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Chemical Physics Letters 486 (2010) 21–26
Contents lists available at ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
3
H NMR of the tritiated isotopologues of methane in nematic liquid-crystal solvents
E. Elliott Burnell a,*, Cornelis A. de Lange b, Donatella Capitani c, Giancarlo Angelini c, Ornella Ursini c
a
Chemistry Department, University of British Columbia, 2036 Main Mall, Vancouver (BC), Canada V6T 1Z1
Atomic, Molecular and Laser Physics, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
c
Chemical Methodologies Institute, Consiglio Nazionale delle Ricerche, Area della Ricerca di Roma, C.P. 10 00016 Monterotondo Staz. (RM), Italy
b
a r t i c l e
i n f o
Article history:
Received 18 November 2009
In final form 29 December 2009
Available online 4 January 2010
Dedicated to the memory of Annalaura
Segre (deceased 25 April 2008) and Jaap G.
Snijders (deceased 13 August 2004).
a b s t r a c t
The NMR spectra of the tritiated isotopologues of methane dissolved in several nematic liquid-crystalline
solvents are measured. The spectral parameters obtained agree extremely well with those predicted from
earlier NMR studies of the deuterated isotopologues, providing excellent confirmation of the theory for
vibration–reorientation interaction developed earlier.
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
The study of small, well-characterized probe molecules dissolved in liquid-crystal solvents has been of great importance for
the understanding of the mechanisms that are responsible for the
partial orientational order of solutes in anisotropic environments.
For instance, experiments on molecular hydrogen [1] and its deuterated [1–4] and tritiated [5] isotopologues as solutes in nematic
phases have played a key role in this respect, and have shown that
the degree of orientational order for the hydrogens is dominated
by the interaction between solute molecular quadrupole moment
and the average solvent electric field gradient felt by the solute
[6,7]. In addition, studies on dideuterium led to the discovery of
‘magic mixtures’, liquid-crystalline phases in which the interaction
between the dideuterium solute molecular quadrupole moment
and the average electric field gradient of the solvent is removed
[2]. For solutes other than the hydrogens the degree of orientational order in such mixtures is predominantly determined by
the solute size and shape anisotropy [8,9].
In the early days of liquid-crystal NMR it came as a surprise that
solutes with tetrahedral symmetry, when dissolved in a nematic
phase, showed spectral splitting that on the basis of a ‘rigid’ structure for the solute should not be there. Methane (CH4) was a case in
point [10]. An extensive set of dipolar and quadrupolar splittings
for methane and many of its deuterated isotopologues dissolved
in several nematic liquid crystals was obtained from a careful series of NMR experiments [11]. It soon became apparent that an
* Corresponding author.
E-mail addresses: elliott.burnell@ubc.ca (E.E. Burnell), cdelange@few.vu.nl (C.A.
de Lange).
URL: http://www.chem.ubc.ca/personnel/faculty/burnell (E.E. Burnell).
0009-2614/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2009.12.087
interaction between methane vibrational normal modes of symmetry other than A1 and the solute reorientational motion was at
the root of these observations [12–14].
A proper understanding of these phenomena was in fact hampered by historical factors. The initial theoretical treatment that
described the orientational order of solutes in anisotropic phases
started from the picture of a ‘rigid’ solute [15–17]. Soon discrepancies in solute structure determination with liquid-crystal NMR led
to the realization that solute vibrational effects were essential, and
harmonic ‘corrections’ were then introduced in an ad hoc manner
[18–20]. However, this two-step development could not envisage
the possibility of an interaction between solute vibrational and
reorientational motions.
In a subsequent, more fundamental treatment the solute was
considered to be a vibrating and rotating entity which was perturbed by the liquid-crystal environment [12,14]. This perturbation was assumed to be a product of a solvent ‘field’ and some
solute electronic property with which this field interacted. In a
complete perturbation treatment it was found that only the solute
rotational wave functions were somewhat affected and that the
anisotropic couplings could be expressed as a sum of several terms.
These terms involve a ‘rigid’ contribution in which the solute is assumed to exist in a ‘vibrationless’ equilibrium geometry (leading to
zero anisotropic splittings for all methanes), a term associated with
the anharmonicity of the vibrational potential, and a term associated with harmonic vibrational behaviour. Finally, a new term
was found which involved a coupling between non-totally symmetric solute normal modes and reorientational motion. This contribution (the vibration–reorientation interaction) is present for all
solutes, and forms a serious impediment in obtaining highly accurate structures from observed dipolar couplings [21–23]. In the literature [24] one is often confronted with the notion that solutes
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E.E. Burnell et al. / Chemical Physics Letters 486 (2010) 21–26
could be distorted by the liquid-crystal environment, and that such
a distortion could explain the observed dipolar couplings in the
methanes. We emphasize that this point of view is incorrect, as
discussed extensively in a separate paper [23].
