a tinite probability of being at the nucleus of interest.

The J-coupling Harniitonian may be expressed in terms of a contribution fkom

each mechanism:

Secondsrder perturbation theory is used to solve the above Hamiltonian for expressions

describing each contribution to J:

J = J , + J ~ m - ~ S ~ + 'SD-SD + J ~ ~ - ~ ~ + 'FC-SD

where Jwo involves only the ground electronic states of the molecule. J,, has

contributions involving ground and excited singlet electronic states, while the

contributions involvhg SD and FC (J,,, J,,, and J,d depend on ground and

excited triplet states. The full expressions for each tenn are given el~ewhere.~~*l~I It is

important to note that J,, is completely isotropie; hence. it contributes only to I,.

The FC-SD cross term. J,,. is completely anisotropic; hence, it contributes only to

hl. Ramsey's formalism for J coupling does not account for relativistic effects. An

extension of Ramsey's theory to include relativistic effects was developed by Pyykk6.l"

As with calculations of nuclear magnetic shielding , modem ab inifio programs

calculate J as a second derivative of E, in this case with respect to the nuclear magnetic

moments of the coupled nuclei, M, and Ms. Here, it is given in terms of the reduceà

coupling tensor, K(I,S):8*1*

K(M) =

As with nuclear magnetic shielding, the derivatives can be evaluated

numerically , lw*lm*lq or anaîytically . Equation 2.49 may be rewritten as follows to show

explicitly the dependence of the wavefiinction on M:

For each K(I,S) it is necessary to determine the response of the wavefunction with

respect to the magnetic moment of one of the nuclei, via the factor dA/dM,.

Determination of the full set of Jcoupling tensors for a molecule is thus considered

computatiody more expensive than calculations of nuclear magnetic shieldiag, where

al laB need only be determined once to obtain all the shielding tensors.

A nurnber of different models have been used for the calculation of J coupling .

While HF methods have been applied, this approach usually fails because it cannot

accurately describe the contribution from triplet States to the FC and SD mechanisms,

termed the 'triplet iastabiiity" pr~blem.'-~~ This can lead to calculations of Jcoupling

constants with significantly different magnitudes comparecl to experimentim or even the

wrong sign. It has been generally recognized that molecules containing multiple bonds

andfor electron lone pairs should not be investigated using the HF appr~ach.'*~~ More

success has ken obtained with the MCSCF approach. Calculations of I coupling using

MCSCF theory with analytical evaluation of the derivatives in equation 2.49 (tenned

multiconfiguratiooal linear response (MCLR) theory) were fust reported in 1992.'"

The agreement between calculated and experimental results are generally very

good,n*lOg*L1O although this rneihod is still limited to small molecuies. A coupled cluster

approach has also been used in the calculation of J coupiing . l 1 1 ~ 1 1 2 ~ 1 l3 Polarization

propagator methods with acronyms such as SOPPA (second-order polarization

propagator approximation) and CCDPPA (coupled cluster doubles polarization

propagator approximation) focus on the perturbation rather than the

wavehinction.114~115*116*117 Density fiuictional theory has also been applied; the first

attempt was by Fukui in 1976.118 The combination of D R methoâs with a completely

andfical evaluation of the derivatives in equation 2.49 was reported recently . la Some

recent examples of I coupling where relativistic effects are accounted for include results

for MH, (M=C. Si, Ge, Sn, Pb) and Pb(CH,),H.119 A relativistic correction to just the

FC term within the DFT formalism has been d i s c ~ s s e d . ~ ~ Examples of systems where

relativistic corrections have been applied to DFT calculation of J couplhg have ken

reponed. 12l.lZl23

The choice of buis set is crucial in calculations of J coupling. In particular,

accurate representation of the electronic structure near the nucleus is necessary. The

convergence behaviour of correlationconsistent basis sets (denoted cc-pVXZ, where

X=2 to 6) indicaies that the good results are obtained when core-valence s-type orbitals

(cc-pCVXZ) are included, and the best results are obtained with the cc-pVXZ-sun bais

set, where the s-type tùnctions are decontracted and n tight s-hinctions are added.

Unfortunately, these basis sets are not generally available for al1 elements.

If reports of reliable first-principles calculations of J-couplhg constants are

scarce, then reports of calculations of J are rarer still. As discussed previously (section

2.1.6). experimental measurement of l is difficult. However, it is imperative to

characterize the tensor nature of this interaction to understand its relationship to

molecular and electronic structure. Some examples of ab initio calculations of J include

42

work on J(X,193 (X = lH , 13C, l9F)lU and J(*F ,%i). lm Extensive calculations of J in

ditomic molecules established the importance of spin-spin coupling mechanisms other

than FC."*lU The symmetry properties of JPC1,l9F) and J(IgF,l9F) for CFj and

J(19F,170) for OF2 were explored in a subsequent publication. l l0 It has been

demonstrated that the inclusion of relativistic considerations tends to increase AJ. '26

Chapter 3: Phosphorus Chernical Shift Tensors for Tetramet hy ldiphmphine DiSulphide: A Single-Crystal "P NMR, Dipolar-Chernid Shift NMR and Ab Initia Molecular Orbital Study

3.1 Introduction

Alkyldiphosphine disulfides have been of some interest to NMR spectroscopists

due to the relationship between the indirect 31P-31P spin-spin coupling and structure.

The investigation of diphosphine disulfides with various alkyl groups bonded to the

phosphorus nuclei allows one to examine the effect of geometry differences such as the

P-P bond iength or the C-P-C bond angle on the phosphorus chemical shift and spin-

spin coupling temors. Solution NMR studies have been performed, l4 and a few

alkyldiphosphine disulfides have k e n investigated by NMR in the solid state, for

example TEPS (tetraethy ldiphosphine disul fide)lO*" and TBPS (teuabuty ldiphosphine

disulfide).16 Initiai reports indicated that anisotropy in 1J(31P,3'P) for both TEPS and

TBPS was substantial, 2.2 kHz1' and 1.9 kHz, respectively . However, subsequent

work on TEPS indicated that the upper Iimit is 462 Hz.l0

There are no extensive ub inirio studies of phosphorus rnagnetic shielding teosors

in the licerature for these compounds and ab initio calculations of J in molecules of this

size are impractical at the present the. Some experimental and ub in- shielding

investigations of related compounds, the dithiadiphosphetaws, [RSP(S)S], (R = H,

CH,, CH2CH3, Ph, cyclo-C,H,,, CH,Ph, or 4-methylphenyl), and

dithioxophosphoranes, RPS, (R = H, CH,, phenyl, or 2,6dimethylphenyl) have ken

reported.ln For A&P,O,, a signifiant anisotropy in 1Jc'P.3'P) has been reported,

W = 800 f 80 Hz.'=

In this chapter, the characterization of phosphocus chernid shift and spin-spin

coupling tensors for TMPS, 1, by "P singlecrystal NMR is described. The structure is

shown again in figure 3.1 (a) for convenience. These results are compared with lhose

obtaîned from an independent aaalysis of "P NMR specua of crystalline powder

samples. In addition, the quality of ab initio calculations of phosphocus magnetic

shieldiog tensors is evaluated by comparison with the experimental results. Fioally, our

analysis ieads to an upper limit on the anisotropy of 1J(31P,31P) for TMPS.

Cornparison of results obtained from combining NMR studies of crystalline

powder samples with ab initio calculations us results from a single-crystal NMR study

allows one to evaluate the various methods for characterizing chernical shift and spin-

spin coupling tensors. 19*'2g ln principle. the latter experiments provide the principal

components and orientations of the chernical sbiH tensors. as well as dipolar and indirect

spin-spin coupling teasors. Recent advances in hardware and software have made the

single-crystal NMR experiment more efficient.lM This NMR investigation of TMPS is

ideal for such a comparison of data obtained from single-crystal NMR studies vs data

from NMR studies of crystaliiae powder samples and ub initio shielding caiculations. It

is straightforward to grow a large single crystal of TMPS and the molecule is

sufficiently smail, allowing for ub initio caiculations with acceptably large basis sets and

various levels of theory .

Figure 3.1 (a) Schernatic representation of tetramethy ldiphosphine disul fide, TMPS . (b) Labelling scheme for the TMPS structure obtained h m an X-ray diffraction study (see table 3.1). Note that there are two molecules in the asymmetric unit.

3.2 Experimetltal and Computational DdPils

A sample of TMPS was obtained ffom Johnson Matthey Electronics.

X-ray Dam CoLIection Md Processing: For reasons diiussed below, the X-ray

structure of TMPS was redetermined by J. F. Britten at McMaster University. A single

crystal of dimensions 0.02 mm x 0.20 mm x 0.45 mm, fiom a sample of TMPS

recrystallized in CHFI,, was mounted on a glass fiber. X-ray diffraction experiments

were carrieci out on a Siemens P4RA diMactometer (Mo Ka, A = 0.710 69 A, graphite

monochrornator) at room temperature, using the o and 4 scan technique with a CCD

area detector. The maximum 28 value was 55.0". The parameters for the monoclinic

ce11 were o = 18.860(6) A , b = 10.693(6) A, c = 7.021(4) A, and P = 94.608(3)",

with Z = 6. Wiîh formula weight of 186.20 glmol, the calculated density is 1.3 1 1

g/cm3. Of the 5 143 reflectiotis collecteci, 1686 were unique. The data were corrected

for Lorentz and polarization effects and for absorption using an empirical model. 13'

The structure was refmed in C21m,1x where al1 atoms with the exception of

hydrogen atoms were refiwd ushg anisotropic temperature factors. Hydrogen atoms in

their observed positions were refined isotropically. The final cycle of full-manix least-

squares refmement, using al1 unique reflections ( I > 3o(f)) with 101 variable parameters,

converged with unweighted and weighted agreement factors of R = 0.0327 and

R, = 0.0706, respectively. On the final difference Fourier map, the maximum and

minimum peaks correspondeci to 0.384 and -0.260 electrons k3. AU calculations were

performed with SHELXTL. 13' Structural parameters are given in table 3.1 and the atom

labelling scheme is show in figure 3.1 (b) .

47

Table 3.1: Selected bond lengtbs (A) anâ bond angles (O) for TMPS.

Site 1 Site 2

Phosphom-31 Single-Cwal AMR: A large single crystal of TMPS, grown in CHzCiz

with dimensions of approximately 3 mm x 3 mm x 3 -7 mm, was glued into the corner

of a hollow three-sided crystal holder, made from aluminum oxide, measuring 4 mm on

each side. X-ray diffraction methods were used to determine the orientation of the

rnonociinic crystai system with respect to the cube axes (table 3.2). The ce11 axes were

48

onhogoaaiized using Rollett's convention. * The rotation marrix. RJy)It&P)lQ(a),'U

relates the orthogoaalized crystal system and the cube frame of refereace. For our

sample, a = 120.33O, P = 3.M0, and y = 242.72'.

Table 3.2: Direction cosines to orient the monoclinic crystal axes (a, b, c) with respect to the orthogonal NMR cube fiame ( X , Y, Z) as determineci by X- ray diffraction.

X Y z

Phosphorus-3 1 NMR data fiom the single crystai were obtained on a Bruker

MSL 200 spectrometer (4.7 T. correspondhg to a 31P NMR frequency of 81.03 MHz),

using an automated single-crystal goniorneter probe manufacturecl by Doty Scientific.

Rotations were performed about each of the X, Y, andZ axes of the cube, from O" to

180" in 9" increments. Al1 31P NMR spectra were aquired using C p with high power

proton decoupling. A IH xI2 pulse width of 3.1 p. contact tirne of 5.0 ms, acquisition

time of 41 ms, and a recycle delay of 6 s were used. For each spectnun the sweep

width was 50 kHz; 64 transients were adequate to obtain a good signal-to-noise ratio.

For the FID, 3072 K of zero pohts were added to give a total of 40% K data points

49

before Fourier transformation with 50 Hz of gaussian line broadening . AU spectra are

referenccd to 85% H,PO,(q). The peaks in each spectrum were fitted with a gaussian

hinction to obtain the frequencies of the peak maxima. The "P single-crystal NMR data

for each site were analyzed by linear least squares fit to:lM

where f; is the NMR parameter of interest and Ji tracks the rotation angle of the crystal

in the goniorneter about the im mis (i = X, Y, 2). For the 31P chernical shift data of

each site, the position at the centre of each doublet was ploned. In the analysis of the

31P-31P dipolar couplhg interaction, the splitting between the doublets was plotted for

both sites. Phase angles of -2" for the X rotation, -3 for the Y rotation and -6" for the

Z rotation were introduced in order to compensate for errors in the initial goniorneter

positions. The standard analysis of single-crystal NMR data is described e l~ewhere . l~*~~

Phosphom-32 MUR of Powder Soniples: Phosphorus-3 1 NMR spectra of stationary or

MAS powdered samples were aquued on a Bruker MSL 200, a Chernagnetics CMX

Infinity 200 (4.7 T for both, corresponding to a frequency of 81.03 MHz for "P), or a

Bniker AMX 400 spectrometer (9.4 T, corresponding to a frequency of 161.90 MHz - for "P). C F and high power proton decoupling were used for all experirnents.

Double-air bearing MAS probes were used throughout. Samples were packed hto 7

mm (MSL) , 7 -5 mm (Infinity) and 4 mm ( A m 0.d. zirconium oxide rotors. Typical

parameters were lH ~ 1 2 pulse widths of 4 ps, contact times of 1 ms, and recycle delays

of 4 s for MAS and 8 s for statioaary samples. The sweep width was 62.5 lcHz with

typical acquisition iimes of 41 ms. The FlDs were zero fiiied by 40% K points to a

total of 8192 K points before Fourier transformation. AU spectra are referenced to 85 %

H,PO,(q) by using solid NH,H2Pû4 which bas an isotropie phosphorus chernical shift

of 0.8 ppm from 85 96 HjPû4(aq).

Phosphorus-3 1 NMR spectra of stationary samples were simulated using

WSOLIDS,49 a program developed in this laboratory which incorporates the PûWDER

routine of Alderman et al. 13' NMR spectra of MAS samples were caiculated using

NMRLAB,M which uses the Monte Car10 method to sample crystal orientations for

powder averag hg. In Our calculations 10,000 cry stallite orientations were used for the

powder averaging.

The 2D spin-echo NMR spectnun was acquired on the CMX Infuiity 200, using

a standard spin-echo pulse sequence with the phase cycling of Rance and Byrd. The

experimental parameters were similar to those used for the 1D experiments. To obtain a

2D data set, 64 increments of C, ( s e figure 2.8) were sufficient. A sweep width of 12.5

kHz in the FI dimension was used. The data size for the 2D spectnun was 512 x 128

after zero filling. Gaussian Line broadening of 100 Hz was applied to both dimensions,

then the data were pracessed in magnitude mode. The FI projection of the 2D spectrum

was calculated using SpinE~hoI~~ which uses equatioos 2.40 and 2.41.

Comp~ctc~lio~l Detaik: Ab initio calculations were perfonned using the Gaussian 98

suite of programsM running on an IBM Ml6000 cornputer. The phosphorus nuclear

magnetic shielding was caiculated using the atomic coordinates from the X-ray structure

51

deterrnined in this work. Calculations were performed using the GIA0 methodn at the

HF level of theory as well as with DFT. For the DFT calculations, the k k e three

parameter functi~nal'~ ushg the Lee, Yang, and Parr correlation functio~all*~ (B3LYP)

was used. To compare calculated results with experimental results, the calculated

phosphorus nuclear magnetic shielding was converted to chemicai shift using the

absolute shielding of 328.35 ppm for the phosphorus nucleus in the reference, 85%

w w 0 q )

3.3 Results and Discussion

3.3.1 Phosphorus-31 NMR of a Sigle Crystal

The "P NMR spectra obtained from a single crystal of TMPS are shown in

figure 3.2. The X-ray structure of TMPS indicates the presence of six molecules in the

unit cell. In two of the six molecules, the two phosphorus nuclei are related by

inversion symmetry, hence they are crystallographically and magnetically equivalent,

Le., they form an A, spin p a p (site 1). In the singleîrystal NMR study , site 1 gives

rise to a doublet where the splitting is the 3LP-31P effective spin-spin coupling at that

particular orientation of the crystal in the applied magnetic field, B,,. Since 1 l J(31P,31P) 1

measured in solution is less than 20 Hz,142 the splitthg is dominated by Ren. The

remaining four molecules (site 2) in the unit ce11 of TMPS possess &or planes that

include the S-P-P-S plane; however the phosphonis nuclei are not related by a centre of

inversion; hence, they are not cry stallographidy equivalent .

52 x-rotation y-rotation z- rotation

Figure 3.2 Phosphorus-3 1 NMR spectra of a single crystal of TMPS for rotations of the crystal holder about its X, Y, and Z axes, acquired at 4.7 T .

In most of the NMR spectra of the TMPS single crystal (figure 3.2), four peaks are

evident. The two of lesser intensity are assigned to site 1 and the more intense set is

assigned to site 2 since the two sites are present in a 1:2 ratio. It is not obvious in

figure 3.2 that site 2 is an AB spin system, since the expected four transitions (section

2.2.1) are not immediately apparent. In fact, very few of the rotations produce NMR

spectra where there is any evidence of an AB quartet; one example is sbown in figure

3.3. Since there are kufficient data to analyze site 2 as an AB spin system, it bas been

analyzed as an A, spin system. The plots of the chernical shift and the dipolar splining

Figure 3.3 Example of a 3'P NMR spectcum of the TMPS single crystal (from the rotation about the Y axis of the crystal holder, at 36" €tom the initial position). The asterisks indicate the four peaks attributed to site 2.

54

as a function of crystal rotation are shown in figures 3.4 and 3 3, respectively . The

coefficients of the linear least squares fit to equation 3.1 for the chemical shift tensors

are given in table 3.3. The components of the chemical shift tensors, b,, , an and a,,

and theu respective direction cosines relative to the orthogoaalhed crystal frame of

reference are given in table 3.4. As is evident in this table, the principal components of

the phosphorus chemical shift tensors for sites 1 and 2 are virtually identical. The

orientation of the tensor is illustrated in figure 3.6(a) for site 1. The principal

component of the phosphorus chemical shift tensor which corresponds to the direction of

greatest shielding , 6,,, is closest to the P-S bond, while 6, , is approximately

perpendicular to the plane containhg the S-P-P-S bonds. with a P-P-6,, angle of 83".

