RelatoreDr. Giuseppe Pileio

PhD.: Scienze e Tecnologie delle Mesofasi e dei Materiali Molecolari (STM3) – XVII° ciclo

LXNMR_S.C.An.:SStructural and CConformational AnAnalysis by NNuclear MMagnetic

RResonance spectroscopy of molecules dissolved in LLiquid CCrystals

ProgramProgram Main purpose: knowledge of LXNMR technique for structural and/or conformational information on molecules in liquid-like phases

The Conformational

problem

How to workin practice

Liquid crystals

NMRTheory

Some examples

1st hour

2nd hour

3th hour

4th hour

Liquid CrystalsLiquid Crystals

Liquids Liquid-Crystals solids

thermotropic Lyotropic

Calamitic Discotic Banana

nematics Smectics Colestericsetc

1D solid, 2D liquid

Liquid Crystalline texturesLiquid Crystalline textures

NEMATICS

SMECTICS

Nematic phaseNematic phase

•Absence of polarity n(r) = -n(r)

•Point Group D∞h

•ρ = const (translational symmetry T(3))

•Optically uniaxial (positive is nz=n > nx= ny=n)

n

n

•Absence of polarity n(r) = -n(r)

•Point Group D∞h

•ρx, ρy = const (translational symmetry T(2))

•The uniaxial order parameter is the same as in nematics, but its absolute value SA>SN.

Smectic A phaseSmectic A phase

nqzzn

n cos)(

0

Smectic C phaseSmectic C phase•Absence of polarity n(r) = -n(r)

•Point Group C2h

•Translational symmetry T(2) as in Smectic A

(the position in layer is uncorrelated but the tilt it is)

•Optically biaxial (positive is nz≠ nx≠ ny)

•In SmC the director is free to rotate along the conical

surface with an apex angle 2

Smectic B phaseSmectic B phase

•Absence of polarity n(r) = -n(r)

•The point group symmetry is D6h

•optical uniaxiality n n and nz > nx = ny

•Three dimensional density wave)cos()cos()cos(),,( yqxqzqzyx IIII

Surprising things happen to physical properties like Surface Tension, Osmotic Pressure and Light Scattering when we add surfactant to water.

SurfactantConcentrationin water

Only surfactantunimers exist in

this region

Micelles Begin to form

here

More micellesform in this

region

Osmotic Pressure

Light Scattering

Surface Tension

Lyotropic liquid crystalline phases form by water solutions of amphiphilic molecules. The building blocks of those phases are either bilayers or micelles.

Lyotropic phasesLyotropic phases

The form of the micelles can be spherical or cylindrical and the micelles can be normal (tails in the water, polar heads outside) or reversed (water and polar heads inside, oil outside). Examples of the structureof some typical lyotropic phases (lamellar, cubic, haxagonal) are shown:

NMR Theoretical BackgroundNMR Theoretical Background

NMR HamiltonianNMR Hamiltonian

l

l

lm

mlmlmC ,,_

ˆ1ˆ TA

IRREDUCIBLE IRREDUCIBLE SPHERICAL SPIN SPHERICAL SPIN (or SPIN-FIELD) (or SPIN-FIELD)

TENSOR TENSOR OPERATOROPERATOR

IRREDUCIBLE IRREDUCIBLE SPHERICAL SPHERICAL

SPATIAL TENSORSPATIAL TENSOR

NMRNMRINTERACTIONINTERACTION

TENSOR TENSOR RANKRANK

mm-th -th COMPONENT COMPONENT

OF RANK OF RANK LL TENSORTENSOR

INTERACTION INTERACTION CONSTANT FOR CONSTANT FOR

THE THE -th SPIN -th SPIN INTERACTION INTERACTION

Solids Solids

Anisotropic liquids Anisotropic liquids

Isotropic liquids Isotropic liquids

HH0 0 HHrf rf CS DCS Dshort short D Dlonglong J Q J Q

What is a tensor ? What is a tensor ?

A tensor is a mathematical object that transform under rotation of the frame in a particular way.