In the above perturbative treatment, the solvent ‘field’ G and the
solute electronic property b that it couples to need not be specified.
However, the magnitude of the vibration–reorientation interaction
term depends on derivatives of components of the solute b tensor
with respect to vibrational normal modes. As indicated in the next
section, for the methanes this leads to three unknown parameters:
DGb1 , DGb2 , and DGb3 , one for each non-totally symmetrical normal mode. These parameters can be obtained by fitting the theoretical expressions to the observed anisotropic couplings. For this
fit details about the anharmonic vibrational potential are needed,
and these details are known for methane. We note that the average
geometries of the methane isotopologues are not necessarily fully
tetrahedral. This deviation from full tetrahedral shape gives rise to
‘rigid’ contributions to the anisotropic couplings. In addition, the
so-called ‘non-rigid’ effect that derives from the vibration–reorientation interaction is significant for all isotopologues [12,14].
In this Letter we study the tritium-substituted isotopologues of
methane, 12 CH4n Tn ðn ¼ 1—4Þ. The radioactive tritium isotope has
a half life of 12.26 years, and is the perfect nucleus from the NMR
point of view. First, tritium has the highest gyromagnetic ratio of
all nuclei known, with ensuing unusually high NMR sensitivity.
Secondly, tritium possesses nuclear spin I ¼ 12 and hence dipolar
couplings dominate the anisotropic spectra. Thirdly, there is normally no background signal due to tritium, thus avoiding many
problems commonly encountered with non-radioactive nuclei.
The experiments on tritiated methanes were performed in order
to test further the theories and models that underly our current
understanding of the behaviour of tetrahedral species dissolved
in anisotropic solvents. A detailed analysis of our novel experiments results in impressive agreement with the predictions of
the general model described above for methane and its deuterated
isotopologues, thus providing very strong additional support for
the perturbative model developed many years ago.
2. Theory
The interaction between a uniaxial liquid-crystal tensorial ‘field’
G and a solute electronic tensorial property b that depends on
geometry is assumed to be [12,14]
1
U ¼ DGbkl ðQ m ÞSkl ðXÞ
3
ð1Þ
with the orientation operator
Skl ðXÞ ¼
3
1
cos hkZ cos hlZ dkl
2
2
ð2Þ
where k; l are solute-fixed axes, Z is the solvent director, and
DG ¼ Gk G?
ð3Þ
is the anisotropy of the solvent field.
Anisotropic NMR observables are given by
AðQ m ; XÞ ¼ akl ðQ m ÞSkl ðXÞ
For the dipolar coupling between nuclei
Dlm ¼ hdkl;lm ivibrations hSkl irotations þ hdkl;lm Skl ivibrations; rotations
¼ Delm þ Danharmonic
þ Dharmonic
þ Dnon-rigid
lm
lm
lm
ð6Þ
with
e
Delm ¼ dkl;lm hSkl irotations
X @dkl;lm e
Danharmonic
¼
hQ m iT hSkl irotations
lm
@Q m
m
!e
1 X @ 2 dkl;lm
Dharmonic
¼
hQ m Q n iT hSkl i rotations
lm
2 m;n @Q m @Q n
ð7Þ
ð8Þ
ð9Þ
being the equilibrium geometry contribution (zero for the methanes), and the anharmonic and harmonic vibrational contributions,
all terms in which vibration and rotation are strictly decoupled.
The fourth term
Dnon-rigid
¼
lm
X @dkl;lm e @bij e 1
1
DG
hSkl Sij i
3
@Q m
@Q m x2m
m
rotations
ð10Þ
arises from a coupling between vibrational and reorientational motions. All four terms scale with the anisotropy DG of the liquid-crystal field. The first three terms are proportional to the usual Saupe
order parameters, and the fourth term has another, more complex
orientational dependence. The rotational factors can be calculated
from
R
Skl expðUðXÞ=kTÞdX
Skl ¼ hSkl irotations ¼ R
expðUðXÞ=kTÞdX
R
Sij Skl expðUðXÞ=kTÞdX
hSij Skl irotations ¼ R
expðUðXÞ=kTÞdX
ð11Þ
ð12Þ
The first three terms can be calculated directly from the known
equilibrium geometry and from the anharmonic and harmonic force
fields that are available for methane. The ‘non-rigid’ term depends
on quantities DGð@bij =@Q m Þ which for methane depend on the twofold degenerate bending and threefold degenerate bending and
stretching modes. Without knowing what solute property is signified by b, this contribution cannot be calculated. Instead, the
DGð@bij =@Q m Þ can be viewed as three independent quantities that
are used as adjustable parameters DGb1 , DGb2 and DGb3 . These quantities have either been obtained before in studies of methane and its
deuterated isotopologues in particular liquid crystals, or can be obtained by a fitting procedure. Apart from the three DGb’s the following treatment contains no adjustable parameters. For a more
detailed discussion the reader is referred to the literature [12,14].