The angle between 4, and the P-P bond is 124" for site 1. The chemical shift tensor

orientation at the other phosphocus nucleus of site 1 is shply an inversion of the one

shown in figure 3.6(a). For site 2, the phosphorus chemical shift tensor is oriented in a

similar fashion with respect to the molecule, with a,, at 2.5" fkom the P-S bond and the

P-P6, , angle of 100". The presence of a mirror plane in site 2 requires that the P-P-6,,

angle be exactly 90" ; however, the magnitude of b,, and 6= are similar , thus it is

difficult to determine theu orientations indepeodently . Io

The principal components of the dipolar coupling tensors are given in table 3.4

with their respective direction cosines. The spin-spin couplhg data for TMPS are also

summarized in table 3 .S. As mentioned in section 2.1.5, the dipolar coupling tensor in

its principal axis system is axiaüy symmetric and traceless, with the unique axis dong

the intemuclear vector. The non-zero trace and very slight non-axial symmetry of our

rotation angle / degrees

Figure 3.4 Phosphorus chernical shifi as a fuoction of rotation angle, Ji, for sites 1 and 2. The curves represent the linear least-squares best fit to the experimentai data, shown as O for site 1 and as O for site 2.

-$O00 --

. 1 . , . , . , ~ . 1 . ~ . [ . ~ 1 . 1 . 1 S , . ~

O 2 0 4 0 6 0 0 0 0 2 0 4 0 6 0 8 0 0 2 0 4 0 6 0 8 0

rotation angle / degrees

Figure 3.5 Dipolar spliuiog as a hinction of rotation angle, $, for sites 1 and 2. The curves represent the iinear least squares best fit to the experimental data, shown as O for site 1 anâ as O for site 2.

Table 3.3: Linear least-squares coefficients for the phosphorus cheraical shift and spin-spin coupling interactions in TMPS as functioas of crystal rotation about the cube X, Y, Z axes."

rotation Ai si ci - - -

site 1 (A3

chernical shifeb X 60.18(4) 26.93(6) 8.851(6)

Y 7.406(6) 25.85(8) 62.88(8)

Z 34.72(5) -53.47(7) 17.77(7)

spin-spin couplh@ X -1.37(5) 3.54(7) 0.48(7)

Y -1.15(2) -3.50(2) - 1.22(2)

Z 2.4 lO(7) -0.09(1) -0.06(1)

site 2 (AB)

chernical shift! X 7 1.98(2) 17 .72(2) 4. 295(2)

Y 8.046(4) 47.54(5) -48.33(5)

Z 27.45(3) -62.51(3) 1 1.74(4)

spin-spin couplingc X - 1 .45(4) 3.62(6) O. 52(6)

Y -1.1 l(2) -3.70(3) -Q.37(3)

Z 2.490(4) 0.013(6) -0 .O 1(6)

The phase angles for the best fit to the experimental data are -2Ofor X, -3 O for Y and -6" for 2.

Units of ppm. ' Units of kHz.

Table 3.4: Principal cornponents and orientations (direction cosines) of the phosphorus chernical shift and dipolar coupling tensors relative to the orthogonalized crystal axes (a*bc) for TMPS.

a* b c

site 1 (A3 61, / P P ~ 90.6 -0.1417 0.9836 O. 1 140

/ P P ~ 74.9 -0.5171 -0.1717 0.8385

633 / P P ~ -63.2 0.8441 0 .O599 0.5328

DI 2.538 O .9805 4.1405 0.1373

DdkHz 2.365 O. 1430 0.9897 -0.008I

h3/kHz -5 .O08 -0.1348 0.02753 0.9905

site 2 (AB)

51 I / P P ~ 9 1.8 -0.1120 0.9795 -0.1621

W P P ~ 74.4 0.3955 0.1964 0.897 1

W P P ~ -58.8 0.9106 0.0435 -0.41 10

D, ,/kHz 2.566 0.9916 -0.1273 0.0237

D&Hz 2.358 O. 1280 0.9946 4.0239

D3311rH~ -4.994 -0.0204 0.0268 O. 9994

Table 3.5: Spin-spin coupling data for TMPS.

Method &/kHz ReRIWz RDDIlrHz (JhIIHz W l H z - --

single crysral site 1 (Ad -0.035 1.669" 1.818 18.7b 447

site 2(AB) 4.023 1 -665" 1.816 - 453

2D spin echo - 1.6W - - -

a Estimateci experirnentai error is f 0-050 kHz. From reference 142. ' Experimentai error is f 0.080 kHz.

Figure 3.6 Orientation of the phospliocus chernical shift tensor for TMPS as determinet! by (a) a single-crystal NMR study and (b) ab initio (HF) calculations. The orientations are shown for site 1. The plane of the page coatains the S-P-P-S moiety. In both cases, 6 , , is approximateiy perpendicular to the plane of the page.

dipolar coupling tensors is likely a consequence of experimental erron in the

single-crystal NMR experiment. In addition, anisotropic molecular motion may

c~nt r ibu te .~~*l~~ The experimental values of Rcn are 1.669 f 0.050 lcHz for site 1 and

1.665 * 0.050 Wz for site 2, detennined by averaging Rar obtained from each of the

diagonal components of D (table 3.4). The rotation plot for the dipolar splining (figure

3 -5) indicates that the unique axis of the dipolar teasor, whicb is dong the P-P bond, is

very close to the 2-axis of the cube, since the dipolar splitting for both sites is

59

essentially invariant to rotation of the crystal about that axis. This impiies that r, anci

B,, are approximately perpendicular (c =go0) during the rotation about the Z axis; hence,

a splitting of '1, Rd is observed.

From RD, calculated ushg the P-P bond leagths reporteci in the X-ray crystal

stnicture'" and Re, determined experimentally, one can estimate hl as describeci in

section 2. 1.6.29 The most recently published crystal structure of TMPSIU reports a

signifiant and unexplained difference in the P-P bond lengths of sites 1 and 2,

r = 2.245(6) A and r = 2.16 l(4) A respectively , correspoading to RD, = 1.74 & 0.04

kHz and, using equation 2.29, hl = 0.3 & 0.05 kHz for site 1, while RD, = 1.95 * 0.03 kHz and AJ = 0.9 * 0.05 kHz for site 2. This is clearly suspicious, prompting

our redetermination of the X-ray crystal structure. From our investigation, the general

features of the X-ray structure are similar to those previously reporteci; however the

difference in the geomevy between the two sites is much less dramatic. The P-P bond

lengths from Our X-ray data are 2.2137(14) A and 2.2144(10) j\ for site I and site 2

respectively, resulting in more reasonable values of R, (table 3.5). For site 2, the

major stmctural difference between the two (CH,),PS fragments is the C-P-C bond

angle (106.0(2)" vs 105.5(2)"; see table 3.1). Using our values of RD, for both sites,

the upper limit on AJ(31P,NP) is approximately 450 Hz. in addition, there may also be a

contribution h m librationai motion of the rnolecule, which results in a smaller

observed value for the dipolar coupling constant. The reduction in the dipolar coupling

constant has been estîmated to be between 3 and 5 Sb .45(a)*14S*'Jb

3.3.2 Wospho~s-31 NMR Spectra of Crystalliae Powder Spmpks

The "P NMR spectra of powder sarnples of TMPS were analyzed independently

of the single-crystal work. Before aoalyzhg the 31P NMR spectra of statioaary (figure

3.7) and MAS (figure 3.8) crystalline powder samples of TMPS. the effective dipolar

coupling constant can be measured independently using the 2D spin-echo e~perirnent.~'

From simulations of the Fi projection (figure 3.9) of the 2D spin-echo NMR spectnun,

Rd = 1.69 f 0.08 kHz, in good agreement with the single crystal data. in the

simulations, it is assumed that 11J("P,31P)I = 18.7 Hz which is the value measured in a

previous solution NMR study . 14'

The NMR spectra of the statioaary samples (figure 3.7) are simulated using the

value of Reff from the 2D spin-echo NMR spectrum to obtain the chemical shift tensor

principal components given in table 3.6 and tensor orientation information discussed

below. The principal components of the phosphorus chemical shift tensors as obtained

from the single-crystal NMR study (table 3.4) are reproduced in table 3.6 for

cornparison. The NMR spectra of MAS samples, spinniag at various kequencies, v,,

(figure 3.8) were calculatecl ushg the same parameters as obtained from the stationary

samples, with the exception of the isotropic phosphom chemical shifts for sites 1 and

2. More accurate isotropic chemical shifis are available from the "P NMR spectra of

MAS samples. For site 1, 6 , = 34.9 ppm while for site 2, two peaks are evident at

37.4 ppm and 37.0 ppm (figure 3.8(a), inset). The 31P NMR spectra of MAS samples

c m be successfidly simulated based on this Uiformation and the data obtained from the

Figure 3.7 Experimental and calculated 31P NMR spectra of stationary powder samples of TMPS, acquired at (a) 4.7 T (500 transients, 20 Hz gaussian Liw broadening) d @) 9.4 T (7010 transients, 25 Hz gaussian line broadening). The same experimental NMR parameters were used to simulate the observed spectra at both fields.

Fgw 3.8 Experimental and calculateû "P MAS NMR spectra of TMPS aquired at (a) 9.4 T with v, = 4.00 kHz (172 transients, 10 Hz gaussian line broadening). The inset shows details of the isotropic region. The bottom spectrum (b) was obtained at 4.7 T with v, = 4.00 lcHz (64 transients, 10 Hz gaussian line broadening). The asterïsks hdicate the isotropic

v 1 . w m.

4 2 O -2 -4 k H z

Figure 3.9 Experimentai and calculateci F1 projection of the 2D spin-echo "P NMR spectm aquired at 4.7 T. The large centre peak (mincated in this figure) is an experimental artifact.

simulation of the NMR spectra of statiooary samples. Since the single-crystal NMR

spectra exhïbited very littie AB character, the subtle difference between the non-

quivalent phosphorus environments in site 2 was not apparent from that analysis.

While one cm, in principle, fit the "P NMR spectra to obtain al1 the chernical shift and

coupling information, these spectra (figure 3.8) are essentially featureless, heace it was

necessary to also analyze the NMR spectra of stationary samples, acquired at different

applied magnetic fields (figure 3.7). In addition, one cannot apply the Henfeld-Berger

appr~achl'~ to the spinning sideband manifold of the MAS specua due to the presence of

strong dipolar c~upling.'~

Table 3.6: The isotropie phosphow chemicai shift (ppm), principal componenis of the chernical shift tensot (ppm), Q (ppm), and K. for TMPS.

single crystal site 1 34.3 site2 35.7

stationary powder (4.7 T, 9.4 T) site 1 34.3 site 2 36.0

MAS powder (4.7 T, 9.4 TT site 1 34.9 site 2d 37.0

37.4 HF16-3 1 1G4*

site 1 -19 site 2d -19

-17 HF16-3 1 lG(3df,3pd)

site 1 10 site 2d 10

11 B3LYP16-3 1 lG(d,p)

site 1 52 site 2d 50

52

u n = a,, - 5n; K = 3 - 5, y Q. Experirnental error in the principal components is f 2 ppm. Experirnental error in 6, for site 1 is f 0.03 ppm and f 0.04 ppm for site 2. The phosphocus nuclei at site 2 are not chemically quivalent; hence, two sets of

principal components are given.

In addition to obtaining the principal components of the phosphorus chernical

shift tensors, some tensor orientation information is available from the anaiysis of NMR

spectra of powders containing isolated spin pairs such as those in TMPS. As describeci

in section 2.2.2 the orientations are commoniy described in t e m of Euler angles, a, P

and y .26 The 31P NMR spectra of stationary samples (figure 3.7) were successfully

simulated using A a = 0' for both site 1 and 2, indicating that the &, components for

adjacent phosphorus nuclei lie in the same plane. The angle between 6 , and the P-P

bond, P, is 63" * 3' for site 1 and 65" f 3" for site 2, equally welldescribed by the

supplement angles, 1 17' and 1 lSO, respectively . The orientation of the principal

components of the phosphorus shielding tensor obtained from a dipolar-chernical shift

analysis is clearly consistent with the single-crystal NMR results.

3.3.3 Ab Inilto Caicuiation of Phosphorus Shielding Tensors

The calculated principal compownts of the phosphorus shielding tensors for

TMPS are given in table 3.6 and the orientation for one phosphorus nucleus in site 1 is

shown in figure 3.6(b). The calculated phosphorus chernical shift tensor orientations for

site 2 are similar. Using the 6 3 1 1G** bais set, the HF results for 6 , are about

53 ppm too shielded for both sites; however, the line shapes, as described by 0 and K,

are remarkably accurate. Increasing the size of the basis set to 6-3 11 + +G(3df,3pd)

improves the calculated value of 6,; however, it is stiU too shielded by about 24 ppm

for both sites. The values from D R calculatioos are deshielded by only 16 ppm

compared to experimental resuits, but Q is overestimated. Differences between the

66

isotropie chemical shift measured in the solid state compared with results from ub initio

caiculations are expected since the calcuiatiom are performed on an isolated molecule.

The intermolecular effects may be substantiai. For example, PH&) is more shielded by

28 ppm compared to PH3(1)90 and P4(g) is more sbielded by 93.0 ppm compared to

P4(f).'4g This is a general trend that nuclei in the gas phase are invariably shielded

compareâ to the condeased phase. lM The ub initio meth& reproduce phosphocus

shielding tensor orientations quite well (figure 3 A).

3.3.4 Cornparison of Results

The phosphorus chemicai shift and spin-spin coupling tensors for TMPS obtained

by analysis of 31P NMR spectra of crystalline powder samples are in excellent

agreement with the single-crystal NMR study. The value of R, measured by both

single-crystal NMR and the 2D spin-echo experiment compared to RDD calculated from

P-P bond lengths places an upper limit hl (about 450 Hz), substantially smaller than

originally estimated for similar compounds.~~~ The phosphorus chemical shift tensors

obtained from both single-crystal and powder methods are virniaily identical. In

addition, apalysis of 31P NMR spectra of MAS samples at 9.4 T provide additional

details regarding the chemically noa-equivalent phosphorus nuclei of site 2. From fhe

analysis of the NMR spectra of stationary powder samples, the principal components of

the phosphorus chernical shift tensors are determineci. The orientations of the most

sbielded components relative to the P-P bond as well as to each other are obtained. For

both site 1 and 2, the direction of greatest shieldhg is in the same plane and are closest

67

to the P-S bond. This is consistent with the orientation in other systems coutainhg P=S

bonds.Lo*11*12 Unfortunately, the orientation of the teasor in the molecular frame of

reference can not be detennined by powder NMR methods. The hi11 tensor orientation

is available experimentally from the single-crystal NMR study (figure 3.6(a)). The

orientation information obtaiwd from the powder methods are consistent with the

single-crystal resuits.

The ub inirio rnethods employed in this work produce line shapes that are in

good agreement with experimental results. in addition, the calculated nuclear magnetic

shielding tensor orientations are aimost identical to those obtairied from the single-

crystal NMR study. The invariance of the nuclear rnagaetic shielding tensor orientation

with basis set suggests that calculations at the HF level of theory with moderate-sized

basis sets are adequate for obtaining the shielding tensor orientation. This is

particularly usehl for large systems, where high-level caiculations are very difficult due

to limi ted computational resources .

3.3.5 Trends in Phosphorus Chernieal Shifts for Akyldiphospbiw DisuIfides

It has been suggested that the isotropie chemical shift at the phosphonis nucleus

is directly related to the C-P-C bond angle in alLyldiphosphine disulfides." With the

characterization of the phosphonis chemical shifi tensor in TMPS, this correlation can

be examinec! more rigorously. Table 3.7 lists the phosphorus chernical shift data and

the C-P-C bond angle for [R,P(S)12 where R = CH, ( t h work), CHFH3, 'O n-propyl, 15'

or n-butyl. l6 It is difficult to draw any detinite conclusion based on the first three

compods in the series, partly due to the expetunenml uncertainty in the C-P-C bond

angle; however, it appears that the isotropic shielding trend does not follow the bond

angle, i.e., increasing bond angle does not correlate directiy with an increase or

decrease in the isotropic chernical shift. Attempts have also been made to explain the

difference between the phosphorus chernid shift for R=n-propyl and R = n-butyl by

an effect sirnilu to the y -effect in 13C M. I l b Trends in the principal components of

the phosphorus shift tensors should be considered, as has been done, for example, in the

case of the dithiadiphosphetanes, [RSP(S)S], (R = alkyi or For the

aikyldiphosphine disulfides, the lirnited data available on the phosphonis chemical shifi

tensors (table 3.7) indicate that the intermediate component, &, changes the most (by

about 23 ppm) upon going fkom R = CH, to R = CHFH,. The smallest component,

6, , , changes by about 17 ppm and q3 by about 7 ppm. By contrast, al1 the principal

components are similar for R = CH2CH, compared to R = n-butyl. Unfortunately, no

data on the phosphocus chemical shift tensor are available for R = n-propyl.

Table 3.7: Cornparison of 6, and C-P-C bond angle for [R,P(S)],.

bYO / ppm 8 , ,1 ppm & 1 ppm 833 1 ppm C-P-C ! deg

CH, (site 1)" 34.1 91 75 -63 105.7(2)

n-propyl ' 45.9 - - - 1 07.8(2)

n-butyl 49.5 104.7 97.5 -53 -7 - (multiple sites)d 49.7 106.3 % -53.1

a This thes is. Reference 10. NMR &ta fiom reference 15, X-ray crystal structure from ref 151. NMR &ta from reference 16, m crystai structure available.

3.4 Conclusions

The characterization of the phosphorus chexnical shift anâ spin-spin coupling

tensors for TMPS presented in this paper serves as a benchmark for the evaluation of

experimental NMR powder methods as well as the reliability of ab inirio methods. The

excellent agreement between the calculated and experimental phosphorus chernical sbift

tensor orientations is particularly encourzighg . For TMPS, as for TEPS, l0 AJ(31P,3LP) is

less than 500 Hz. A number of aikyldiphosphiw disulfides have been characterized by

NMR and attempts have been made to account for trends in the isotropie phosphorus

chemical shifts; however, it is c1ear that the entire phosphorus chemical shift teusor

must be considered. In addition, the structural data available in the literature for

alkyldiphosphhe disulfides are limited, hence correlations between a particular

structural feature in this class of compounds aod the phosphom chemical shih are

tenuous at bes t .