Any tensor may be expressed as a matrix of rank r. So:• a rank 0 tensor is a scalar• a rank 1 tensor is a vector • a rank 2 tensor is a matrix n x nAnd so on….

Main Property: The trace of a tensor is unvariant under any change of frame by rotation.

AA

• Addiction: Aij + Bij = Cij

Only for tensor of equal rank• Outer product: Aij x Bl = Cijl

Always possible (rank must be different)• Inner product (contraction): Aij * Bjl = ∑j (Aij * Bjl) =Cil

Is possible when two or more indices are equal

Operations on tensors Operations on tensors

Irreducible spherical tensorsIrreducible spherical tensors

Irreducible spherical tensors have component that transform, under change of frame by rotation defined by euler angles ΩF’-F, as:

l

lm

FFlmm

F

ml

F

ml D '*),(

'

),(

AA Wigner Rotation MatrixWigner Rotation Matrix

The Euler angles The Euler angles

rotation:rotation:The object rotates around its own The object rotates around its own z-axis.z-axis.

rotation:rotation:The object rotates so that the angle The object rotates so that the angle between the two z-axis varies over between the two z-axis varies over 0-360.0-360.

rotationsrotations

rotation:rotation:The object rotates around the z-axis The object rotates around the z-axis of the LAB.of the LAB.

Some Wigner rotation matricesSome Wigner rotation matrices

iii

ii

iii

mm

eee

ee

eee

mm

D

2

cos1sin

2

1

2

cos11

sin2

1cossin

2

10

2

cos1sin

2

1

2

cos11

101\

,,1

1000 D

Rank 0:

Rank 1:

Rank 2:

iiiii

iiiii

iiii

iiiii

iiiii

mm

eeeee

eeeee

eeee

eeeee

eeeee

mm

D

22

222222

2222

222

22

2222

22

222222

2

2

cos1sin

2

cos1sin

8

3sin

2

cos1

2

cos12

sin2

cos1

2

cos1cos2sin

8

3cos

2

cos1sin

2

cos11

sin8

32sin

8

3

2

1cos32sin

8

3sin

8

30

sin2

cos1cos

2

cos12sin

8

3

2

cos1cossin

2

cos11

2

cos1sin

2

cos1sin

8

3sin

2

cos1

2

cos12

21012\

,,

zzyyxx aaaA 3

1)0,0(

2

1 1

2

0

2

1 1

,1

zyyzzxxz

xyyx

zyyzzxxz

m

iaiaaam

aai

m

iaiaaam

A

3

2

6

1 0 ,2

zzyyxxm aaamA

1) axx + ayy + azz = Tr(A)

Symmetrical tensors:Symmetrical tensors:

2) aa

= 1/3 Tr(a)= 1/3 Tr(a)

In the Principal Axis System PASIn the Principal Axis System PAS

3) axy = axz = ayz = 0

Why irriducible spherical tensors?Why irriducible spherical tensors?

zyyzzxxz iaiaaam 2

1 1

yzyzzxxz iaiaaam 2

1 1

It remains only:It remains only:L = 0, 2L = 0, 2m = 0 m = 0

Cylindrical symmetry DCylindrical symmetry D∞∞hh

4) axx = ayy yxxyyyxx iaiaaam 2

1 2

yxxyyyxx iaiaaam 2

1 2

CA

(Space part)

T(Spin or spin-field part)

Zeeman -

CS -

CSA -

D (homonuclear) 1

D (heteronuclear) 1

J (homonuclear) 2

J (heteronuclear) 2

LABLAB

A

000

00

3A

LABLAB

A

000

00

3A

PAS

m

PAS

m A

2

0

22

3A

PAS

m

PAS

m A22 A

LABLAB

A

0000 2

1A

LABLAB

A

0000 2

3A

PAS

m

PAS

m A22 2

3A

j

LAB

TB 100003

1T

j

LAB

TB 10020 3

2T

j

LAB

TB 100003

1T

jk

LAB

T2020 T

jk

LAB

T0000 T

SISISI

LAB

TTTTTT 11111111101020 26

1 T

SISISI

LAB

TTTTTT 111111111010203

1 T

kjjk

kjzkzjjk

kjkzjzjk

kjzkzjjk

kjkjjk

kjjk

jj

jzj

IIT

IIIIT

IIIIT

IIIIT

IIIIT

IIT

IT

IT

2

12

1

36

12

122

13

1

... spins two2

1

...spin one

22

12

20

11

10

00

11

10

Space, Spin (or Spin-Field) part of Hamiltonian and Space, Spin (or Spin-Field) part of Hamiltonian and pure irreducible spherical spin tensor operators pure irreducible spherical spin tensor operators TT