3. Experimental
3.1. Synthesis of multitritiated methanes
ð4Þ
l and m we have:
hcl cm akl ðQ m Þ ¼ dkl;lm ¼ cos hlm;k cos hlm;l =r 3lm
2
4p
For the equilibrium bond length between carbon and the nucleus
(H, D or T) directly bonded to it a value of 1.0858 Å is used. Taking
as zero-order wave functions products of electronic, harmonic
vibrational, and rigid rotor rotational wave functions, we obtain
from perturbation theory
ð5Þ
with again k; l axes fixed in the solute.
Since the equilibrium geometry is identical for all isotopologues, this is taken as the starting point. Whenever Taylor expansions are required, this equilibrium geometry is always taken as
the basis. In this way the same theory is valid for all isotopologues.
Following a well described procedure [25,26], a mixture of multitritiated methanes was obtained by the reaction between aluminium carbide and tritiated water. The latter was prepared at the
maximum activity available by the redox reaction between copper
(II) oxide and tritium gas:
CuO þ T2 ! T2 O þ Cu
Al4 C3 þ 12T2 O ! 3CT4 þ 4AlðOTÞ3
Several blank runs, using deuterium gas, were carried out to define
the operating parameters (reagent ratios, volumes of the reactor,
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E.E. Burnell et al. / Chemical Physics Letters 486 (2010) 21–26
23
Fig. 1. Reactor for synthesis.
temperatures, reaction times, etc.) so as to obtain the maximum level of the multilabelled methanes.
The radiolabelled synthesis was carried out using 4.33 mg
(54.1 lmol) of CuO (Sigma–Aldrich) which was introduced into a
very dry Pyrex reactor (5.2 mL vial A of Fig. 1). Using a vacuum line,
55.6 lmol, 3.24 Ci (120 GBq) of tritium gas (ARC, American Radiolabeled Chemicals, Inc.) was added to vial A at the pressure of
200 Torr. Vial A was sealed off (S1 of Fig. 1) and heated at 550 °C
for 6 h, avoiding carefully the breaking of the internal break-seal
(BS1 of Fig. 1). The red colour associated with metallic copper formation revealed the success of the redox reaction. At this point in
vial A was present 3.15 Ci (117 GBq) of T2O at the theoretical specific activity of 58.2 KCi/mol (2153 TBq/mol).
About 5.97 mg (41.5 lmol, a large excess with respect to the
stoichiometric ratio) of aluminium carbide Al4C3 (Sigma–Aldrich)
was charged into vial B of the reactor (Fig. 1) and it was activated
by heating at 400 °C for 16 h under vacuum. The bottom of the
reactor was then sealed off at S2.
After cooling, the internal break-seal (BS1) was broken with the
glass hammer and the whole system was heated at 120 °C for 5 h.
The bottom of the reactor was then connected to the vacuum line
and the radioactive methane was transferred into it, after the
opening of the break-seal BS2.
The overall yield of the mixture of the different multitritiated
methanes was 11.1 lmol (chemical yield: 81%) with an overall
radioactivity of 1.0 Ci (37 GBq), indicating an average radiochemical yield of 63%. The experimental specific activity was 90.1 KCi/
mol (3333 TBq/mol), which is about 75% of the theoretical maximum value if only the formation of CT4 is assumed. Obviously
residual traces of H2O in the reactor and OH sylanol groups of
the glass diluted the tritiated water. As a consequence a mixture
of different tritiated methanes was obtained. This result was consistent with that obtained during the blank deuterium runs, where
a high-resolution mass-spectrometric study (carried out with an
Ion Cyclotron Resonance Fourier Transform Mass Spectrometer) revealed at least 60% of CD4, 30% CHD3 and 10% CH2D2.