Chapter 4: Cbaracterizltion of Phosphorus Chemicai S M Tenson in a Phosphole Tetramer: A Combined Experimentai NMR and Theoreticai Study

4.1 introduction

The phosphole tetramer, 2 (figure 4. l), was first synthesized in 1982lS and the

X-ray crystai structure was reported s~bsequently.~~ Solid-state NMR investigations of

similar systems where two three-coordinate phosphorus nuclei are directly bonded are

relatively rare.i3*17*19a In the case of the phosphole tetramer, analysis of the "P NMR

spectra acquired with cross polarhtion and MAS revealed a difference in the isotmpic

phosphorus chernical shifis of 1.7 ppm with 1J(31P,31P)I, = -362 Hz.153*Ls Here, we use

the presence of phosphonis spin pairs to characterue the phosphorus chernical shift

tensors via the dipolar-chernical shift NMR method (section 2.2). In contrat to the

earlier 31P NMR investigations of MAS sarnples,lB-lY NMR spectra of stationary

samples obtaiaed at different applied magnetic fields are hilly analyzed. It is also

demonstrated that analysis of the "P 2D spin-echo NMR spectnun of the phosphole

tetramer is invaluable for refiniog the coupling parameters. Ab inifio calculaiions

complement the experimental data and suggest orientations of the phosphonis chernical

shift tensors in the molecular frame of reference. Inconsistencies between the NMR

data (vide infa) and the original X-ray data2' prompred a redetermhtion of the crystal

structure.

Figure 4.1 Molecular structures of the phosphole teuamer (2) and the mode1 structure for 2 used for ub initio calculations (4). For clarity, the methyl and phenyl groups have ben removed f'om the 3D representation on the left .

4 3 Experimentai and Computatiod DetPitF

The synthesis of the phosphole tetramer has been describeû previ~usly.'~~ A

sarnple was provided by Professor F. Mathey (DCPH Ecole Polytechnique).

Phosphorus-31 W R S p e m : Al1 )'P NMR spectra of stationary and MAS sarnples

were acquired on Bniker MSL 200 (4.7 T), Chemagnetics CMX Infinity 200 (4.7 T)

anci Bruker AMX 400 (9.4 T) spectrometers operating at NMR frequencies of 81.03

MHz and 16 1.98 MHz, respectively . Cross polarizations under the Hartmann-Hahn

match condition and hi&-power proton decouplhg were us& for d l NMR experiments.

72

At the lower field, double air beariag MAS probes were useâ with the sample packed in

7 mm O .d. (for the MSL) and 7.5 mm O .d. (for the C m zirconium dioxide rotors.

For the stationary sample, a lH ni2 pulse of 3.6 ps, contact time of 5 ms, acquisition

tirne of 43 ms, and a recycle delay of 5 s were used. A sweep width of 24 kHz was

used and 100 Hz of gaussian line broadening was applied before Fourier transformation.

For spectra acquired with MAS at 1.50 or 2.00 kHz, simüar pulse widths were used.

The acquisition time was 20 ms and the sweep width was 40 kHz. A total of 40% data

points were acquired. Before Fourier transformation, 40% zero points were added and

10 Hz of gaussian line broadening was applied.

A double air bearing MAS probe was used at the higher tield as well, with the

sample packed in a zirconium dioxide rotor (4 mm 0.d.). For both MAS and statîonary

saniples, a IH x/2 pulse of 3.6 ps with a contact t h e of 3 ms and a recycle delay of 10

s were used. For the stationary sample, an acquisition time of 8 ms was used. The

sweep width was 65 kHz and 1024 points were acquired. The data were zero filled by

1024 points and 100 Hz of gaussian line broadening was applied. With MAS at 2.00 or

4.00 kHz the sweep width was 100 kHz and acquisition time was 30 ms. In total, 4096

points were aquireû and zero filleci by 40% points. Gaussian line broadening of 20 Hz

was applied before Fourier transformation. Al1 IIP NMR spectra are referenced to the

primary standard, 85% HIPO,(aq) by setting the jlP isotropie peak of solid JY&H,PO,

to +O. 8 ppm. Spectra of stationary samples at both fields were sirnulateci using

WSOLIDS.4g Spectra of MAS samples were calculated using NMRLAB." In our

simulations, 10,000 cry stallite orientations were used.

73

2D Spin-Echo 31P NMR Specttum: The 2D spinecho NMR specmim was acquired at

4.7 T (Bniker MSL 200) with a standard spinecho pulse sequence using the phase

cycling of Rance and Byrd. 13' A lH x12 pulse of 5.5 ps was used with a contact time of

5.5 ms and a recycle delay of 10 S. For each t , increment, 64 transients were acquired

for a total of 64 increments. Gaussian line broadenings of 200 Hz and 100 Hz were

applied to the FI and FL projections respectively. The experimental and calculated 2D

NMR spectra were processecl in magnitude mode. The Fi projection was calculated

using SpinEcho. lS9

X-Ray Data Collection and Processing: The X-ray difiaction study was carried out by

T. Stanley Carneron at Dalhousie University. A crystaî of approximate dimensions 0.10

x 0.10 x 0.10 mm, recrystallized from chlorobenzene, was mounted on a glas fibre.

A Rigaku AFCSR diffiactometer was used for al1 measurements. Calculations were

performed us h g texsan. lS5 The crys tals have ce11 dimensions a = 1 1 .523 (4) A, b =

23.083 (1) A. c = 15.115 (1) A, a = 89.99 (l)", P = 92.71 (1)" and y = 89.99 (1)".

The merging R, for the reflection data, merged on the assumption that the ce11 is

monoclinic, is 3 .O448 for 244 quivalent reflections with I > 50(1). The reflections for

which h = 2n + 1 are weak in intensity and are gewrally diffuse. The strong

reflections thus belong to a ce11 where a = 5.762 (1) A. Both cells have systernatic

absences consistent with a space group Pt,lc. The molecule for the structure in the

larger ce11 refmes to R = 4.796. The cefinement used unit weights.

Cbmputatio~i Details: Theoretical caiculations were perfomed with the Gaussian 94

suite of programsm running on aa iBM RISC16000 cornputer. Using RHF tûeory and

74

the GIA0 methoci," the phosphorus nuclear magnetic shielding tensors were determined

for the mode1 geometry, 4 (figure 4. l), of the phosphole tetramer baseâ on the X-ray

crystallography results for half of the molecule with the methyl and phenyl groups

replaced by hydrogen atoms. A partial geometry optimization using HF theory with the

6-31 1G basis set on d l the atoms was canied out. The P-P bond length, the dihedral

angle between the rings, and the C-H bond lengths were fixed at the X-ray structure

values for the optimization. Ab inirio calculations of nuclear magnetic shielding were

perfomed using the 6-3 1 1 + +G(d,p) bais set on phosphonis and wighbouring nuclei,

while the 6-3 11G basis set was used on the remaining atoms to keep computation times

within reasonable limits . IM To compare with experirnental results , the calculated

phosphorus shielding is converted to chernical shift by usiog the absolute shielding of

328.35 ppm for the phosphorus reference, 85 96 H3Pû,(q).90

4.3 Results and Discussion

4.3.1 Experimental Deteradnath of Phosphorus Chemicai Shift Terisors

Tbe observed and calculated 31P NMR spectra of stationary sarnples of the

tetramer are show in figure 4.2, while NMR spectra of MAS samples are shown in

figures 4.3 and 4.4. Best-fit parameters are given in table 4.1. In the text to follow , a

brief account of how these parameters were obtained is presented.

The "P NMR spectra of the phosphole tetramer with MAS indicate the presence

of a unique phosphonis spin pair in the crystalLn** and, as indicated in table 4.1, the

Figure 4.2 Experimental anà calculated "P NMR spectra of stationary samples of the phosphole tetramer acquired at a) 4.7 T (2 180 transients) and b) 9.4 T (458 transients). in both cases, 100 Hz gaussian line broadeaiag was applied .

calc

calc J V L

Figure 4.3 Experimental and calculated 31P NMR spectra of crystalline powder sarnples of the phosphole tetramer spinning at the magic angle, acquired at 4.7 T for v, of a) 2 kHz or b) at 1.5 Wz. For each specmim 256 mients were aquired and 10 Hz of gaussian line broadening was applied. The asterisic indicates O,.

Figure 4.4 Experimental and calculated 31P NMR spectra of crystailine powder samples of the phosphole tetramer spioniog at the rnagic angle, acquired at 9.4 T for v, of a) 4 kHz or b) 2 kHz. For each spectnim 512 transients were aquired ad 20 Hz of gaussian line broadening was applied. The asteris k indicates 6,.

Table 4.1: Experimentai and caiculated isotropic phosphom chernical shift, principal componentsa of the phosphorus chemical shift iensoa, 0, and K for the phosphole tetramer.

Site

a All chemical shifts and Q are given in ppm. Esthteci error on the principal components is f 5 ppm. GIAOs were used with the 6-31 1 + +G(d,p) basis set on phosphorus and adjacent

atoms for structure 4. The 6-3 1 1G basis set was used on the remaining atoms.

NMR spectra have been aaalyzed accordingly. However, in the prevîously reporteâ

crystal structure of the phosphole tetrame8' there are two molecules in the asymmetric

unit related by a pseudo mirror plane, hence four unique P-P bond lengths were

reported; r = 2.198(6), 2.191(6), 2.201(6) and 2.175(6) A.21 Given the reported X-ray

structure, one would expect to see potentially 8 different phosphorus sites in the jlP

MAS NMR spectrum; simüarly up to 16 different methyl carbon sites could be

anticipated in the 13C MAS NMR specmim. Expehentally, we observe only two

unique "P sites at both 4.7 and 9.4 T. Carbon-13 NMR spectra of MAS samples

revealed two I3C sites at both fields (6 , = 15.5 I: 0.1 ppm and 17.1 * 0.1 ppm).

This apparent disagreement between our NMR results and the reported X-ray data

prompted a redetermination of the X-ray data. Repeated attempts were made to grow

suitable single crystals; however, the best crystals obtaiwd were less than ideal for

X-ray diffraction. The R factor for our X-ray &ta is 0.047, compared to the R factor of

O -089 reporteci previously .'' The space group obtained from the new X-ray data is f2,lc with the asyrnmetric

unit consisting of one molecule, rather than a space group of Pr with two molecules in

the asyrnmetric unit as had been previously r e p ~ n e d , ~ ~ hence there are four

crystailographicaily non-equivalent phosphorus sites and potentiaily eight non-equivalent

methyl groups. In both cases. the unit ce11 contains four molecules. The rnolecular

structure obtained fiom our X-ray data is essentially the same as the reported

structure;21 however, our results indicate that the molecule contains a near perfect C,

axis which relates the two phosphom spin pairs (figure 4.1, structure on the left). This

also reduces the number of different phosphom sites fiom four to two and the number

of different methyl carbons dom to four. Given that the isotropie jLP chernical shifts of

the two phosphorus sites only differ by 1.7 ppm,'53*Ls it is not surprishg that the four

methyl carbons in the C, position (figure 4.1, middle structure) are isochronous;

similarly for those in position 4.

Within the unit ceil the two phosphorus spin pairs related by the near perféct C,

axis have very similar environments though the two atorns of each pair are in different

envirooments. From the difhise reflections for which h = 2n + 1, it would appear that

there are stacking enors in the a direction. The molecules are packed in layers

approximately perpendicular to the a direction; however, there are too few reflections

80

for which h = 2n + 1 (51 out of a total of 766) to test this suggestion. Using equation

2.20, and an average P-P bond length of 2.192(9) A ftom the new X-ray crystal

structure, RDD = 1.873 kHz with an estimated error of f 0.05 kHz. based on the error

in the X-ray &ta. Also, with four phosphorus nuclei in each molecule. each ''P-"P

spin pair is not truly isolated since there WU be muaial dipolar coupling. From the

internuclear distances between phosphonis nuclei that are not directly bonded to each

other, the values of RD, are 233 Hz (r = 4.392 A) and 169 Hz (r = 4.882 A), hence

the NMR spectral features are largely detennined by the much larger dipolar coupling

between phosphorus nuclei that are directly bonded to each other rather than the

phosphorus nuclei fonning the other spin pairs in the rnolecule.

The value of Re, and the relative signs of R, and 11(31P,"P), are obtained from

the 2D spin-echo experiment. Figure 4.5 shows the experimentai and calculated FI

projections of the 2D spin-echo NMR spectrum of the phosphoie tetramer. Using

J , = -362 Hz,"~*~" the best value of R, is 1.80 * 0.05 kHz (figure 4.5(a)), which is

in good agreement with the value calculated fiom the crystal structure. The difference,

Reg - RDD = 73 f 50 Hz, is very srnall and could arise ftom vibrational averaging and

possibly A.J. The stnailer dipolar couplings between the phosphorus nuclei that are not

directly bonded to each other wwt likely contribute to line broadening; however, it is

possible they couid slightly modify the value of Rew The semitivity of the Fl projection

to R, c m be seen in figure 4.5(b), where the agreement between the experimental

spectnim and one calculated using %, = RDD = 1.873 kHz is not as good. As well, the

F i 4.5 The calculated (dashed line) and experimental (solid line) R projections of the 2D spinecho 31P NMR spectnm of the phosphole tetramer, acquired at 4.7 T. The best fit is obtained for a) Rcff = 1-80 kHz, J , = -362 Hz. If & = RDD = 1.873 kHz and J , = -352 Hz, the projection shown in b) is obtained. If Refi = 1.80 lrHz and J , = + 362 Hz the splitting between the 'honis' is increased, as shown in d).

82

poor fit in the simulation using 1Jc1P,3'P), = + 362 Hz with Rer = 1.80 Wz (figure

4.5(c)) indicates that R, and l JC1P,3 'P), must have opposite sigm. In fact, for

1J(31P,xP), to be positive. Re* must be less than 1.20 Wz to obtain a satisfactory fit of

the two most intense peaks. which seems unreasonable in light of previous investigations

1JC1P,31P). 'O A negative J-coupling constant is consistent with I N W (intermediate

wglect of differential overlap) calculations of 1J(3'P, IIP). For example, the calculated

1Je1P,31P) in (CH3)2P-P(CH1)2 is -254 HZ for a dihedral angle between the forma1 low

pairs of 74" which is similar to the dihedral angle for the phosphole tetramer, 78".

The dependence of J on conformation is discussed in more detail in chapter 5.

The spin-spin coupling data (1J(3'P,NP), = -362 Hz a d R, = 1.80 Hz) were

used to simulate the experimental 31P NMR spectra of a stationary sample shown in

figure 4.2 to obtain the principal components of the chemical shifi tensor given in table

4.1 and tensor orientation information discussed below . The experimental error in the

principal components of the two chemical shift tensors is estimatecl to be * 5 ppm. As

a result, a,, , oz, and &,, are virtually identical for the two phosphorus chernical shift

tensors.

The NMR spectra of MAS samples, sbown in figure 4.3 and 4.4. demonstrate

that the quality of the simulations using these new parameters is comparable to

previously published w ~ r k . ' ~ + ' ~ Although the agreement between the calculated and

experimental NMR spectra is good at both fields for stationary and MAS samples, there

are some subtle differences between observed and calculated NMR spectra. These

differences probably arise because neither of the two phosphonis spio pairs in the

Figure 4.6 The relative orientation of the two phosphorus chemical shift tensors in the phosphole tetramer, determined from simulation of the "P NMR spectra acquired at 4.7 T aad 9.4 T. For PA, the Euler angles are EL = 0°, P = 78O and y = 167". For PB, u = 82", P = 78" and

cule is strictly isolated (Le., these spin pairs interact with one another).

As detailed in section 2.2, it is possible to obtain some chemical shift tensor

orientation information from the NMR spectra of systems containing spin pairs. For the

phosphole tetramer, the NMR line shape is panicularly sensitive to Aa, which is the

dihedral angle between the &, components of the two phosphorus chernical shift tensors.

Best-fit calculated NMR spectra were obtained with Aa = 82 f 3 O - For both

phosphorus chemical shift tensors, the &, componeat is tipped away fiom the

Figure 4.7 The phosphorus chernical shift tensor orientations for 4 determined by ub inirio calculations. For PI, b, is out of the plme of the page, while for PZ, &,, is approximately out of the plane. In the case of P 1. the a,, and ti3, components are situated at angles of 19.3 O and 79.1 O respectively from rpp . FOC PZ, 4, is at an angle of 27.5" and 8, at an angle of 79.0" from q,.

internuclear vector by P = 78 * 5'. In figure 4.6, the relative orientation of the two

phosphorus chemical shift tensors is illustrated. In both cases, y = 167 & 5 places the

least shielded component, 6 , , , closes t to r,. Unfortunately , the ambipities associated

with the dipolarchernical shift method prevent the determination of the absolute

orientation of the chernical shift tensor in the molecular fiame of teference.

4.3.2 Ab ln& Caiculations of Pûosphonis Shielding Tensors

As aiready mentioned, ab initio calculations may be used to help fix the relative

85

orientations (figure 4.6) in the moleculai axis system (figure 4.7). Ab initio calculation

results for the phosphonis nuclear magnetic shielding teasors in the mode1 system, 4,

for the phosphole tetramer are given in table 4.1. The two phosphorus sites are labelled

as Pl and PZ rather than PA and PB (figure 4.1) since it is not known how the two sites

in the NMR spectra should be assigned to the molecule. In a partial optimization of the

geometry, the P-C bond lengths and the ring bond angles were allowed to change,

resulting in changes that were largely within the errors stated in the crystal structure.'l

The calculated tensor orientations, depicted in figure 4.7. are similar for both Pl

and P2 with respect to the local geometry about each phosphocus nucleus. The &,,

components are closest to the P-P bond at angles of 19.3" and 27.5' for Pl and P2,

respectively while the 4, component for P l f o m an angle of 79.1 O with the

internuclear vector. and the correspondiiig angle for P2 is 79.0". The calculated

orientations of &,, and 4, for both phosphonis nuclei are consistent with the

exper imental observations. In addition, the dihedral angle between the 4, principal

components is W.$", in good agreement with the value of 82" determiad by analysis

of "P NMR spectra. These ab initio calculaiions indicate thai the 6, components are

not aligned in the general direction of the formal lone pairs, as had been previously

sugge~ted.~~*~" In fact, 4, is closest to the direction of the fornial lone pairs. For the

phosphole tetramer, the 633 components are in the plane of the respective phosphole

rings and approximately perpendicular to the P-P bond.

With respect to the magnitudes of the principal components. the experimental

and calculated results show s idar treids (table 4.1). The small calculated isotropie 3'P

chetnical shift difference, 4 ppm, between the two sites is consistent with experiment.