SYS

Zeeman LAB -- -- --

CS LAB jjisoiso -- -- --

CSA PAS -- 00

D (homonuclear) PAS -- 00 00

D (heteronuclear) PAS -- 00 00

J (homonuclear) LAB √√33JJ -- -- --

J (heteronuclear) LAB JJ -- -- --

SYS

A00

SYS

A20

SYS

A12

SYS

A22

jkb6

jkb2

j

iso

PAS

zz 0

j

iso

PAS

zz 0

6

Pure irreducible spherical space tensor Pure irreducible spherical space tensor AA

3

20

4

3

1

jk

Ijk

jiso

PAS

zz

PAS

xxyy

PAS

zzyyxxj

iso

rb

Two great hypotesesTwo great hypoteses

High Field limit:High Field limit: The high magnetic field, make Z axis in the laboratory frame the axis of quantization. For just a 100 MHz spectrometer HZ >> HQ ≈ HD

>> HJ so that all off-diagonal matrix element of H can be neglected ( m = ±1 and a part of m = ±2 are removed )

Apolar nematic phase:Apolar nematic phase:Uniaxial phase (D∞h symmetry), remove m = ±2 at all.The apolarity of phase reduces to L = even the tensor elements; (remember that NMR can give only information up to rank 2)

anisoiso0,20,20,00,0

_

HHˆˆˆ TATA

L = 0 isotropic contributionsL = 2 anisotropic contributions

then

Molecular motions and NMR interactionMolecular motions and NMR interaction

solidssolids

Intramolecularinteractions

Intermolecularinteractions

H=Ĥ

Isotropic Isotropic liquidsliquids

Intramolecularinteractions

Intermolecularinteractions

H=Hiso

Short-range Long-range

0 ≈ 0

rotations

translations

anisotropic anisotropic liquidsliquids

Intramolecularinteractions

Intermolecularinteractions

H=Hiso+Haniso

Short-range Long-range

0 ≈ 0

rotations

translations

gasesgases

Intramolecularinteractions

Intermolecularinteractions

H=Hiso 0

rotations translations

Euler Euler angles between the LAB and the PAS angles between the LAB and the PAS

'' ,, imimLmm ede D

From PAS to LAB From PAS to LAB Since T is usually expressed in the laboratory frame (LAB) while A in the Principal Axis System (PAS) it is necessary to transform the spatial tensor A from PAS to LAB using the Wigner rotation matrices D:

l

lm

LABDIRlmm

DIR

ml

LAB

ml D *),(),(

AA

This operation will be carried out in two step:This operation will be carried out in two step:1)1) From DIR to LABFrom DIR to LAB2)2) From PAS to DIR From PAS to DIR

l

lm

DIRPASlmm

PAS

ml

DIR

ml D *),(),(

AA

Wigner Rotation MatrixWigner Rotation Matrix

Microscopic order parametersMicroscopic order parameters

1)1)

2)2)

