Relatore Dr. Giuseppe Pileio PhD.: Scienze e Tecnologie delle Mesofasi e dei Materiali Molecolari...
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Transcript of Relatore Dr. Giuseppe Pileio PhD.: Scienze e Tecnologie delle Mesofasi e dei Materiali Molecolari...
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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