The calculations also predict that 6,, and b, are similar, while 6, is quite distinct, as

reflected in the skews of about 0.5, comparable to the skews of 0.7 observed

experimentally. However, the calculated isotropic cherniai shifts are too srnall by

about 43 ppm and the values of are significantly larger than the experimental results.

Some reasons for this discrepancy between calculated and experimental results

have been discussed in the previous chapter (section 3.3.3). In addition, the presence of

formal lone pairs in the phosphole teaamer makes ab initio calculations more

chailenging. Inclusion of electron correlation has been shown to be important for

obtaining good quantitative agreement between calculated and experimental shielding

tensors in systems with formal lone pairs a d multiple b ~ o d s . ~ ~ * ~ * " The hprtance of

lone pairs in detemiining the nuclear magnetic shielding in phospholes has been

demonstrated in a series of ub initia calculations on phospholes and the phospholide

ion.Isa A recent investigation of some model phosphorus systems, for example PH3,

inâicates that the hclusion of electron correlation in ob initio calculations yields

improved results for isotropic shielding . '" The use of a model geometry consisting of

half of the phosphole tetramer may also contribute to this discrepancy. Given these

factors, quantitative agreement between the experimentai and ab inifio values is not

expected, and seemingly good calculateci results may be due to the fortuitous

canceilation of errors. The primary goal with respect to ab initio calculations of nuclear

magnetic shielding teosors is to obtain the teasor orientation in the molecular fiame of

reference. The results for TMPS (chapter 3) and previous re~ul ts~ '*~*~@ suggest that ab

Nlitio methoch repruduce well the expehental tensor orientation.

The relative orientation of the 8, wmponents of the two phosphows shielding

tensors in the phosphole tetramer appears to be related to the relative orientation of the

adjacent phosphole rings (see figure 4.7). in the crystal structure. the rings are

arrangeci such that the ring planes are approximately parallel to each other and twisted

about the bridging P-P bond (figure 4.1. structure on the left). The twist angle between

adjacent phosphole rings, @,, ranges between 102°-1050, which can be equally well

described by the supplement angle range of 75"-78". This agrees weU with Aa which is

82 O detedned experimentally and 87.8 " from ab initio calculations . This structure-

teasor relationship can be m e r demonstrated by ab inirio calculation of the

phosphorus tensor orientations at various values of 4,. Further calculations on Our

mode1 system using 6, = O", 70". 110" and 180' indicate that the 4, components are

orienteci relative to the local geometry in a similar marner as show in figure 4.7, with

Aa reflecting a, (Aa = 0°, 60.5", 109.5" and 180° for the correspondhg listed

above).

4.3.3 T r e d in Phosphorus Cbemicai Sbilts for Phospholes

There has been some discussion in the literature over the aromaticity of

phospb~les,'~~ recently revived by the synthesis of some planar phospholes. 162

Aromaticity in phosphocus heterocycles was recentiy reviewed.la While 31P solution

NMR has been used routinely to characterize this important class of compounds, there

are few comprehensive NMR investigations of the chernical shift tensors. The

phosphorus chetnid shift teosors of several phosphole derivatives have also been

characterwd recently by solid-state NMR? Compatison of the phosphocus cherniai

shift teasors in phospholes (table 4.2 with structures given in figure 4.8). reveals that

6, in the phosphole tetramer is smaller compared to the other phospholes. For ali

phospholes investigated by 31P solid-state NMR thus fa-. the spans of the phosphorus

chemical shift tensors are relatively small cornpared with systems where the phosphorus

nucleus is known to be participahg in a delocalized electron ftamework. For example,

the span of the phosphorus chemical shift tensors in Mes0P=PMes' is 1239 ppm17 and

Q = 779 ppm in benzo-1,3,2dithiaphospholium aluminurn ch1oride.l" The iarge spans

in these systems have been amibuted to the piesence of low-lying excited States with the

proper symmetry to mix with the highest occupied molecular orbitals (equation 2.44).'"

Table 4.2: Phosphorus chemicai shift tensor principal compents" for some phospholesb.

5-pheny ldibenzophosp hole -17.3 12 -19 -45 57 O 163 (two sites) (5) 164

cis-2,Lû- 75.3(PS3 129 122 -25 154 0.9 168 dimethyl[l,2,3]benzothia-di-

phospholo[2.3b][l,2.3] 53.7(PCJ 190 25 -54 244 O beozothiad iphosphole (7)

a Al1 chernical shifts and Q are given in ppm. Structures are shown in figure 4.8.

F ' i 4.8 Molecular structwes of compounds 5.6, and 7 in table 4.2.

4.4 Conclusions

The analysis of 31P NMR spectra of a stationary and MAS samples of the

phosphole tetramer indicates that the principal compownts of the two phosphorus

chernid shift tensors are virtually identical. Regarding the phosphorus chemical shiH

tensor orientation, the &,, components of bth tenson are closest to r,, while the q3

components are tilted away at an angle of 78". in addition to king twisted relative to

each other by an angle of 82". This latter angle is thought to reflect the relative

orientation of the phosphole rings, which are related by a dihedral angle ranging from

75" to 78 O . Ab initio results support the experimental conclusions and iedicate that the

8, components are not aligned with the formal lone pairs on the phosphorus nuclei.

The characterization of the phosphorus chemical shifi tensors in the phosphole tetramer

is greatly aided by the 2D spinaho experiment as well as by employîng ub initio

calculations to suggest an orientation of the tensor in the molecular hame.

Cbapter 5: 'JPP,"P) Coupüng Tellsors - Conformational Studies in Mode1 Systems and Structural Cbaracterizatioa of [WQ-PPhJ[GaCW

5.1 Introduction

Phosphinophosphonium cations are representative of a new class of

cornpound~;~ however , the lack of X-ray diffraction dataa means that alternative

methods such as NMR are vital for characterizhg these compounds in the solid state.

in addition, 1J(31P,xP) is not observed in solution NMR for some of these compo~ods,~~

most likely due to interrnolecular exchange. One can apply the dipolar-chernical shift

method (section 2.2.2) to characterize the phosphorus chernical shift tensors as well as

the 3iP,3LP spin-spin coupling interactions. From the dipolar coupling constant, the P-P

bond length may be estimateci according to equation 2.20. However, as discussed in

section 2.1.6, the Harniltonians describing the dipolar interaction and the contribution

from the anisotropy in J are identical in form; hence, they are inseparable

experimentally . For this reason, accurate measurement of intemuclear distances via RDD

requires some knowledge of AJ.

Comprehensive understanding of how trends in J reflet molecular and electronic

structure is still lacking, primarily a consequence of the difficulty in characterizhg the

complete tensor experimentally. For one-bond J-coupling involvhg phosphorus nuclei,

' Since the preparation of this chapter, the X-ray crystal smctwes of [Pû,P-PPùJ[GaCiJ and [Ph,P-PPhJ[SO,CF,] have been obtained (N. Buiford, T. S W y Cameron, P. J. Ragogna, E. Ocmddo- Mavarez, M. Gee, Robert McDonald, and R. E. Wasylishen, J. Am. Chem. Soc. î23,7947 (2001)).

91

92

reports in the literature indicates that hl may be s ~ b s t a n t i a l ; ~ ~ * ~ ~ ~ however, as is evident

from the work on TMPS (chapter 3) anâ the phosphole tetramer (chapter 4). it is

difficult to distinguish the effect of hl from the consequences of vibrational averaging.

A possible avenue for determinhg the contribution of hl to Re, is via <ib initio

calculations. Details of ab iriitio methods for calculating J have been discussed in

section 2.3.2. In addition, first-p~ciples calculaiions of 1J(31P,31P) allow one to

investigate the infiuence of formal electron lone pairs as well as determine rhe

dependence on conformation of the low pairs with respect to rotation about the P-P

bond. While variable temperature NMR studies in solution bave provided some

insight,'' many conformations are not experimentally accessible.

For a representative phosphinophosphonium sait, [Ph,P-PPhJ[GaCi,J, compound

3 (figure S.l(a)), the calculation of 1J(3'P,3'P) has been used to obtain an estimate of

RD,, from the experimentally measured value of Re, (see equation 2.29). From RD, the

P-P bond length may be estimated according to equation 2.20. H,P-PH,+ is used as a

model system for Ph3P-PPh,+ since ab initio computational methods currently avaiîable

are limited to small molecules for J-coupling calculations. To further examine the

relationship between molecular structure and trends in J, calculations on H2P-PH2 have

also been performed. In addition, the phosphorus chernical shift tensors have ben

characterized and these experimental results are complemented by ab inifio calculation

of phosphorus shielding tensors in a model compound, (CH3,P-P(CH,),+.

Structures of the molecules discussed in tbis chapter; (a) [Ph3P-PPhJ [ W h ] , indicahg the labelling convention for the two phosphorus nuclei; (b) (CH,)3P-P(CH,)2+ and a Newman projection defining &&p; (c) H2P-PHI and a Newman projection defining epp; (d) H3P-PH2+ and a Newman projection denning, @,+ .

5.2 Experimental and Computationai Deta&

SMiple Preprdon: A sample of IW,P-PPhJ[GaClJ was provided by Dr. Edgar

Ocando-Mavarez and Professor Neü Burford. AU samples for NMR work were

prepared in an inert atmosphere as this compound is air sensitive. Details and

suggestions for handling air-sensitive NMR samples are presented in Appendix 2.

NMR S p e m : Phosphorus-3 1 NMR spectra were acquired for stationary or MAS

samples of powdered crystalline [W3P-PPhJ [GaCl,] at applied magnetic fields of 4.7 T

(Chemagnetics CMX 200 spectrometer) and 9.4 T (Bruker AMX 400 spectrometer).

The standard CP experimentY with high-power proton decouplhg was used in both

wes. For experiments at 4.7 T, the sample was packed into a 4 mm (0.d.) zirconium

oxide rotor and a proton 90" pulse of 3.0 ps, contact time of 5 .O ms, and recycle delay

of between 5 and 8 s were used. Typical sweep widths were 50 kHz with acquisition

tirnes of 41 ms. Before Fourier transformation, 2048 points of zero filling was applied.

Experiments at 9.4 T were perfomied on a sample packed into a 2.5 mm (0.d.)

zirconium oxide rotor. Parameters similar to those for experiments at 4.7 T were used.

Al1 31P NMR spectra are referenced to the prirnary standard, 85% H,PO,(aq). by setting

the isotropie peak in the "P NMR spectnun of solid bM4H2P04 to +O. 8 ppm. Gaussian

line broadening of between 20 and 40 Hz for the specûa of MAS samples and between

100 and 200 Hz for speura of stationary samples was applied.

The 2D spin-echo experimeat was perfonned at 4.7 T using parameters identical

to the ID experiments. For each r , iofrement, 224 transients were acquired, for a total

of 64 increments. The sweep width in the E! dimension was 28.6 kHz and the

95

acquisition time was 12 m. In the FI dimension, the sweep width was 12.5 kHz.

Gaussian line broadening of 200 Hz in F1 and 100 Hz in F2 was applied, followed by

processing in magnitude mode. The expimental &ta were zero tilled to 512 points x

512 points.

The spectra of MAS samples were sirnulateci using the prograrn NMRLAB."

whiie the specua of statiooary samples were simulateci using WSOLIDS.49 The F1

projection of the 2D spinccho spectnun was calculated using SpuiEcho. n9

C u m p ~ u t i u ~ l Details: Calculation of nuclear magnetic shielding tensors for

(CH,),P-P(CH3)2+ was carrieci out at the HF level using the 6-3 11G** basis set on the

phosphorus and carbon atom and 3-21G on the hydrogen atoms. The structure was

first optimized at the HF level using the 6-3 1 1G** basis set on al1 atoms, resulting in

(see figure 5.1@) for atom labelling) P(1)-P(2) = 2.219 A, P(2)-C = 1.848 A,

P(1)-C(1) = 1.816 A, P(1)-C(1)' = 1.814 A, C(1)-P(1)-C(1)' = 108.3".

C(1)'-P(1)-C(1)' = lO8.2", C-P(2)-C = 1û2. lo , C(1)'-P(1)-P(2) = 108.0" and

@MePP = 180°. +Mep is the dihedral angle between the plane containing the P(1)-P(2)

bond and dso bisecting the C-P(2)-C bond angle and the plane containing the P(1)-P(2)

and P(1)-C(1) bonds. Al1 C-H distances were 1.08 À and H-C-H bond angles were

lO9.5 O . Al1 caiculations were performed with Gaussian 98" using an iBM R S i 6 0

workstation.

Indirect 31P,3iP spin-spin coupling tensors for H,P-PH, and H,P-PH,' were

calculated using the MCSCF approach with complete active space self-consistent field

(CASSCF) wa~efunctions~~*~~ as implemented in DALTON, an ub initio electronic

structure pr~gram,'~l instaîled on an IBM RSi6000 workstation. For CASSCF

wavefunctions, it is necessary to choose active aad inactive space cornbhtions. The

active space consists of the molecular orbitais into which electrons may be placed to

produce configurations that are used to construct the electronic wavehinctions. It

usually consists of a number of occupied and virnial molecular orbitals. The inactive

space consists of the molecular orbitals which remain doubly occupied for al1 electron

configurations. The selection of active and inactive spaces was made based on MP2

n a ~ a l molecular orbital occupation numbers and energies.In The inactiveiactive space

used are given in the following format: for each molecular orbital symmetry , the

number of ioactive orbitals and active orbitals is given. For example, 101012131

indicates that there are four different molecular orbital symmetries. For the first

symmetry type, 1 molecular orbital is inactive aed 2 are active, O inactive and 1 active

for the second symmetry, 1 inactive anâ 3 active for the third symmetry. and O inactive

and I active for the fourth syrnmetry. Calculations of J for H,P-PH, and H,P-PH,+

were perforrned with cc-pVTZ (correlationconsistent polarkation valence triple-zeta)

basis setdn on al1 atoms.

An experimental ge~metryl'~ was used for H,P-PH, with the exception of @,,

which was varieâ between O' and MO0 in 30" increments, keeping al1 other bond

lengths and bond angles fïxed. 4, is the dihedral angle between the planes which both

contain the P-P bond but each one bisects one of the H-P-H bond angles (see figure

Sl (c ) ) The bond lengths and angles are as follows: P-P = 2.2191 A, P-H = 1.4155

A, H-P-H = 92.0". The experimental value of a,, is 74.0". For H2P-PH2, the

97

inactive/active space used to calculate 'Je1P,31P) as a fiiaction of ePp (table 5.2)

consisteci of 55/54. which corresponds to a total of two unoccupied orbitals in the active

space. one per molecular orbital symmetry. For sndying the effect of other geometry

factors (table 5.4). an inactive/active space consisting of 55/43, which does not include

any uwccupied orbitals. was used.

For HIP-PH2+, the geometry was optimized at the HF level with the

6-3 11 + +G(3df,3pd) basis set on al1 atoms. The optimized structure is as foilows (see

figure 5.l(d) for atom labelling): P(1)-P(2) = 2.209 A. P(1)-H(1) = 1.387 A, P(1)-

H(1)' = 1.386 A, P(2)-H = 1.403 A, H(1)-P(1)-P(2) = 116.6". H(1)'-P(1)-P(2) =

110.2". H-P(2)-P(1) = 92.4". H(1)'-P(1)-H(1)' = 106.3". md H-P(2)-H = %.SO.

Similar to the calculations for H2P-PH2, the angle a,+ was varied between O0 and

180". a,,+ is the dihedral angle between the plane containing the P(1)-P(2) boad and

also bisecting the H-P(2)-H bond angle and the plane containing the P(1)-P(2) and

P(1)-H(1) bonds. MCSCF calculations for the dependence of 'J(xP,3'P) on g,,, for

H,P-PH,' (table 5.3) were performed using an inactiveJactive space 10/8, i.e., one

uwccupied orbital in the active space.

5.3 R d t s and Discussion

5.3.1 Phosphoriis-31 NMR Sptxtra of [Wp-PPûJ[GaCiJ

The ''P NMR spectra for a crystalline powder sample of [Ph,P-PPhJ[GaCh] are

shown in figures 5 -2 (obtained at 4.7 T) and 5.3 (obtained at 9.4 T) for various MAS

rates. From the spectra aquired at the higher MAS rates, the isotropie chernical shifts

expt

Figure 5.2 Experimental and calculated 31P NMR spectra of MAS samples of [Ph,P-PPhJ [GaCi,] , aquired at 4.7 T. The spioning rates are (a) 2.17 kHz (128 transients), (b) 2.72 kHz (256 traasieats), and (c) 5.02 lrHz (256 transients). in each case. 40 Hz of gaussian line broadening was applied. The asterisk aad dagger mark the isotropie region for P(l) and P(2) respectively .

P . . . . . i r . . . . . . . . a

60 40 20 O -20 -40 -6û -80 ppm

C . . . . . . . i . i . . . . . l

60 40 20 O -20 -40 -60 -80 ppm

Figure 5.3 Experhnental and calculated 3'P NMR spectra of MAS samples of [Ph3P-PPhJ[GaCi,,], aquired at 9.4 T. The spioning rates are (a) 2.65 kHz, (b) 5.38 kHz, aiid (c) 7.03 kHz. In each case, 512 transients were acquired and 20 Hz of gaussian liw broadenhg was applied. The asterisk and dagger mark the isotropie rcgioa for P(1) and P(2) respectively . A signai possibly due to a decomposition product is indicated by $.

100

for each phosphorus nucleus and the magnitude of 1Je'P,31P), may be estimatecl and

refined in subsequent simulations of dl the NMR specba. The data are summarized in

table 5.1. The assigrnent of the phosphorus chemical shifts to sites in the molecule is

made on the basis of hown trends and on mults of ob iniiio calculation of phosphorus

nuclear magnetic shielding in a mode1 system. (CH,XP-P(CH3),+ (vide infa).

Calculations for nuclear rnagnetic shielding in Ph,P-PPh2+ would entaii a the-

consuming geometry optimization since an experhental geometry is not available.

For this compound, [Ph,P-PPhJ [GaCî,] , the phosphorus cbemical shifts obtauied

from a sample dissolved in CH,CI, compared to the solid state differ by less than 8

ppm. The impurity peak in figure 5.3 is attributed to a decomposition product. it is not

observed in the spectra at 4.7 T (figure 5.2), probably due to differences in the

effeftiveness of the rotors at excluding air fiom the sample.