Averaged by molecular motions

m’ refers to DIR

m’’ refers to PAS

l

lm

DIRPASlmm

PAS

ml

DIR

ml D *),(),(

AA

Molecule and Phase symmetryMolecule and Phase symmetry

HOW MANY TERMSHOW MANY TERMS

Biaxial molecules (< C3) in Biaxial phases

Uniaxial molecules (> C3) in Biaxial phases

Biaxial molecules (< C3) in Uniaxial phases

Uniaxial molecules (> C3) in Uniaxial phases

m’ = all or m’ = 0, ±2 if the director system is principal;m’’ = all or m’’ = 0, ±2 if the molecular system is principal;

m’ = 0, ±2 if the director system is principalm’’ = 0

DIRPASlm

PAS

ml

DIR

ml D

*0

),(),(

AA

m’ = 0 m’’ = all

l

lm

DIRPASlm

PAS

ml

DIR

ml D *

0),(),(

AA

m’ = 0 m’’ = 0

DIRPASl

PAS

ml

DIR

ml D *

00),(),(

AA

m’ refers to DIR

m’’ refers to PAS

go

Order ParametersOrder Parameters

Molecular Order Parameters are averages of the Wigner’s Rotation Matrix elements

*'

lmmD

They are appropriate for all phases and molecular symmetryThey are appropriate for all phases and molecular symmetry

Motional Constants are averages of Spherical Harmonics

*lmY

They are usually used in case of cylindrical symmetry about the directorThey are usually used in case of cylindrical symmetry about the director

Saupe Order Parameters are averages of transformation matrix elements in Cartesian frame

2/coscos3 S

They are usually used for uniaxial phasesThey are usually used for uniaxial phases

Independent Order Parameters Independent Order Parameters in uni-biaxial phasesin uni-biaxial phases

Nematic (uniaxial)Nematic (uniaxial) Smectic C (biaxial)Smectic C (biaxial)

Molecular Molecular symmetrysymmetry

Location of Location of axesaxes

Independent Independent Wigner Wigner

matrices matrices elementselements

Independent Independent Saupe matrix Saupe matrix

elementselements

n° of n° of Order Order ParamParameterseters

Independent Independent Wigner Wigner

matrices matrices elementselements

n° of n° of Order Order

ParameParametersters

CC11,C,Cii Not specialNot specialSSaaaa,S,Sbbbb-S-Scccc, ,

SSbcbc,S,Sabab,S,Sacac

55 1010

CCss, C, C22, C, C2h2h aa parallel to the parallel to the axis or normal axis or normal to the plane;to the plane;

SSaaaa,S,Sbbbb-S-Scccc,S,Sbcbc 33 66

CC2v2v

aa parallel to the parallel to the axis; axis;

bb normal to the normal to the planeplane SSaaaa,S,Sbbbb-S-Scccc 22 44

DD22, D, D2h2h a,b,ca,b,c parallel to parallel to 2-fold axis2-fold axis

DD2d2d, C, Cnn, C, Cnvnv, ,

CCnhnh, D, Dnn, D, Dnhnh, ,

DDndnd, S, S44, S, S2n2n, ,

nn3 3

aa parallel to n- parallel to n-fold axis or fold axis or

intersection of intersection of mirrormirror

SSaaaa 11 22200D

202

200 , DD

202

202

200

Im,Re

,

DD

D

202

202

201

201

200

Im,Re

Im,Re

,

DD

DD

D

0,2m

20

mD

0,2m

0,2m'

2'

mmD

2m of ImRe,

0m0,2m'

2'

mmD

2,1m of ImRe,

0m0,2m'

2'

mmD

Dipolar couplings DDipolar couplings Dijij

kzjzzzjk

IjkD

kzjzkjkzjz

LAB

D

jk

I

PAS

D

PAS

Dzz

PAS

DDIRPAS

D

PAS

DDIRPAS

Dm

DIR

D

DIR

D

DIR

DLABDIR

D

DIR

DLABDIR

Dm

LAB

D

IISr

H

IIIIIIT

rA

C

ASAAA

AAAA

ˆˆ4

3

2

1cos3ˆ

ˆˆ6

3ˆˆˆˆ36

1ˆ

46

1

2

1cos3

3

20

2

Bhigh 20

3

2020

2020200

202

-2m

20

20

202

20200

202

-2m

20

20

DD

DD

SSαβαβ

SSzzzz

SSxx-yyxx-yy

SSzyzy

SSxzxz

SSyzyz

2mnD200D

220

22023 DD

220

22083 DDi

210

21083 DDi

210

21083 DD

m’ = 0 if phase is uniaxial (nematic)

m’’ = 0 if molecule is uniaxialAngle between ZLAB and ZDIR

The Conformational ProblemThe Conformational Problem

What is a model (1) ?What is a model (1) ?