The difference between the isotropic chemical shifts of the two coupled

phosphorus nuclei is 33.2 ppm, which is 2.61 Wz or 5.38 kHz at an applied magnetic

field of 4.7 T or 9.4 T respectively. These conditions are ideal for the rotational

resoaance (RR) e~periment,'~~ whereby the dipolar coupling interaction is restored for a

homonuclear spin pair when the difference between the isotropic chemical shifts is nv,

where n is typically 1 to 3. Indeed, the "P NMR spectra shown in figures 5.2@) and

5.3(a).(b) were aquired under conditions of RR. While Rer may have been meamred

from Rit by generating Zeeman magwtization exchange curves, for this compound it

was simpler to use the results of the 2D spinecho experiment, presented below, to

ob<ain Re@

Table 5.1: Phosphorus chernical shift t ewr principal components and spin-spin coupiing parameters for [Ph3P-PP~LJ[G~C~].

solution: a

4 m 1 PPm LJ("P.3'P) I Hz

solid state and ab initio data:

6 , / ppm '

4 1 1 PPm

b,/ PPm

4 3 1 PPm

Q 1 P P ~ K

1J,(31P,31P) 1 Hz

Ren I kHz

expt . ab initio expt. ab initio

15.4 -40 -17.8 -79

36 -22 23 3

23 -43 -8 -73

-14 -56 -68 - 167

50 34 91 170

0 A8 0.28 0.32 O. 10

-323 * 2

1.70 * 0.05

a E. Ocando, N. Burford, unpublished results. The solvent is CHFI,. Ab initio data are for the optimized (CH3,P-P(CH,h+ structure. Calculations are

carried out at the HF level using 6-3 1 1G** basis set on phosphocus and carbon atoms while the 3-21G basis set was used on al1 the hydrogen atoms.

Experimental error on &,, is * 0.1 ppm, obtained from specaa of MAS samples. Experimental error on the principal components is f 2 ppm, obtained from spectra of

stationary samples .

102

The FI projection fiom the 2D spin-echo 31P NMR specinun is show in figure

5.4 dong with simulations using opposite signs (figure 5.4(a)) aid the same signs for

l J(31P,31P)I, and R& (figure 5.4(b)). From these simulations, Rem = 1.70 * 0.05 kHz

and 1Jc1P,31P), is clearly negative relative to R,. Using the data from 31P NMR

spectra of MAS samples and the spin-spin foupling data from the 2D spin-echo

spectnun, the 31P NMR spectra obtained at two applied magwtic fields for a stationary

sample may be analyzeâ. The best simuiatioas are shown in figure 5.5 and the principal

components of the two phosphorus chemicai shifi teasors as well as spin-spin couplhg

parameten which give the best overall fit to al1 the experimental spectra are given in

table 5.1. The two features of note in the phosphorus nuclear magnetic shielding are

that one of the phosphorus nuclei is more shielded than the other and its chemical shift

tensor has a larger span. Based on kwwn trends in phosphonis shielding, that

phosphines are in gewral more shielded than phosphonium the specua may

be assigned to the phosphorus nuclei as in table 5.1. in addition, calculated phosphonis

chemical shift tensors in (CH,),P-P(CH&+ indicate that the phosphine centre, P(2). is

more shielded and has a significantly larger span (table 5.1).

Regarding shielding tensor orientations in the molecular frame of reference, the

position of the 4, components relative to the P-P bond, given by P, and the orientations

relative to each other, given by Au, have been determined experimentally. For P(L) and

P(2), P = 81 * 2" and 78 * 2" respectively and A a = 25". The third Euler angle, y,

is 2 * 5" for P(1) and 78 f 2" for P(2). Note that y for P(l) bas a larger error than y

for P(2). The angle y detemines whether o1, or b, is closest to r,,. The spectrum is

expt calc

expt

calc

Figure 5.4 Experimental and caiculated F I projections of the 2D sph-echo jLP NMR specmun of ph,P-PPhJ[GaC&] acquired at 4.7 T. The peak rnarked by an asterisk is an experimentai artifact. Simulations are shown with Ra = 1.70 kHz and (a) 1J(31P,31P)m = -323 Hz and (b) 1Je1P,31P), = + 323 Hz.

P(1) subspectnun

~ . . . . . . . . . r . . r . . . . r i . . . . lm 100 NI M) 40 20 O -20 4 UI -80 -100 '-120 ' ' ppm

expt

calc

P( 1 ) subspecüum

P(2) subspectnim t i i i i r i r r i i i i i i i m i i . i i l

80 60 40 20 O -20 -40 -60 -80 -100 ppm

Figure 5.5 Experimeatal and calculated "P NMR spectra of stationary powder sampks of [W,P-PPhJ[GaCLJ aquked at (a) 4.7 T ( 5 0 transien%, 200 Hz gaussian line broadening) and (b) 9.4 T (3774 traasients, lûû Hz gaussian liw broadening). Aiso shown are the calcuiated subspectra for each phosphorus site.

relatively insensitive to y for P(1) since the difference between 6,i and 6, for P(l) is

much smaller than for P(2); hence the position of 6,, and &a is w t as easily defined in

the case of P(1). The calculated orientation of the q3 component for P(1) (figure 5.6(a))

is in agreement with experiment; however, this is not the case for P(2) where the 6,,

component is calculated to be 34" away from the P-P bond (figure 5.6(b)). This is

significantl y different €tom the experimentai result , P = 78 O . in addition, the

calculations predict that the 6, components for both tensors are aligned, i.e., Ba = O",

whereas the experimental results predict an offset, Aa = 25 * 2". While it may be

tempthg to further compare the experimental and calculated phosphorus shielding tensor

orientations, it should be noted that calculations are performed on an optimized

geometry of a mode1 cation. in contcast to the situation for TMPS (chapter 3) and the

phosphole tetramer (chapter 4), much less information is available about the

experimental structure of [Ph,P-PPhJ [GaCL].

5.3.2 Dependeuce of lJ('lP,'lp) on codocm8tion: H2P-PH2 vs. H,P-PH,+

If one wishes to compare experimental and cakulated results, as well as use the

calculated J coupling to obtain structural information in these types of systerns,

knowledge of how J depends on the conformation is essential. H2P-PH2 and H,PPH,+

are prototypical molecules for such an investigation. Indirect experimental evidence that

'Je1P,"P), depends on conformation was first reporteci in 1970 in a variable

temperature NMR study of P2F41n and in 197 1 for 1,2dimethyl- 1.2-diphenyl

biphosphine. Since then, chis phenomewn has been observeci in a number of other

Figure 5.6 Calculated orientation of the phosphorus chernical shift tensors for (a) P(1) and (b) P(2) in (CH,)3P-P(CH3k+. In both cases, the il, compownt is perpendicular to the plane of the page. The hydrogen atom have been ornitteci for clarity .

s y s t e n ~ s - ~ ~ e ~ ~ ~ The general trend for biphosphiaes appears to be as fouows: a mal1

positive 1J(31P,31P), is observed for the conformation where the formai lone pairs are

tram with respect to each other (+, = 180°) whiie 1Je1P,31P)b is large and wgative

for the cis conformation (4, = in addition, biphosphines are not fixed in a

particular conformation, hence the observed value of 1J(31P,31P), must be averaged over

several conformations. The calculated potential energy curve for rotation of the PH2

fragment about the P-P bond in H,P-PH, indicates rhat the cis and t r m arrangements of

the formai electron lone pairs about the P-P bond have ewrgies of 11.3 and 3.3 Id mol"

respectively relative to the energy minimum at @, = 77" (note that RT = 2.45 W mol-'

at T = 295 K). Our calculations at the HF level of theory using the cc-pVTZ basis

set on al1 atoms give results that are in qualitative agreement with reference 181 and

indicate that the energy for rotation about the P-P bond is relatively Bat for

conformations between @pp = 60' and +,, = 180" (figure 5.7).

Sbown in figure 5.8 is the dependence of 1J(31P,31P) on 4, in H2P-PH,. The

data are given in table 5.2. The experimental value for 'J(31P,xP), is -108.2 * 0.2

Hz. '" While it is apparent that the quantitative agreement is no< very good, it is evident

ihat 1J(3 l P,31P) is highly dependent on the dihedral angle. nie FC mechanism is largely

responsible for the dihedral angle depenâence of L/(f1P,3iP)),, although the SD

mechanism makes a non-negligiôle contribution to the magnitude. An early molecular

orbital SCF study also found a similar dependence of 1J(3'P,31P), on 4pp.1(D Our results

are compared to results fkom otber c a l ~ u l a t i o n s ~ ~ ~ ~ ~ in table 5.2. it is intetesthg to

Figure 5.7 Plot of the totaî energy for H,P-PH, as a fùnction of Al1 ewrgies are relative to aPp = 180'.

note that the calculated 1J(31P,31P), results differ significantly with respect to the

magnitude of the FC contribution; however , the trends are the same. The anisotropy in

J is calculated to be significantly larger than LJ(31P,31P), and it is also very dependent

on @,, for H,P-PH, as illustrated in figure 5.8(b).

in contrast to H2P-PH2, lJCIP:lP) for H3P-PH,+ is relatively dependent of

4,+, defined in figure S.l(d). Figure 5.9 illustrates the dependence of J in H,P-PH,'

on a,, , with the &ta given in table 5 -3. This result is teasonable, since rotation of the

PH, group does not result in a signifiant change in the overall structure as îs the case

Figure5.8 Calculatedvalws~f(a)'J~'P,~'P),and(b)hlasahurtionofdihedral angle for H2P-PH2.

Table 5.2: Calculated values of lJCIP,"P) for H2P-PH2 as a m i o n of 6,.

Contributions to 1Jc1P,31P), / Hz

aPP 1 O 1J(31P,31P)to AJ(31P,31P) DSO PSO SD FC /Hz /Hz

this work O 30 60 90

120 150 180

SCF MO 1 (12s9p) -[6s4p] O

75 120 180

SOS-CI / STO-431G O

74 180

SCF 1 ( 1 2 ~ 8 ~ ) - [6s4p] ' 81

" Calculated using the MCSCF approach with cc-pVTZ bais set and an inactivelactive space consisting of 55/54.

From reference 183. ' The total orbital contribution is given. DSO + PSO. SOS-CI (sum-over-states configuration interaction) &ta are from reference 184. STO

stands for Slater-type orbital. ' From reference 185. The bais set has added polarization functions.

From reference 182.

Figure 5.9 Calculateci values of (a) 11(3'P,3iP), and @) AJ as a function of dihedral angle for H,P-PH,+. The scale is the same as in figure 5.8 to emphasize the difterence benveen the two molecules.

112

Table 5.3: Calcufared values of LJe1P,31P) for H3P-PH2+ as a function of @,+.a

Contributions to LJC1P,31P), /Hz

@pp+ 1 O 'J(3LPT3iP)y. Hz h1(31P,31P) / Hz DSO PSO SD FC

Calculations performed at the MCSCF levei with the cc-pVTZ basis set using an inactive/active space of 1018.

when one of the PH, groups in H2P-PH, is rotated with respect to the P-P bond. For

H3P-PH2+, the magnitude of 1J(31P,31P), is much larger than in H,P-PH,, with the

dominant contribution fiom the FC mechanism. For H3P-PH,+, the anisotropy in J is

smaller relative to 1J(NP,31P), in coatrast to the situation for H2P-PH,. The trend in

J(31P ,"P) for H,P-PH2 vs. H3P-PH2+ bas also been reportai in semi-empirical

calculations of J(15N, "N), for the aoalogous nitrogencontaining compounds . l M As

weîl, it was noted that the calculated valw of 1J(13C,"N), in methylamiw is virtuaily

independent of rotation of the MI, fragment about the C-N bond.'"

The replacement of one of the loue pairs in H2P-PH, with a bonding pair (CO a

hydrogen atom) in H3P-PH2+ r d t s in a decrease in iJ('1P,3'P), as well as a decrease

in the anisotropy in J. In t e m of reduced coupling constants (see epuation 2.24),

113

iK(P,P), for H,P-PH, vs. H W H 2 + with 6, = +,+ = O0 are -22 x IOi9 NA-%nm3 and

-99 x IOi9 NA%-3 respectively. This is contrary to the generaily observed lone pair

effect, where an increase in IK, is observai when a lone pair is replaced by a

For example. 'K(N,C), for CH3CH2cH,NH2 is 12.7 x lOI9 N A k 3 vs.

14.4 x IOi9 NA-k3 for CH3CH&H2NH,+, la and for P(CH,), vs. P(CH3),+, 'K(P,C),

= -1 1.1 x 1019 NA-%m3 and 45.3 x IOs9 NA-%rr3 respectively . Two exceptions are

(CH,),P-P(CH3), vs. (CH,)2P-P(S)(CH3)2, with IK(P,P), = 91 x lOI9 NA%-' and

'K(P,P), = -1 14 x IOL9 NA-%r3 respectively,ln and Ph2P-PPh, ('K(P,P), = -101 x

IOL9 NA-%r3)I3 vs. Ph,P-PPh2+ (IK(P,P), = -164 x IOt9 NA%-), this work). It should

be noted that lK(P.P), for ?h,P-PPh2 is lilcely very dependent on the lone pair

conformation and hence changes in the dihedral angle rnay change the trend with respect

to Ph3P-PPh2+.

Another factor that must be considered is a change in structure besides rotation

about the P-P bond. It has been claimed that 'J~'P,"P), for RR'P-PRR' is sensitive CO

the R-FR' bond angle (where R, R' are any one of the following: H, an alkyl group, or

phenyl).lW To investigate the influence of geoinetry, iJ(31P,3'P), was calculated for

H2P-PH, geometries where one bond length or angle was changed to match the

corresponding parameter in the geornetry used for H3P-PH,' (table 5.4). in this

manner, the effect of changing each bond length or angle may be determineci. The

calculated iJ(31P.HP), values for H,P-PH, using two different active spaces are given in

the f ~ s t two liws of table 5.4. This illustrates that using a larger active space (first

line) does not significantly change the calculated cwpling constant compared to the

114

results obtained using a smaller active space (second line). The wxt four lhes present

the calculaied 1J(31P,3LP), values obtaioed when a given bonâ length or angle in

H2P-PH2 is changed to match the correspondhg boad length or angle in H3P-PH2+. As

is evident from the &ta in table 5.4, none of the geometry differences between H,P-PH,

anci H,P-PH,' can account for the difference in 1J(31P,NP), for these two molecules.

Unforninately, m e r MCSCF caiculations on systems of this size are oot possible with

available computatiooal resources .

Table 5.4: Geometry dependence of 1J(31P,31P), for H2P-PH,."

geometry alteration 1J(31P.xP), I Hz -- -

H,P-PH2 experimental geometry (&, = O") a

H,P-PH2 experimental geomerry (#,, = O")

P-P in H,P-PH, cbaoged to 2.2192 A H-P-H in H,P-PH2 changed to 95"

H-P-H in H2P-PH2 changed to 106.37O

H-P in H,P-PH2 changed to 1.386 A H3P-PH2+ (+pp+ = 0")

a From table 5.2. MCSCF calculations using the cc-pVTZ basici set on al1 atoms and an inactivelactive

space of 55/43. From table 5.3.

115

5.3.3 Estimate of r, in ~@PPhJ[GaCW

As was stated in the introduction (section 5. l), to obtain an estimate of the P-P

bond length in ph3P-PPhJ[OaCi,], it is necessary to have an estimate of the anisotropy

in the J coupling, shce it is experirnentally inseparable fiom RD,. With a value for AJ,

one can obtah RDD from & according to equation 2.29. As mentioned in section 2.1.6,

reliable measurements of hl are scarce. An estimate of hl may be obtained tiom ab

initio calculations; however cornputer resources lirnit the size of the molecule one can

use for J calculations. In this case, H,P-PH,+ is the smallest possible mode1 compound

for Ph3P-PPh2+. As the results for H,P-PH,+ indicate that AJ is vimially independent of

app+ (figure 5.9). one may use the average AJ over al1 conformers of H,P-PH,+,

121 Hz. Using this value in equatioa 2.29. a value of 1.74 I0.05 l d z is obtained for

RD,, hence r, = 2.25 f 0.03 A in [Ph3P-PPhJ[GaCiJ, accordhg to equation 2.20. If

one assumes that R, = RD,, then r,, = 2.26 f 0.03 A which is within experimental

error of the fust estimate. In this case, A J is relatively small, hence a reliable estimate

of the vibratioaally averaged P-P bond length may be obtained for R,,. However, the

ob initio calculations of J for H2P-PH, indicate that one m o t necessarily assume that

AJ for d l one-bond P-P J-coupling teosors will be small.

5.4 Conclusions

The phosphorus chernical shift and 31P-31P dipolar coupling tensors in

Ph3P-PPhJ[GaCW have been characterimi by solid-state NMR. By combining the

experimentai results with ab initio dculations of 'J(3'P,"P) for H,P-PH,+, a reliable

Il6

estimate of the P-P bond le- in [Pb3P-PPhJ[GaClJ has been obtained, 2.25 * 0.03 A. It should be mted that vibrationai averaging and possible rockhg motion of the

P-P bond have been ignored. in addition, the dependence of indirect spin-spin couplhg

on lone pair conformation has been investigated for H,P-PH, and H,P-PH,+ using the

MCSCF approach. It was found that 1J(3LP,nP) for H2P-PH, is very depenâent on

conformation, in contrast to H,P-PH,+.

Cbapter 6: Conclusions

The phosphorus chemical shift and spin-spin coupling tensors for tbtee different

compounds containing P-P bonds have been characterized by solid-state "P NMR. The

combination of experimental methods and ab inirio calculations has proven to be very

usehl for explorhg the tensor nature of each interaction.

For the first example, TMPS (chapter 3), the phosphorus NMR parameters were

characterized by NMR studies on both a single crystal and a powder crystailine sample.

There are two molecules in the asymmetric unit; however the difference between the

two sites is very subtle, as evident in a redetenninatioa of the X-ray crystal structure.

This difference is also clearly evident in the )lP NMR spectra, from which two unique

phosphorus chemical shift tensors have been characterized. The tensor orientation is

such that the direction of greatest shielding, a,,, lies dong the P=S bond. The

experimental and calculated orientation of the phosphonis chemical shift tensors are in

excellent agreement. It was also shown that the anisotropy in the nP,31P indirect spin-

spin coupling for TMPS is less than 500 Hz, contrary to earlier reports for similar

cornpo~nds.~*~~~ This compound serves as a benchmark for testing the reliability of ub

initio calculations of nuclear magnetic shieldiag tensors.