Observations

Model A

Model B

Model AModel B

What is a model (2) ?What is a model (2) ?

If no information on the error are available, the two model are resonable.

If some information on the error are available, one may discriminate between them.

Rigid and flexible molecules: a simple classificationRigid and flexible molecules: a simple classificationInternal motions:

a) small amplitude - high frequency motions (vibrations)b) large amplitude - low frequency motions and puckering of unstrained ringsc) puckering of strained rings and rotations along double bonds

Rigid molecules have only small amplitude motions Rigid molecules have only small amplitude motions

Flexible molecules have also large amplitude motions Flexible molecules have also large amplitude motions

Being Being {{’’}} the set of internal angles describing all internal motions and the set of internal angles describing all internal motions and {{}} the set of angles the Order the set of angles the Order Parameters are depending on:Parameters are depending on:• Order Parameters are independent (in first approximation) from small amplitude motions (vibrations averaged order parameters) < Dl

m’m(Ω)>v

• Order Parameters depend on large amplitude motions (average over orientations) Dlm’m(Ω,{})

l

lm

DIRPASlmm

PAS

ml

DIR

ml D

),(),( AA

l

lm

DIRPASlmm

PAS

ml

DIR

ml D

),(),( AA

Order-conformation decoupling

Orientational Distribution FunctionOrientational Distribution FunctionThe average of any “single-molecule” property X(Ω) over the orientation of all molecules is defined by introducing a singlet distribution function f(Ω) as:

*

0 ,28

12)(

LmmmmL

L

LmmmmL

L

Lmm

Da

DaL

f

Microscopic order parametersMicroscopic order parameters

Supposing f(Ω) originating from an orientational pseudo-potential V(Ω), then:

dZ

ZfV

V

exp

/exp)(

Nematics must be approssimated by cilindrical rods so V is independent of (phase is unaxial) and (molecule have cylindrical symmetry)hen,asm is restricted to 0:

coscoscosV

thenphase ofapolarity for the vanish of valueodd

2

0 1cos with

2

12)(

22

000

00*

00

PP

l

lS

lPDDD

lf l

l

l

ll

Mean Torque PotentialMean Torque Potential

Ω are the Euler angles | | |

For furher informations: R. Y. Dong, in “NMR of Lyquid Crystals”, Springer-Verlag, New York, 1994.

In order to perform the average on different conformational states we must introduce the equilibrium probability function P() for finding the molecule in the n-th conformation defined by the set of internal angles and to sum the NMR interaction on the N available conformations:

d d sen d ),,,(P ),,,(

),,,( ),,,(

LC''

),(),(

lmm

lmm

LCmlml

DD

ddddsenPAA

dKTUZ

and

KTUZ

PISO

/)(exp

/)(exp1

)(

int

int

In isotropic phases

)(),,,(),,,(

/),,,(exp1

),,,(

int

UUU

and

KTUZ

P

ext

LC

Conformational distribution functionConformational distribution function

In anisotropic phases

The shape anisotropy of molecules influence the intermolecular potential

AP[1] (Additive Potential) Fourier Expansion

k n

nkn kVU cos)(int

The internal potential for a n-rotor molecule can be, always, expanded in Fourier series of cosine functions:

k=0,1,2,3…n is over the number of torsional angles, that is the number of rotating subunits

Sometime may be useful to add a Lennard-Jones term to take into account of sterical repulsion

612

int )(ij

ij

ij

ijLJ

r

B

r

AKU

K is the dept of potential A, B are the Lennard-Jones parameters

),,,( extU )(int U

The molecule can be divided into a small number of rigid fragment each of them associated with an interaction tensor (εj

2r) independent of the conformation. The tensor of the whole molecule is calculated by transforming the fragment tensors into a common system and then adding them together

r

jr

jmr

jm D 2

*22

j is the fragment; εj2r is the fragment interaction tensor in

a local axis system; εj2r({}) is the fragment interaction

tensor in a molecular frame;

),,(1,,, ,2,2 m

mmm

ext CU

εε22m m is the molecular interaction tensor.

The external part of mean torque potential is:

j

jmm 22

R

xmol

ymol

zmol

y frag

z fragx fra

g

R R

R

jr2 m2 j

nnD *2

R

xmol

ymol

zmol

y frag

z fragx fra

g

R R

R

jr2 m2 j

nnD *2

)(),,,(),,,( int UUU ext

[1] J. W. Emsley, G. R. Luckhurst and C. P. Stockley, Proc. R. Soc., London Ser. A, (1982), 381, 117.

ij m

mmijij DDU ,,~

,,, 202

Another Two Different ApproachesAnother Two Different Approaches

The distribution compatible with the set of observable may be derived with the “unbiased” Maximum Entropy method making use of the Lagrange Multipliers techniqe:

Dipolar couplings irreducibleDipolar couplings irreduciblespherical tensorspherical tensor

Lagrange MultipliersLagrange Multipliers

MEME[1][1] (Maximum Entropy) (Maximum Entropy)

RISRIS[2][2] (Rotamer Isomeric State) (Rotamer Isomeric State)

Supposing that only a finite set of N conformers are populated ({n}) with the probability pn for each of them, the internal potential function cam be written:

N

nnnVU

1int

Dirac Delta functionDirac Delta functionNumber of minima inNumber of minima inThe potential functionThe potential function

[1] D. Catalano, L.Di Bari, C. A. Veracini, G. N. Shilstone and C. Zannoni, J. Chem. Phys., (1991), 94, 3928 [2] J. W. Emsley, in “Enciclopedia of NMR”, ed. D. M. Grant and R. K. Harris, Wiley, New York, 1996.

The Vibrational ProblemThe Vibrational Problem

5

4

3

)coscos7(coscos25

)coscos(cos5

coscoscoscoscos5

coscos

r

CCCC

r

r

h

va

e

A model to treat vibrational motionsA model to treat vibrational motionsUsing cartesian notation and supposing no vibro-rotational coupling, dipolar coupling may be expressed by:

ije

ijij

vij

ijijijijijij rrr

r

rrSkD

5

,,,,

...... hae

Being re the equilibrium distance and r’ the istantaneous excursion of r from re we may approximate:

Where e, a, h mean equilibrium, anharmonic and harmonic

and dipolar couplings expanded as: ...... hae ddDD

re

rr’

N

jiiji

ii Zuu

Mu

3

1

)()(2

1-

2

1-

21

)()( FGG W

W

vC

T

BAZTf

v

coth),( 2

TfuuuuCN

jijiij ,

3

1

)()()()(

Covariance MatrixCovariance Matrix

Covariance Matrix is a matrix whose elements are the products of Cartesian displacements

In order to calculate these, we need the molecule Force Field (F) and to extract from it IR frequencies and normal modes of vibrations. Having:

Where G is diagonal containing the mass of atom i, and Z the amplitude of the -th vibrational coordinate.Finally,

For furher informations: S. Sỷkora, J. Vogt, H. Bösiger and P. Diehl, J. Magn. Reson., (1979), 36, 53-60

Some resolved samplesSome resolved samples

What we have to do ?What we have to do ?

Record the spectrum

prepare the sample (distillation, dissolution in LC, etc)

prepare the experimental conditions (T, homog., etc)

record the FID

Analyse the spectrum

Searching for starting data set (isotropic indirect couplings and

Chemical Shifts, Dij)

definition of spin system

Fit experimental spectrum by calculated one to extraxt Dij

Fit the experimental data ( Dij’s )

Searching for a starting geometry

Searching for a potential curve

Fit experimental Dij by calculated ones optimising parameters

Analise the problem in terms of observations/parameters

Search or calculate Force Field

(Hz)