The second system described in this thesis was the phosphole tetramer. Since a

large single crystal was not available, the phosphorus NMR parameters for this

compound were characterizeû by analysis of "P NMR spectra of powdered sarnples

118

(chapter 4). In this case, ab initio calculations of chernical shift tensor orientaiions

proved to be invahiable. It was found that il, is closest to the P-P bond for both

phosphorus chernical shift tensors. The b33 component is situated in the same plane as

the phosphole ring. The relative orientation of the 6, components for the phosphorus

nuclei reflects the local geometry of the phosphole rings.

The third compound described here, [Ph3P-PPhJ [GaCl.,] , was prepared in the

Burford lab. The solid-state NMR investigation of this compowid provided the P,P

bond length (chapter 5). Ab initio caiculations of 1J(31P,31P) on mode1 systems provided

insight into the dependence of J on molecular structure. For H,P-PH,, 1J(31P,31P) is

very dependent on the rotation of the PH, fragment about the P-P bond while it is n a l y

independent of rotation in H,P-PH2+.

From the results of these three projects some general conclusions rnay be drawn.

It is evident from the results for the phosphole tetramer and for [Ph,P-PPhJ[GaCl,] that

one cannot assume that the direction of greatest shielding corresponds to the generaily

perceived direction of greatest electron density, Le., dong the formal lone pairs.

Furthemore, knowledge of the anisotropy in 1J(31P,31P) is important for obtaining an

estimate of the bond length from ReR. The investigation of hl in TMPS M e r

establishes the observation that AJ(3iP,31P) is small in diphosphine disulfides, contrary

to earlier rep~rts.l'*'~ On the other W, first-priociple calculations indicate signifiant

anisotropies for LJ(31P,3LP) in HIP-PH2 and H,P-PH,+. In each of the projeds discussed

in this thesis, ub initio calculations of NMR parameters play a significant role. The

reliabiiity of d~ initio calculations for characterizhg phosphorus chernical shift tensor

orientations is established by compafison with results fiom a single-crystal "P NMR

study of TMPS. For the phosphole tetramer, it is possible to fU the chemicai shift

tensor orientation in the molecula. frame of reference by cornparhg calculated tensor

orientations with the orientation information available from the analysis of spectra

obtained from powder crystalline samples . First-principles calculations of 'Je 1P,31 P)

were aecessary to establish tbat hJC1P,31P) mkes a very small contribution to RM,

hence a reliable estimate of r, could be obtained for m3P-PPhJ[GaClJ.

In the past few years, the value of ab initio caiculations as a complement to

experimental results in the field of NMR has been recognized. The continuous

improvement and availability of computational methods and resources have undoubtedly

contributed to extending the range of systems which may be studid. While ub initio

calculations are yielding reliable qualitative results for nuclear magnetic shielding

tensors, much more work needs to be dom io reach the same level of confidence with J

coupling. in this respect, it is essential that the results from first-principle calculations

be compared with reliable experimental data. Some specific suggestions are given in the

next chapter. At the same the , it is important for NMR spectroscopists to use more

quantum chemistry methods and keep up to date with the latest developments Ui this

field.

Chapter 7: Future Research Directions

7.1 Introduction

Several extensions of the research presented in this thesis are worthy of

consideration. Suggestions include an investigation of phosphom chernical shift teasors

in other phosphinophosphoaium cations (section 7.2) as well as further 1 initio

calculations (section 7.3). While the calculations of J appears to be promising, much

more effort neeâs to be expeaded in this area. Ab inirio calculations are presently

limited to relatively small systems. The recent success of DFT approaches at

calculating J for numerous spin pairs are most encouraging . 12'g'u*1U Obviously , the

potential of this approach for calculating 1J(3iP,31P) should be investigated. Section 7.4

presents some preliminary resuits and suggestions for hirther theoretical studies of

indirect spin-spin coupling for systems containhg phosphorus spin pairs. All the spin

systems discussed in this thesis involve two coupled spin-% nuclei. An example of a

system consisting of three coupled spin-% nuclei is outlined in section 7.5.

7.2 [W,(Cî)P-PPbJ[GaCiJ

The precursor to [Ph,P-PPhJ [GaCb] (chapter 5), [Ph2(Cl)P(1)-P(2)PhJ [GaCl.,] ,

has also been isolated.l* In this case, the coupling of P(1) to a chlorine nucleus

cornplkates the appearance of the spectra. Chlorhe hm two naniraliy occurring

isotopes; 3sCl: spinin3/,, N.A. = 75.53 % and )'Cl: ~ p i o - ~ l ~ , N.A. = 24.47 1.

Phosphotus-31 NMR spectra of MAS samples are shown in figure 7.1, obtained at

120

. - , . . - , . . - , . , . LOO 80 60 40 20 0 -20

LOO 80 60 40 20 O -20

PPm

Figure 7.1 Phosphocus-3 1 NMR spectnun of solid [pb,(Cl)P-PPhJ[GaCî,,], with MAS at (a) 4.53 kHz at an applied magnetic field of 4.7 T.

acquired Sixteen

transients were acquired and 10 Hz of gaussian line broadening was applied. A specrnim aquired at an applied magnetic field of 9.4 T with MAS at 13 lrHz is s h o w in (b). Sixteen iransients were acquired and 50 Hz of gaussian line broadening was applied. The asterisks indicate spioning sidebands.

applieâ magnetic fields of 4.7 T and 9.4 T. The adysis of the spectra arising from a

spin-% nucleus couplai to a quadrupolar nucleus has been presented in the

literat~re;'~'- '~ however, many of the simulations are suspect, e.g., reference 192.

Carbon-13 coupld to 3sa7Cl bas been investigated in chloroketosulfones. L93 It is

important that experiments be carrieci out at several applied magnetic fields, as is

evident in re ference 193. The line shape for [PhZ(Cl)P-PPhJ [GaCî.,] is further

cornplicated by the coupling of P(1) to the phosphine centre. Initial simulation of the

MAS spectra proved to be unsuccessful. Reliminary 31P NMR studies of

[Ph2(Cl)P-PPhJ[GaCW by CP experiments indicate that the proton relaxation times are

long; recycle delays in excess of 2 minutes were needed to avoid saturation. Funher

experiments on this compound are in progress.

7.3 Ab Inirio Calculatioiis of Phosphorus Chernid Shift Tenson

The results from ub initio calculations of phosphonis chemical shift tensors

presented in this thesis indicate that qualitative agreement with expriment may be

expected. However, there appears to be a systematic discrepancy between the

experirnental and calculated results. For al1 three compounâs presented in this thesis,

the values of 6, calcdatd ai the HF level are more shielded by about 50 ppm. As

mentioned in section 3.3.3, changes in the phosphonis chernicd shift on the order of

teas of ppm have been observed upon changing from the gas to liquid state. Clearly,

the influence of intennolecular effefts on the phosphonis chemical shift weds to be

considered if one is to obtain quantitatively reliable results. Investigations dong these

123

lines on mode1 systems, such as PH3 or P,, for which the gas to liquid shifts are known

(see section 3.3.3), are recornrnended.

7.4 Characterization of 'J(31P:1P)

While 1J(31P,31P), is large and negative in H2P-PH2,Ln a large positive value,

+720 Hz, is observed in molecules of the type H,(CH,),,PPF5,lw and a value of +766

Hz was reported for the potassium sait of F02PPû2F+. lW Successful calculation of

'J(%P,"P), for these molecules which, together with H,P-PH,, span the range of

observed lJ("P?'P), values, would be of great value. A survey of MW results (FC

contribution only ), which includes the above-mentioned molecules, has ken reported ."

In addition, a large wgative values of 1J(31P,31P),, approximately 480 Hz, have been

observed for a series of dipho~pholes.~% Given the success of MCSCF37*1Q*110 and DFT

r n e t h ~ d s ~ ~ ~ * ~ ~ * ~ ~ for calculating J coupling, application of these theoretical approaches to

the above systems would be of interest. For the larger molecules, DFT may be the only

possibility with cunentiy available cornputer resources. initial results are promising;

however, systematic studies to reproduce experimental trends are warrant&.

There are a number of other small phosphonis-containing molecules besides

H,P-PH, for which experimental data are avaiiable." One system of fiindamental

importance is diphosphene, P,H,, as well as the analogous nitrogen compound, diazene,

N,H,. Results for J from calculations using the MCSCF approach with the cc-pVTZ

bais set for the tronr isomen of these two compounds are given in table 7.1. For

cornparison, data from an early ub initio studylW using smaller basis sets are also given.

Contributions to 'JJHz

'J(X,X)f iz hl(X,X)Rlz DSO PSO DS FC trm-N,H, O< = 15N)

CAS1 -249 -220 O -115 -16 -118 CASII -25 74 O 10 1 -36 SOS CI -17 - O -15 0.2 -2

diazenes * 10 to 20 tram-P,H, (X = 31P)

CASüI -1985 1076 0.2 -531 -1069 -385 CASIV -348 - 1463 O -386 49 -12 SOS CI -552 - O -498 9 -76

diphosphenes' & 5 10 to 670

Contributions to 'K, / IOi9 N A - k 3

lKO(,X)J ,I(X,X)/ DSO PSO DS FC 10i9 N A - k 3 1019 NA-%r3

trm-N2H2 (X = N) CAS1 -20 17 -1782 O -932 -130 -956 CAS11 -203 598 -0.3 79 12 -293 SOS CI -138 - 0.1 -122 2 - 16 diazenes & 80 to 160

tram-P,H, (X = P)

CASm -1006 174 0.1 -269 -542 -195

CASIV -176 -742 0.1 -1% 25 -6 SOS CI -280 - O -262 5 -39

diphosphenes' * 260 to 340

a Calculations p e r f o d at the MCSCF level with cc-pVTZ basis set. From reference 197. The geometq for tram N2H2 was not given. From reference 201. From reference 197. using the ST016-3 lGf* basis set. The geometry used for truns

P,H, is as foîlows: P-P = 2.034 A, P-H = 1.44 A, and P-P-H = 95.6". From reference 204.

The reduced coupling tensor, K (equation 2-24), is also presented in table 7.1.

The molecular geometries used are as foliows. For trm-P2H2, the P-P bond

length = 2.00 A, the P-H bond length = 1.40 A aad the P-P-H angle = 108". based on

typical values for diphosphenes. 198-199 For tm-N,H,, the N-N bond length = 1.247 A,

the N-H bond length = 1 -029 A, and the N-N-H bond angle = 106.3 O .m

The smallest active spaces used in both cases, 10101 1120 (denoted by CASI) for N2H,

and 414113 120 (CASIII) for P2H, do not include virtual molecular orbitals, and thus

give the same results as an HF ~alculation.'~ The larger active spaces, 10101223 1

(CAS@ for N2H, and 414114231 (CASiV) for P2H2, include a virhial orbitai for each

molecular orbital symmetry. As is evident for N,H,, the magnitude of 'J(lSN * NI,

calculated with CASII is in reasonable agreement with experirnental values that are

typicai of diazenes?' Unfortunately , the sign of this coupling is not known; however,

early semi-empuical calculations predicted that 'J(15N, I J N ) is negative except possibly in

hydrazine type c o m p o u n d ~ . ~ ~ ~ ~ The MCSCF results discussed above and early ab

initio resultsL* for N,H, in table 7.1 are in agreement with this prediction.

For P2H2, calculations using the larger active space, CASIV, predict a value of

-348 Hz for 1J(3tP,3'P), and a large negative hl of -1463 Hz. Unfortunately, no

experimental data are available for P2H2; however typical values of ' J(31P,3 'P), for

diphosphenes range between 5 10 and 670 Hz in magnitude, depending on the

substituent~.~~ The sign of the coupling is not known, but it bas been s u g g e ~ t e d ' ~ ~

that it is negative on the bais of early ab initio dcuiatiom which predicted a negative

value,tn 1J(31P,31P)im = -552 Hz, due to the large negative contribution from the orbital

126

mechanism. The type of basis set used for the early ab initio calculations,

ST016-3 le**, is known to be unreliable for indirect spin-spin coupling ~alculations.~

Semi-ernpiricai approaches predict a large positive value, +830 Hz when ody the FC

mechanism is conside~ed.'~

Also given in table 7.1 are the contributions of each cnechanism to lJh and 'Kb.

For P2H2, the magnitude of lJCIP,NP), is dominated by the PSO contribution; however,

it not definitive which mechanism dominates 'J(15N,1"N in NN,H2. Cornparison of the

contributions obtained using an active space with no virtual orbitals vs the results using

one that does include virtual orbitals illustrates the triplet iastability problem discussed

in section 2.3.2 where the contributions that depend on the triplet States are known to be

poorly calculated if virtual orbitals are not included in the MCSCF space. While

calculations qualitatively predict the trend in ' J , for P2H, vs N2H2, cornparison of the

values of 'Km is more telling of problems with the ub initio results. In this case, the

calculated results are clearly wrong ~~rnpated to the experimental results, i.e., using the

larger active space, the magnitude of [Km for N2H2 is larger than that for P2H2,

contrary to the experimental trend. For these systems, hirther work is necessary ,

possibly ushg restricted active s p a c e ~ . " * ~ ~ ~ ~ Even for a molecule as small as P2H2,

extensive study of the dependence of the calculated J on the active space is not possible

with currently available computational resources. It should be noted that systems such

as N,H, and P2HL, where there are multiple bonds and formal electron lone pairs,

present a difficult computatiorial chaUenge.'

127

7.5 NMR Spcdra Arising from Tbnc Coupied Homonuclear Spin-% Nuclei in the

Solid State

A logical extension to the investigations of spin pairs presented in this thesis is to

systems of multiple coupled spins. Analysis of spectra arising fkom multiple spin

systems are of interest in biomolecules where multiple labelling allows for more

information to be ext ra~ ted .~ The theory for the analysis of spectra arising fiom three

coupled heteronuclear spin-% nuclei has been presented in the literature, for the

AA'X,m ABXVm and AXZm cases. The iterative fitting of MAS spectra arising fmm

an ABX spin system to obtain chernical shift tensors has been reported.*1° In principle,

the ambiguity regarding the orientation of the chemicai shik tensor with respect to the

molecular frame of reference, which is an inherent limitation of the dipolar-chernical

shift method (section 2.2.2), is elhinateci in the analysis of spectra for three coupled

spins. For example, it was demoostrated for doubly 13C labelled L-alanine that the

carbon chemical shift tensors obtained from an analysis of powder samples211 agreed

well with results from a single-crystal NMR study.'12 In this case, the presence of both

the 13C-i3C, and L3Ca-14N spin pair was exploited to fm the carbon chemical SM tensors

relative to the molecule.

The above discussion pertains to multiple heteronuclear spin systems. A

homonuclear four spin system, the fully 'C labeUed monoarnmonium salt of maleic

acid, has been investigated by solid-state An example of a homonuclear three

spin system is iiiustrated in figure 7.2, where a linear arrangement of three phosphorus

Figure 7.2 Structure of a phosphorus-containing homonuclear three-spin system.

nuclei is pre~ent.~" A linear arrangement of phosphorus nuclei will simplify the

analysis of the spectra. An investigation of the phosphorus chernical shift tensors and

spin-spin coupling parameters in such a unique molecule would be a valuable

contribution to an understanding of the relationship between structure and NMR

parameters. A program available for simulating solid-state NMR spectra, SIMPSONVs'

is capable of calculating spectra arisiag from multiple coupled spins with the inclusion

of chernical shift, dipolar aod spin-spin coupling interactions and may be useful for this

project .

Appendix 1: Performing the 2D Sph-Echo NMR Expriment on the CMX Infinity 200 at the University of Alberta

The 2D spin-echo NMR spectra presented in this thesis were obtained ushg a

Bruker MSL 2 0 sptxtrometer (figure 4.5) or a Varian Chemagnetics CMX Infinity 2ûû

(figures 3.9 and 5.4). For the benefit of future users, the details of the procedure used

to obtain 2D spin-echo NMR spectra using the CMX Infhty 200 and to process the

data to a fonn that can be used for simulation with the program SpinEcholY> are

presented here. The following description pertains to the pulse program show in figure

2.8. The phase cycling of Rance and Byrd was used.IM

After setting up the parameters for a standard 1D NMR expriment using CP,

the x pulse on the X chamel needs to be caiibrated. This must be doue using the sarne

X power settings as used for CP. The important 2D parameters are dw2, tl - evolve,

and a12. The dwell tirne for the second dimension, dw2, should be set so that the sweep

width in the Fi projection (sweep width = lldw2) is larger than the largest splitting

expected, i.e., larger than 2& for a spin pair where the two nuclei are aot magnetically

equivalent anci 3R, for the case of magnetic equivalence (see figure 2.4). The

parameter t l - evolve corresponds to the time between the CP part of the pulse program

and the x pulse as well as the time following the x pulse aod before acquisition. In the

version of the 2D spin-echo pulse sequence used on the CMX mnity 200, the

parameter is calculated based on the value of a12, which is the number of times

129

130

t1 - evolve is incrernented, and dw2. The maximum value of tl-evolve is dwPai2.

UsuaUy a12 = 64 experiments is acceptable.

Once the data are collected, they are pracessed using Spinsight software.21s It is

recommeeded that zero filling and gaussian line broadeniog be applied in both

dimensions. To obtah a symmetric 2D NMR specmun, it is necessary to process in

magnitude mode for both dimensions. To ease simulation of the Fl projection with

S p i n E ~ h o , ~ ~ ~ it is usehl to bave the Ne in a format that is usable with WSOLIDS49 or

other processing software available for PCs. At the t h e of preparation of this thesis,

there is no direct method for doing this. uistead, a print out of the R projection is

scannai and a program called SPECMAKI? which is part of the WSOLIDS49 software

package, is used to convert the scanned image to a data file. The print out of the Fi

projection is obtained by executing a macro with Spinsight, called ldshowgroj . Note

that in the display, Spinsight uses the wrong value of the dwell t h e to calculate the

sa le (dw instead of dw2). This is corrected by changing the value of dw to the value

used for dw2 in the acquisition panel before the FI projection is printed out. If the 2D

spectnun is p ~ t e d out, the scale for the fl projection is correct. While it is not

necessary to convert the spectrum data in this way, simulation of the specaa and

preparation for publication is easier.

This appendix is intended to provide some details with regards to handling air-

sensitive sarnples for NMR studies. Some generai strategies will first be presented,

followed by some comments pertalliing to specific rotor designs.

For samples that are extremely air-sensitive, sealed Pyrex MAS rotor inserts

may be ~sed .~" The sample is heat sealed into the inserts or an epoxy sealant may be

used. Heat sealing is generally more difficult given the srnail size of the inserts and the

need to obtain as symmetric a seal as possible so as not to harnper MAS. If the sample

is packed directly into the MAS rotors, an additional precautionary masure to avoid

contact with air is to seal the rotor itself into a glass tube and break it open once the

NMR experirnent is set up.

The rotors used to obtain the NMR spectra presented in this thesis are

manufactured by either Bniker or Varian-Chemagnetics. It has been the experience of

the solid-state NMR group at Dalhousie University and University of Alberta that the

Bruker rotors are gewrally sufficiently air-tight and no special precautions are needed

beyond ensuring b t the rotor caps are tight fitting. For the VarianChemagnetics

rotors, there are a number of strategies for dealing with air-sensitive smples, for

example the use of glas inserts as discussed above is a cornmon solution. Lnserts are

commerciaiiy available for various Varian-Chemagmtics rotors. The rotor illustrated in

figure A2.1 was used to obtain NMR spectra of &-sensitive sarnples on the Varian-

Chemagnetics spectrometer. The ody modification to the commercial design is an

131

Figure A2.1 An illustration of a Varian-Chemagnetics rotor. (a) drive tip. (b) spacer . (c) zirconjum o d e sleeve. (d) epoxy seal. (e) end cap, with a hole for variable temperature experiments .

epoxy seal applied to the inner surface of the end cap, which is manufactureci with a

vent hole for variable temperature experiments. The drive tips usually fit very tightly,

hence there is no difficulty with excluding air at the other end of the rotor.

References

D. L. Pavia, G. M. Lampman, and G . S. Kriz. htroduction to Spectroscopy, 1 Ed. Saunders College Riblishing, Fort Worth, Texas. 19%.

U. Haeberlen. In Advances in Magnetic Resonance. Edired by J . S . Waugh. Acadernic Press, New York. 1976, Supplement 1, p. 1.

J. B. Robert and L. Wiesenfeld, Physics Repons 86, 363 (1982).

K. R. Dixon. In Multinuclear NMR. Edired by J . Mason. Plenum Press, New York. 1987, p. 369.

C. J. Jameson, AMU. Rm. Phys. Chem. 47, 135 (19%).

H. Fukui, Prog. Nucl. Magn. Reson. Spectrosc. 31.3 17 (1997).

A. C. de Dios, Prog. Nucl. Mugn. Reson. Spectrosc. 29, 229 (l996).

T. Helgaker, M. Jasniiiski, and K. Ruud, Chem. Rev. 99, 293 (1999).

C. J. Jameson. In Modeling NMR Chernical Shifts: Gaining Insights into Structure and Envuonment. Edired 6y J. C . Facelli and A. C. de Dios. American Chernical Society, Washington, K. 1999, p. 1.

K. Eichele, G. Wu, R. E. Wasylishen, and J. F. Britten, J. Phys. Chem. 99, 1030 (1995).

P. N. Tuniojian and J. S. Waugh, J. Chem. Phys. 76, 1223 (1982).

J. B. Robert and L. Wiesenfeld, Mol. Phys. 44, 319 (1981).

T. Nakai and C. A. McDowell, J. Am. Chem. Soc. 116, 6373 (1994).

(a) S. Aime, R. K. Hams. E. M. McVicker, and M. Fild, J. C h . Soc., Dalton T r m . 2144 (1976). (b) F. Sarürahya, Y. Sarikahya, 1. Topaloglu, and 1. O. Sentiirk, Chimica Acta Turcica 25, 35 (1997).

R. K. Harris, L. H. Merwin, and G. Hiigele, J. Chem. Soc., Farodoy Trans. 1. 83, 1055 (1987).

P. N. Tuaiajian aod J. S. Waugh, J. Magn. Reson. 49, 155 (1982).

K. W. Zilm, G. G . Webb, A. H. Cowley, M. Pakulski, and A. Orendt, J. Am. Chem. Sac. 110,2032 (1988).

R. Chaiionet, C. A. McDoweîi, M. Yoshifuji, K. Toyota, and J. A. Tosseiî, J. Mugn. Reson. A 104,258 (1993).

K. Eichek, G. C. Ossenkamp, R. E. Wasylishen, and T. S. Cameron, Inorg. Chem. 38, 639 (1999).

G. M. Bernard, G . Wu, M. D. Lumsden, R. E. Wasylishen, N. Maigrot, C. Charrier, and F. Mathey , J. Phys. Chem. A 103, 10L9 (WW).

J. Fischer, A. Mitschler, F. Mathey, anâ F. Mercier, J. Chem. Soc. D a h n T r m . 841 (1983).

(a) F. S. Shagvaleev, T. V. Zykova, R. 1. Tarasova, T. Sh. Sitdikova, and V. V. Moskva, J. Gen. Chen. USSR 60, 1585 (1990). (b) N. Burford, T. S. Cameron, J. A. C. Clybunie, K. Eichele, K. N. Robertson, S. Sereda, R. E. Wasylishen, and W. A. Whitla, Inorg. Chem. 35, 5460 (19%). (c) N. Burford, T. S. Cameron, D. J. LeBlanc, P. Losier, S. Sereda, and G. Wu, Organometallics 16, 4712 (1997). (d) N. Burford and D. J . LeBlanc, Inorg. Chem. 38,2248 (1999).

R. K. Harris. Nuclear Magnetic Resooaoce Spectroscopy . John Wiley and Sons, inc., New York. 1986, p. 10.

F. A. L. Anet and D. J. O'Leary, Concepts in Magn. Reson. 3, 193 (1991).

F. A. L. Anet and D. J. O'Leary, Concepts in Magn. Reson. 4, 35 (1992).

K. Schmidt-Rohr and H. W. Spiess. Multidimensional Solid State NMR and Polymers. Academic Press, London. 1994, p. 444.

J. Masoa, Solid Srare Nucl. Magn. Reson. 2,285 (19%).

(a) C . J. Jarneson, Solid Stae Nucl. Magn. R e m . 11,265 (1998). (b) R. K. Harris, Solid State Nucl. Magn. Reson. 10, 177 (1998).

R. E. Wasylishen. In Encyclopedia of Nuclear Magnetic Resoaance. Edited by D. M. Grant and R. K. Harris. Wiley hc., Chichester, UK. 1996, p. 1685.

C . I. lameson and J. Mason. In Multinuclear NMR. Edited by J . Mason. Plenum Press, New York. 1987, p. 3.

G. E. Pake, J. *m. Phys. 16,327 (1948).

C. J. Jarneson. In Multinuclear NMR. Edired by J . Mason. Plenum Ress, New York, 1987, p. 89.

A. D. Buckingham, P. Pyykko, J. B. Robert, and L. Wieseofeld, Mol. Phys. 46, 177 (1982).

W. T . Raynes, Magm Reson. Chem. 30,686 (1992).

A. D. Buckingham and 1. Love, J. Magn. Reson. 2, 338 (1970).

H. W. Spiess, hM.R Basic Princ. Prog. 15, 55 (1978).

D. L. Bryce and R. E. Wasylishen. J. Am. Chem. Soc. 122, 3197 (2000).

R. von Boeckh, G. Griff, and R. Ley, 2. Phys. 179,285 (1%4).

R. E. Wasylishen, K. C. Wright, K. Eichele, and T. S. Cameron, Inorg. Chem. 33,407 (1994).

M. D. Lumsden, R. E. Wasylishen. and J. F. Britten, J. Phys. Chem. 99, 166M (1995).

M. D. Lumsden, K. Eichele, R. E. Wasylishen, T. S. Cameron, and J. F. Britten, J. Am. Chem. Soc. 116, 11 129 (1994).

(a) W. P. Power, M. D. Lumsden, and R. E. Wasylishen, J. Am. Chem. Soc. 113, 8257 (1991). (b) W. P. Power and R. E. Wasylishen, Inorg. Chem. 31, 2176 (1992).

(a) D. L. VanderHart and H. S. Gutowsky, J. Chem. Phys. 49, 261 (1%8). (b) M. Linder, A. Hohener, and R. R. Ernst, J. Chem. Phys. 73,4959 (1980). (c) R. E. Wasylishen, R. D. Curtis, K. Eichele. M. D. Lumsden. G. H. Pemer, W. P. Power, and G. Wu. In Nuclear Magnetic Shieldings and Molecular Structure. Edited &y J . A. TosseIl. Kluwer Academic Publishers, Dordrecht. 1993, p. 297.

W. P. Power anci R. E. Wasylishen, Ann. Rep. NMR Spectrusc. 23, 1 (1991).

(a) K. W. Zilm and D. M. Grant, J. Am. Chem. Soc. 103. 2913 (198 1). @) G . Wu and R. E. Wasylishen, M d Sfate Nucl. Magn. Reson. 4-47 (1995).

H. van Wiiiigen, R. G. Griffin, and R. A. Haberkom, J. Chem. Pliys. 67,5855 (1977).

(a) R. D. Curt'i, J. W. Hiibom, G. Wu, M. D. Lumsden, R. E. Wasylishen, and l. A. Pincock, J. Phys. Chem. 97, 1856 (1993). (b) M. D. Lumsden, G. Wu, R. E. Wasylishen, and R. D. Curtis, J. Am. Chem. Soc. 115,2825 (1993).

K. Eichele a d R. E. Wasylishen, J. Mugn. Reson. A 106, 46 (1994).

K. Eichele and R. E. Wasylishen, WSOLIDS, 1994 and 2000.

B. Sun and R. G. Griffin, unpublished results.

M. Bak, J. T. Rasmussen, and N. C. Niclsen, J. Magn. Reson. 147. 2% (2000).

(a) A. Kubo and C. A. McDowell, J. Chem. Phys. 92, 7156 (1990). (b) E. Klaus a d A. Sebald, Angew. Chem. Iht. Ed. 34,667 (1995). (c) S. Dusold, E. Klaus, A. Sebald, M. Bak, and N. C. Nielsen, J. Am. Chem. Soc. 119,7121 (1997)

R. R. Ernst, G. Boâenhausen, and A. Wokaun. Principles of Nuclear Magnetic Resonance in One and Two Dimensions. Clarendon Press, Oxford. 1987.

A. Pines, M. G. Gibby, and J. S. Waugh, J. Chem. Phys. 59, 569 (1973).

S. R. Hartmann and E. L. Hahn, Phys. Rev. 128,2042 (1%2).

T. Nakai and C. A. McDowell, Chem. Phys. Leu. 217,234 (1994).

K. Eichele, R. E. Wasylishen, R. W. Schurko, N. Burford. and W. A. Whitla, Gm. J. Chem. 74, 2372 (1996).

S. Dusold, J. Kümmerlen, and A. Sebald. J. Phys. Chem. A 101,5895 (1997).

T. Nakai and C. A. McDowell, Solid State Nucl. Magn. Reson. 4, 163 (1995).

(a) N. F. Ramsey, Phys. Rev. 77,567 (1950). (b) N. F. Ramsey, Phys. Rev. 78, 699 (1950). (c) N. F. Ramsey, Phys. Rev. 83, 540 (1951). (d) N. F. Ramsey, Phys. Rev. 86, 243 (1952).

N. F . Ramsey, Phys. Rev. 91, 303 (1953).

N. F. Ramsey . Molecular Beams. Oxford University Press, London. 1956.

P. Pyykk6, nieor. Chem. Acc. 103,214 (2000).

J. H. Van Vleck. The Theory of Electric and Magnetic Susceptibilities. Oxford University Press, London. 1932.

C. J. Jameson and J. Mason. In Muttinuclear NMR. Edited liy J. Mason. Plenum Press, New York. 1987, p. 51.

D. B. Chesnut, Ann. Rep. NMR Spearosc. 29.71 (1994).

R. W. Schurko and R. E. Wasylishen, J. Phys. Chem. A 104, 3410 (2000).

D. L. Bryce and R. E. Wasylishen, J. Phys. Chem. A 104,7700 (2000).

U. Fleischer, C. van Wüllen, and W. Kutzelnigg . In Encyclopedia of Computational Chemistry. Edited by P. von R. Schleyer. John Wiley and Sons, Chichester. 1998, p. 1927.

W. Kutzelnigg, U. Fleischer , a d M. Schindler, NMR Basic Princ. Prog. 23, 163 (1990).

S. 1. Chan and T. P. Das, J. a e m . Phys. 37, 1527 (1962).

C. W. Kern and W. N. Lipscomb, J. Chem. Phys. 37, 260 (1%2).

(a) R. Ditchfield, Mol. Phys. 27, 789 (1974). (b) K. Wolinski, J. F. Hinton, and P. Pulay, J. Am. Chm. Soc. 112, 825 1 (1990). (c) G. Rauhut, S. Puyear, K. Wolinski, and P. Pulay, I. Phys. Chem. 100, 6310 (19%).

M. Schindler and W. Kutzelnigg, J. Chem. Phys. 76, 19 19 (1982).

A. E. Hansen and T. D. Bouman, J. Chem. Phys. 82, 5035 (1985).

T. A. Keith and R. F. W. Bader, Chem. Phys. Laa. 194, 1 (1992).

(a) J. Gauss, Chem. Phys. Lm. 191,614 (1992). @) J. Gauss, Chem. Phys. L m . 229, 198 (1994).

B. O. Roos, Adv. Chen. Phys. 69,399 (1987).

K. Ruud, T. Helgaker, R. Kobayashi, P. Jmgensen, K. L. Bak, and H. J. Aa. Jensen, J. Chem. Phys. 100,8178 (1994).

(a) M. Biihl, M. Kaupp, O. L. M a l b , and V. G. Malkin, J. Cornp. Chem. 20 91 (1999). (b) V. G. Maikin, O. L. MalLina, M. E. Casida, a d D. R. Salahub, J. Am. Chem. Soc. 116,5898 (1994). (c) V. G. Malkin, O. L. Maikina, and D. R. Salahub, Chem. Phys. Lm 204.87 (1993). (d) V. G. MalLin, O. L.

Mafkina, and D. R. Salahub, &m. Phys. Le#. 2-04. 80 (1993).

G. Scbreckenbach. R. M. Dichon, Y. Ruiz-Morales. anci T. Ziegler. In Chemical Applications of Density Funaional Theory . Edited by B. B. Laird, R. B. Ross, and T. Ziegler. American Chemical Society, Washington. 19%. p. 328.

(a) G. Schreckenbach, S. K. Wolff, a d T. Ziegler, J. Phys. Chem. A 184, 8244 (2W). (b) S. K. Wolff, T. Ziegler, E. van Lenthe, ami E. J. Baerends, J. Chem. Phys. 110,7689 (1999).

Gaussian 94, Revision 8.2. M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G. Zaknewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe. C. Y. Peng, P. Y. Ayala. W. Chen. M. W. Wong, J. L. Andres, E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox. J. S. Binkley, D. J. Defrees, J. Baker. J. P. Stewart, M. Head-Gordon, C. Gonzalez, ancî J. A. Pople, Gaussian, hc., Pittsburgh, PA, 1995.

Gaussian 98, Revision A.4, M. J. Frisch, G. W. Trucks, H. B. Schiegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery, Jr., R. E. Stramÿinn, J. C. Burant, S. Dapprich, J. M. Millam, A. D. Daniets, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Carnmi, B. Mennuai, C. Pomelli, C. Adamo, S. Clifford, I. Ochterski, G. A. Petersson, P. Y. Ayala, Q. Cui, K. Morokuma. D. K. Malick. A. D. Rabuck, K. Raghavachari, J. B. Foresmao. J. Cioslowski, J. V. Ortiz, B. B. Stefanov, G. Liu, A. Liashenko, P. Piskon, 1. Komaromi, R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A. Al-Laham, C. Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P. Gill, B. Johiison, W. Chen, M. W. Wong, J. L. Andres, C. G o d e z , M. Head-Gordon, E. S. Replogle. aod J. A. Pople, Gaussian, ïnc., Pittsburgh PA, 1998.

E. Frisch and M. J. Frisch. Gaussian 98 User's Reference, 2"d Ed. Gaussian hc., Pittsburgh PA. 1999, p. 126.

C.J. Jameson. In Encyclopedia of Nuclear Magnetic Resonance. Edited by D. M. Grant anâ R. K. Harris. Wiley Inc. Chichester, UK. 19%, p. 1273.

A. K. Jarneson and C. J. Jameson, Chm. Phys. Len. 134, 461 (1987).

R. E. Wasylishen, S. Mooibrœk, aad J. B. Macdonald, J. Chem. Phys. 81, 1057 (1984).

C. J. Jameson, A. K. Jarneson, aod P. M. Bumll, J. Chem. Phys. 73,6013 (1980).

C. J. lamson, A. C. de Dios, and A. K. Jameson, Chem. Phys. Let?. 167,575 (1gm.

M. Gee, R. E. Wasylishen, and A. Laaksouen, J. Phys. Chem. A 103, 10805 (1999) =

J. E. Rich, M. N. Mando, and A. C. de Dios, J. Phys. Chem. A 104,5837 (20OQ

B. Celda, C. Biamonti, M. J. Arneau, R. Tejero, and G. T. Montelione, J. Biomol. NMR 5, 161 (1995).

D. D. Laws, A. C. de Dios, d E. Oldfield, J. Biomol. NMR 3,607 (1993).

(a) A. J. Dingley and S. Grzesiek, J. Am. C h . Soc. 120, 8293 (l998). (b) A. J. Dingley, J. E. Masse, R. D. Peterson, M. Barfield, J. Feigon, and S. Grzesiek, J. Am. Chem. Soc. 121, 6019 (1999). (c) F. Cordier and S. Grzesiek, J. Am. Chem. Soc. 121. 1601 (1999). (d) G. Cornilescu, J.-S. Hu, and A. Bax, J. Am. Chem. Soc. 121,2949 (1999). (f) F. Cordier, M. Rogowski, S. Grzesiek, and A. Bax, J. Magn. Reson. 1 4 , 510 (1999).

C. Scheurer and R. Briischweiier, J. Am. Chem Soc. 121, 8661 (1999).

D. L. Bryce and R. E. Wasylishen, J. Biomol. NMX 19, 371 (2001).

H. Beuedict, 1. G. Shenderovich, O. L. Malkina, V. G. Malkin, G. S. Denisov, N. S. Golubev, and H.-H. Limbach, J. Am. Chem. Soc. 122. 1979 (2000).