-6000-4000-20000200040006000800010000120001400016000

{ Dij }

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PL

C

0,0

0,2

0,4

0,6

0,8

1,0

ZLI1132

I35

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PL

C

0,0

0,2

0,4

0,6

0,8

1,0

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PL

C

0,0

0,2

0,4

0,6

0,8

1,0

ZLI1132

I35

{ S }, { G }

ARCANA

ARCANA

ANACON

ANACON

SPECTRUM

SPECTRUM

RESULTS

RESULTS

Analysis of the problem

C C

H

H H

BrWith only DHH couplings

+DC1 H couplings

13C 13C

+DC2 H couplings

3

3

3TOTAL = 9

N° of observables

N° of parameters

Order parameters = 3 (simmetry Cs )

geometrical parameters = 5 (atoms) x 2 (xi, zi) – 4 (C=C fixed) = 6TOTAL = 9

A rigid molecule: VinylBromideA rigid molecule: VinylBromide

Searching for the Jij

Prepare the sample

An amount of VinylBromide (gas) was dissolved in ZLI1132, CCN55 and in a mixture (45:55) of ZLI1132 and EBBA (Magic Mixture, MM), by gurgling it in an NMR tube and keeping all at liquid nitrogen temperature

The spectra

ZLI1132

MM

CCN5513C1

13C2

The force field of molecule was calculated by Gaussian 98W package at three levels of approximation, PM3, B3LYP/6-31G*and MP2/6-31G* but experimental frequencies were used[1].

Phase ZLI1132 CCN55 MM

FF MP2 B3LYP PM3 MP2 B3LYP PM3 MP2 B3LYP PM3

r41 1.0796 1.0794 1.0781 1.0845 1.0842 1.0842 1.0830 1.0826 1.0808

r51 1.0740 1.0736 1.0738 1.0763 1.0758 1.0763 1.0793 1.0789 1.0784

< 412 122.31 122.29 122.36 122.21 122.18 122.12 122.37 122.34 122.36

< 512 118.89 118.89 118.84 119.02 119.03 119.05 118.94 118.93 118.83

< 621 124.54 124.52 124.53 123.90 123.89 123.90 124.89 124.87 124.88

RMS 0.35 0.36 0.39 0.21 0.21 0.24 0.38 0.39 0.41

What have we found?

[1] W. A. Herrebout, B.J. Van der Veken and J. R. Durig, J. Mol. Struct., (1995), 332, 231-240

r12 = 1.3320 from [2]r62= 1.0870 from preliminary calculation

[2] D. Coffey, J. B. Smith and L. Radom, J. Chem. Phys., (1993), 98, 5, 3952-3959

A flexible molecule: StyreneA flexible molecule: StyreneAnalysis of the problemN° of parameters

Order parameters = 3 (if planar, Cs) or 5 (if nonplanar C1)

geometrical parameters = 16 (atoms) x 3 (xi, yi, zi) – constrains = ?

C

C

H

HH

H

H

H

H

H

N° of observables

With only DHH couplings 18+

DC1 H couplings 6

13C

+DC2 H couplings 6

13C

TOTAL = 30

(ppm)

-1.5-0.50.51.52.53.54.55.56.57.58.59.510.5

(Hz)

-5000-3000-1000100030005000700090001100013000

13C-α-Styrene dissolved in a namatic phase (I52)

Styrene dissolved in CClD3

Prepare the sampleAn amount of 13C-1-styrene and 13C-2-styrene (≈10% wt ) was dissolved in ZLI1132 and in I35. The samples were bought from Aldrich.

The spectra

13C-α-styrene in ZLI1132

13C--styrene in ZLI1132

In order to reach a full conformational analysis of the whole molecule:

2

20

2heAP

C1

H9

H10

C2

H11

X

First optimising ene and ring geometries alone

and

Varying only the r2X and the angles and including vibrational corrections

Using a probabilistic approach to describe directly the conformational distribution:

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PLC

0,0

0,2

0,4

0,6

0,8

1,0

ZLI1132

I35

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PLC

0,0

0,2

0,4

0,6

0,8

1,0

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

PLC

0,0

0,2

0,4

0,6

0,8

1,0

ZLI1132

I35

A maximum is found with the ene out of ring plane of about 18 ° and with a standard deviations of 8 °.

The End The End (Many Thanks)(Many Thanks)

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