H. Fukui, Prog. Nucl. Magn. Reson. 35,267 (1999).

N . F. Ramsey . In -Experimental Nuclear Physics . Edited by E . Segr&. John Wiley and Sons, New York. 1953, vol. 1, part III, p. 358.

J. Kowalewski and A. laaksouen. In Theoretical Models of Chernical Bonding. Edited by 2. B. Maksic. Springer, Berlin. 1991, part 3, p. 387.

P. PyykE, Chem. Pliys. 22,289 (1977).

V. Sychrovsw, J. Grâfenstein, and D. Cremer, J. Chem. Phys. 113, 3530

1. Carmichael, J. Phys. Chen. 97, 1789 (1993).

O. L. Malkina, D. R. Salahub, and V. G. MalLin, J. Chem. Phys. 105, 8793 (19%)

V. G. MalLin, O. L. Malkioa, and D. R. Salahub, Chem. Phys. Lan. 221.91 (1994) -

M. F. Guest, V. R. Saunders, and R. E. Overill, Mol. Phys. 35, 427 (1978).

O. Vahtras, H. Agren, P. Jergensen, J. J. Aa. Jensen, S. B. Padkjzr, and T. Helgaker, J. Chem. Phys. 96, 6120 (1992).

(a) A. Barszczewicz, T. Helgaker, M. Jasnidski, P. Jmgensen, and K. Ruud, J. Magn. R e m . A 114, 212 (1995). (b) A. Barszczewicz, T. Helgaker, M. JaszuBski, P. Jergensen, and K. Ruud, J. Chem. Phys. 101, 6822 (1994). (c) J. Kaski, P. Lantto, J. Vaara, and I. Jokisaari, J. Am. Chem. Soc. 120, 3993 (1998). (d) J. Kaski, P. Lantto, T. T. Raniala, 1. Schroderus, J. Vaara, and J. Jokisaari, J. Phys. mem. A 103, %69 (1999).

D. L. Bryce and R. E. Wasyiishen, J. Am. Chem. Soc. 122, 11236 (2000).

J. F. Stanton and R. J. Bartien, J. Chem. Phys. 98,7029 (1993).

S. A. Perera, H. Sekino, and R. J. Bartlett, I. Chem. Pliys. 101, 2186 (1994).

S. A. Perera, R. J. Bartien, and P. von R. Schleyer, J. Am. Chem. Soc. 117, 8476 (1995).

J. Oddershede, P. Jergensen, and D. L. Yeager, Cornput. Phys. Rep. 33,2 (1984).

J. Oddershede. In Methods in Computatioiial Molecuiar Physics. Edited &y S. Wilson and G. H. F. Diercksen. Plenum Press, New York, 1992, p. 303.

T. Enevoldsen, J. Oddershede, and S. P. A. Sauer, Theor. Chem. Acc. 100,275 ( 19%).

S. A. Perera and R. J. Bartien, J. Am. a e m . Soc. 122, 1231 (2000).

H. Fukui, J. Chem. Phys. 65, 844 (1976).

T. Enevoldsen, L. Vischer, T. Saue, H. J. Aa. Jensen, and J. Oddershede. J. Chem. Phvs. 112.3493 (2000).

3. Khandogin and T. Ziegler, J. Phys. Qirm. A 104, 1 13 (2ûûû).

J. Autschbach and T. Ziegler, J. Am. C'hm. Soc., 123, 3341 (2001).

J. Autschbach and T. Ziegler, J. Chem. Phys. l U , 936 ( 2 0 ) .

J. Autschbach and T. Ziegler, J. Chen. PM. 113, 9410 (2000).

T. Helgaker, M. Jasnihski, K. Ruud, aiid A. Gorska, nieor. Chem. Acc. 99, 175 (1998).

J. Vaara, J. Kaski, and J. Jokisaari, J. Phys. C h . A 103, 5675 (1999).

A. Viste, M. Hotokka, L. LaaiCsonen, and P. Pyykk6, Chem. Phys. 72,225 (1982).

(a) K. Krüger, G. Grossmann, U . Fleischer, R. Franke, and W. Kutzelnigg , Mogn. Reson. Chem. 32, 5% (1994). (b) G. Ohms, U. Fleischer, and V. Kaiser, J. G e m . Soc., Dalron Tram. 1297 (1995).

A.-R. G r b e r , R. Peter, and E. Fechner, 2. Chem. 18, 109 (1978).

(a) R. J. Iuliucci, C. G. Phung, J. C. Facelli, and D. M. Grant, J. Am. Chem. Soc. 118. 4880 (1996). (ô) R. J. Iuliucci, C. G. Phung, J. C. Facelli, and D. M. Grant, J. Am. Chem. Soc. 12û, 9305 (1998). (c) R. W. Schurko, R. E. Wasylishen, and H. Foerster, J. Phys. Qlom. A 102,9750 (1998). (d) D. L. Bryce and R. E. Wasylishen, J. Phys. Chem. A 103,7364 (1999).

(a) T. Vosegaard, P. Daugaard, E. Haid, and H. J. Jakobsen, J. MW. Reson. 142, 379 ( 2 0 ) . (b) T. Vosegaard, J. Skibsted, and H. J. Jakobsen, J. Phys. Chem. A 103.9144 (1999). (c) T. Vosegaard, E. Hald, V. Langer, H. J. Skov, P. Daugaard, H. Bildsae, and H. I. Jakobsen, J. Magn. Reson. 135, 126 (1998).

(a) SADABS. G. M. Sheldrick, and Bruker AXS, Inc., Madison, Wisconsin, 53719 USA. (ô) R. H. Blessing, Acta Crysrallogr. A51, 33 (1995).

S. N. Dutta, and M. M . Woolfson, Acta. Cpal logr . 14, 178 (1%1).

SHELXTL (5.10) program library (G. Sheldrick, Siemens XRD, Madison Wisconsin).

J. S. Rollen, Computing Methods in Crystallography . Pergamon Press, New York. 1965.

E. Prince. Mathmaticai Techniques in Crystailography and Material Science. Springer-Ver lag , Berlin. 1994.

(a) M. A. Kemedy and P. D. Ellis, Concepts in Magn. Reson. 1, 35 (1989). (b) M. A. Kennedy and P. D. Ellis, Concepts in Mogn. Reson. 1, 109 (1989). (c) K. Eichele, J. C. C. Chan, R. E. Wasylishen, aad J. F. Britten, J. Phys. Chem. A 101,5423 (1997).

D. W. Aldemian, M. S. Solum, and D. M. Grant, J. Chem. Phys. 84,3717 (1986).

M. Rance and R. A. Byrd, J. Magn. Reson. 52, 221 (1983).

SpinEcho, K. Eichele and R. E. Wasylishen, unpublished.

A. D. Becke. J. Chem. Phys. 98, 5648 (1993).

C. Lee, W. Yang, anâ R. G. Parr, Phys. Rev. B. 37,785 (1988).

R. K. Harris and R. G. Hayter, Can. I. C h . 42,2282 (1964).

(a) J. M. Mfllar, A. M. T'hayer, D. B. Zax. and A. P k s , J. Am. Chem. Soc. 108, 5113 (1986). (b) T. Nakai, J. Ashida, and T. Terao, Mol. Phys. 67, 839 (1989).

J. D. Lee and G. W. Goodacre, Acra. CrystaZlogr. B27, 302 (1971).

M. G. Munowitz and R. G. Griffin, J. Chenz. Phys. 76,2848 (1982).

Y. Ishii, T. Terao, and S. Hayashi, I. Chem. Phys. 107, 2760 (1997).

J. Henfeld and A. E. Berger, J. Chem. Phys. 73,6021 (1980).

R. E. Wasylishen, W. P. Power, G. H. P e ~ e r , and R. D. Curtis, Can. 3. Chem. 67, 1219 (1989).

G. Heckmann and E. Fluck, Mol. Phys. 23, 175 (1972).

C. 1. Jarneson, Buü. Magn. Reson. 3, 3 (1980).

R. Sillanpaa. O. Ergin, and S. Çelebi, Am C'alfogr. C49, 767 (1993).

F. Mathey, F. Mercier, F. Nief, J. Fischer, aod A. Mitschier, J. Am. Ckm. Soc. 104,2077 (1982).

143

G. Wu and R. E. Wasylishen, J. Chem. Phys. 99, 6321 (1993).

G. Wu. B. Sun, R. E. Wasylishen, and R. G. Gnnin, J. Magn. Reson. 124,366 ( 1997)

teXsan for Windows version 1-05: Crystai Structure Analysis Package, Molecular Structure Corporation (1997-8).

(a) D. B. Chesnut and K. D. Moore, J. C o q . Chem. 10,648 (1989). (b) D. B. Chesnut, B. E. Rusiloski, K. D. Moore, and D. A. Egolf, J. C o q . Chem. 14, 1364 (1993).

S. Dumgthai and G. A. Webb, Orgarùc Magn. Reson. 21, 199 (1983).

D. B. Chesnut and L. D. Quin, J. Am. Chem. Soc. 116, %38 (1994).

D. B. Chesnut and E. F. C. Byrd, H e t e r ~ m Chem. 7, 307 (19%).

G. M. Bernard, G. Wu, and R. E. Wasylishen, J. Phys. Chem. A 102, 3 184 (1998).

(a) F. Mathey, Chem. Rev. 88,429 (1988). (b) F. Mathey, Coordination Chem. Rev. 137, 1 (1994).

(a) L. Nyulhzi, 3. Phys. Chem. 100, 6194 (1996). (b) A. Dransfeld, L. Nyuihzi, anâ P. v. R. Schleyer, Iiwrg. Chem. 37,4413 (1998). (c) F. G. N. Cloke, P. B. Hitchcock, P. Humble, I. F. Nixon, L. Nyulhszi, E. Niecke, and V. Thelen, Angew. Chem. IM. Ed. 37, 1083 (1998).

L. Nyulâszi, Chem. Rev., in press, 2001.

K. Eichele, R. E. Wasylishen, J. M. Kessler, L. Solujic, and J. H. Nelson, Inorg. Chem. 35, 3904 (19%).

R. D. Curtis, B. W. Royan, R. E. Wasylishen, M. D. Lumsden, and N. Bdord, Inorg. &m. 31,3386 (1992).

J. B. Gmtzner . In Recent Advances in Organic NMR Spectroscopy . Edited ûy 3. B. Lambert a d R. Rittrier. Noreii Press, Landisville, NJ. 1987, chapter 2, p. 17.

G. H. Penner and R. E. Wasylishen, Clm. J. Chem. 67, 1909 (1989).

G. Wu, R. E. Wasylishen, W. P. Power, anâ G. Baccolini, Cnn. J. Chem. 70,

N. Burford, E. Ocando-Mavara, unpubüshed.

W. Haubenreisser, U. Sternberg, and A.R. Grimmer, Mol. Phys. 9, 15 1 (1987).

"DALTON, an ob initio electronic structure program", written by T. Helgaker, H.J. À. Jensen, P. Jargemea, J. Oka, K. Ruud, H. Agren, T. Andersen, K.L. Bak, V. Bakken, O. Christiansen, P. Dahle, E.K. Dalskov, T. Euevoldsen, B. Fernandez, H. Heiberg, H. Hettema, D. Jonsson, S. Kirpekar, R. Kobayashi, H. Koch, K.V. Mikkelseo, P. N o m , M.J. Packer, T. Saue, P.R. Taylor, and O. Vahtras; Release 1 .O (1997).

(a) H. J. Aa. Jensen, P. Jergensen, H. Àgren, and J. Olsen, J . Chem. Phys. BS, 3834 (1988). (b) J. Guilleme and J. S. Fabian, J. Chem. Phys. 109, 8168 (1998).

T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989).

J. R. Durig, L. A. Carreira, and J. D. Odorn, J. Am. Chem. Soc. 96,2688 (1974).

(a) E. R. Aadrew, A. Bradbury, R. G. Eades, and V. T. Wym, Phys. Lm. 4, 99 (1963). (b) D. P. Raleigh, M. H. Levitt, and R. G. Griffin, Chem. Phys. Len. 146, 71 (1988). (c) D. L. Bryce and R. E. Wasylishen. In Encyclopedia of Spectroscopy and Spectrometry. Edited by J. C. Lindon, G. E. Tranter, and J. L. Holmes. Academic Press, San Diego. 2000, p. 2 136.

(a) G. A. Olah and C. W. McFarland, J. Org. Cliem. 34, 1832 (1%9). (b) B. E. Mann, J. Chem. Soc., Perkin Trans. 2.30 (1972). (c) S. O. Grim, E. F. Davidoff, and T. J. Marks. 2. Nmuforsch. 26b, 184 (1971). (d) G. P. Schiemenz, Phosphorus 3, 125 (1973).

R. W. Rudolph and R. A. Newmark, J. Am. Chem. Soc. 92, 1 195 (1970).

H. C. E. McFarlane and W. McFarlane, J. Chem. Soc., Chem. Commun. 1589 (1971).

W. McFarIane, N. H. Rees, L. Constanza, M. Patel, anci 1. J. Colquhoun, J. Chem. Soc., Dalton Tram. 4453 (2000).

C. I. Jarneson. In Phosphorus-31 NMR Spectroscopy in Stereochemical Analysis. Edired by J. G. Verkaâe and L. D. Quin. VCH Publishers, Inc., Deerfield Beach. Fla. 1987. D. 205.

U. C. Singh, P. K. Basu, and C. N. R. Rao, J. Mol. Stnîct. 87, 125 (1982).

R. M. Lyaden-Bell, J. Chem. Six., Farad@ Tron. 57,888 (1961).

J. P. Albrand, H. Faucher, D. Gagnaire, and J. B. Robert, Chem. Phys. Lm. 38, 521 (1976).

V. Galasso, J. C h m . Phys. 80,365 (1984).

D. Chakraborty and P. Chandra, J. Mol. Struct. 434,75 (1998).

J. M. Schulman, J. Ruggio, and T. J. Venanzi, J. Am. Chem. Soc. 99,2045 (1977).

V. M. S. Gil and W. von Philipsbom, Magn. Reson. Chem. 27,409 (1989).

S. Berger and J. D. Roberts, J. Am. Chem. Soc. 96, 6757 (1974).

W. McFarlane, Proc. R. Soc. Lordon, Ser. A. 306, 185 (1968).

H. C. E. McFarlane and W. McFarlane, J. Chem. Soc., Chem. Commun. 582 (1975).

(a) D. L. VanderHart, H. S. Gutowsky, and T. C. Farrar, J. Am. Chem. Soc. %9, 5056 (1%7). (b) H. W. Spiess, U. Haeberlen, and H. Zimmermann, J. Magn. Reson. 25, 55 (1%7). (c) M. M. Maricq and J. S. Waugh, J. Chem. Phys. 70, 3300 (1979). (d) E. Menger and W. S. Veeman, I. Magn. Reson. 46,257 (1982). (e) J. G. Hexem, M. H. Frey, anci S. J. Opella, J. Chem. Phys. 77, 3847 (1982). (f) J. Bohm, D. Fenzke, and H. Pfeifer, J. Magn. Reson. 55, 197 (1983). (g) D. L. Sastry, A. Naito, and C. A. McDowell, Chem. Phys. Lm. 146, 422 (1988). (h) A. C. Olivieri and R. K. Harris, Prog. Nucl. Magn. Reson. Spectrosc. 24,435 ( l m ) .

N. Zumbulyadis, P. M. Henrichs, and R. H. Young, J. Chem. Phys. 75, 1603 (198 1).

K. Eichele, R. E. Wasylishen, J. S. Grossert, and A. C. Oüvieri, J. Phys. Chem. 99, 101 10 (1995).

C. W. Schultz and R. W. Rudolph, J. Am. Chem. Soc. 93, 1898 (1971).

H. Falius and M. Murray, J. Magn. Reson. 10, 127 (1973).

F. Breitsameter, K. Polborn, and A. Schmidpeter, Eur. J. Inorg. Chem. 1907 (1998).

V. Galasso, (Tiem. Phys. 83,407 (1984).

A. H. Cowley and N. C. Norman, Prog. Inorg. Chem. 34, 1 (1986).

D. G. Gilheany . In The Chemistry of Organophosphonis Cornpounds. Edired by F. R. Hartley. John Wiley and Sons, Chichester. 1990, p. 43.

J. Demaison. F. Hegeluad, and H. Burger, J. Mol. Strun. 413,447 (1997).

M. Witanowski, L. Stefaniak, and G. A. Webb, Ann. Rep. W R Spectrosc. l lb , 1 (1981).

T. Khin and G. A. Webb, J. Mugn. Reson. 33, 159 (1979).

M . Witanowski, L. Stefaniak, and G. A. Webb, Am. Rep. MMR Spectrosc. l lb , 140 (1981).

H .-P. Schrikiel and A. Schmidpeter, Phosphorus, Suiphur, und Silicon 129, 69 ( l m *

P.-A. Malmqvist, A. Rendell. and B. O. Roos, J. Phys. Chem. 94,5477 (1990).

(a) Y. Ishii and R. Tycko, J. Am. Chem. Soc. 122, 1443 (2000). (b) F. M. Marassi, A. Ramarnoorthy, and S. J. Opella, Nd. Aca. Sci. U.S.A. 94, 8551 (1997). (c) C. H. Wu, A. Ramamoorthy, and S. J. Opella, J. Magn. Reson. A, 109, 270 (1994). (d) A. Ramamaorthy, C. H. Wu, and S. J. Opella, J. Magn. Reson. B , 107, 88 (1995).

G. Wu and R. E. Wasylishen, Mol. Phys. 83, 539 (1994).

R. Challoner and C. A. McDowell, J. Magn. Reson. 98, 123 (1992).

H. Bai and R. K. Harris, J. Magn. Reson. 96.24 (1992).

S. Dusold and A. Sebald, Mol. Phys. 95, 1237 (1998).

M. Bak and N. C. Nielsen, J. Chern. Phys. 106,7587 (1997).

A. Naito, S. Ganapathy, K. Akasaka, and C. A. McDowell, I. Chem. Phys. 74, 3190 (1981).

S. Dusold. H. Maisel. and A. Sebald, J. Mam. Reson. 141, 78 (1999).

214. H. Luo, R. McDonald, and R. G. Cavell, Angew. Chem. Int. Ed. 37, 1098 ( 1998).

215. Spinsight 4.1, Varian Associates, Inc., 1998.

216. SPECMAKE, a program by K. Eichele, 1998.

217. P. J. Giarnmatteo, W. W. H e h t h , F. G. Ticehurst, and P. W. Cope, J. Magn. Reson. 71, 147 (1987).