3.2. Preparation of the NMR tubes with nematic solvents
The multitriated methanes were diluted with CD4 in the ratio 1–
3, and aliquots of this mixture of about 50/80 mCi (1.85/2.96 GBq)
each were taken using a mini Toepler pump (V = 50 mL) and
pushed into the NMR tubes which were previously filled with
the nematic liquid crystal. The NMR tubes were maintained at
Fig. 2. Experimental and predicted (from DGbm of Ref. [14]) 640.12 MHz 3H NMR
spectra of tritiated methanes in 1132 (frequency scale in Hz). The linewidth of the
calculated spectra is 1.5 Hz, and the relative integrals of the isotopologues are the
same as in Fig. 3. The frequency origin has been adjusted to line up the calculated
with the experimental spectrum, and the relative chemical shifts are the same as for
Fig. 3. The experimental spectrum is the average of 9445 scans at 300 K.
low temperature and flame sealed. The solubility of gaseous methane was increased by performing several cycles of shaking and
cooling.
3.3. NMR spectroscopy
Tritium NMR spectra were acquired on a Bruker Avance 600
spectrometer operating at 640.12 MHz. Spectra were obtained at
T = 300 K in the nematic phases of Merck ZLI 1132 (1132), 4-n-pentyl-40 -cyanobiphenyl (5CB) and p-ethoxybenzylidene-p0 -n-butylanaline (EBBA) and in isotropic CDCl3. The temperature was
carefully controlled by means of a variable temperature unit and
kept constant to 0:1 K. Before inserting samples into the NMR
spectrometer, they were shaken up to ensure optimum diffusion
of solute throughout the solvent. The spectra were collected without spinning the sample and without the use of a lock signal. A recycle delay of 0.1 s and a 90° pulse width of 15 ls were used. A
time domain of 16 K data points was used.
4. Results and discussion
Two of the 640.12 MHz 3H NMR spectra obtained for the various
H/1H isotopologues of methane are displayed in Figs. 2 and 3. The
spectra are a superposition of those from CT4 (a 1:3:3:1 quartet
with splitting 3jDTT j), CT3H (a 1:2:1 triplet with splitting 3jDTT j,
each line further split into a doublet with splitting jð2DTH þ J TH Þj),
CT2H2 (a 1:2:1 triplet with splitting jð2DTH þ J TH Þj, each line further
split into a doublet with splitting 3jDTT j) and CTH3 (a 1:3:3:1 quartet with splitting jð2D TH þ J TH Þj).
Only the absolute values of the splittings are obtained from the
spectra. Thus, in order to determine DTH couplings, the relative
signs of J TH and DTH must be known. There is general agreement
that two-bond indirect J HH couplings are negative. As the gyromagnetic ratios c of all three isotopes of hydrogen are positive, all J
3
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E.E. Burnell et al. / Chemical Physics Letters 486 (2010) 21–26
Table 1
Dipolar couplings of tritiated methanes in 1132: experimental values as well as those
calculated from published [14] DGbm parameters.
DGb1
(105 erg/cm)
0.25831
DGb2
(105 erg/cm)
0.73695
DGb3
(105 erg/cm)
0.17768
Drigid calc
Dnon-rigid calc
Dtotal calc
Dexperimental
CH3T
DTH
4.0137
2.5805
6.5942
Not measured
CH2T2
DTH
DTT
0.1702
7.4334
0.0757
5.1174
0.2459
12.5508
0:38 0:14
12:9 0:1
CHT3
DTH
DTT
3.4132
3.6404
2.7097
2.4485
6.1229
6.0891
6:37 0:09
6:2 0:08
CT4
DTT
–
0.1626
0.1626
0
A weighted least-squares fit to only the experimental dipolar couplings above gives:
DGb1 ¼ 0:26 0:08, DGb2 ¼ 0:81 0:26, DGb3 ¼ 0:16 0:14. These numbers
agree with those listed above for the original 1H and 2H experiments.
Fig. 3. Experimental and fitted 640.12 MHz 3H NMR spectra of tritiated methanes
in 5CB (frequency scale in Hz). The linewidth of the calculated spectra is 1 Hz. The
relative integrated intensities of the calculated spectra correspond to 67.3%
tritiation. The experimental spectrum is the average of 2166 scans at 300 K.
couplings between hydrogen isotopes in the various isotopologues
of methane are expected to be negative, and to scale with the c’s. In
the earlier study of the various deuteriated isotopologues of methane, J HD was measured to be 1.92 Hz for 13CH3D in the isotropic
phase of p-methoxybenzylidene-p0 -n-butylanaline (MBBA) [11].
Scaling by c T =cD predicts the value J TH ¼ 13:34 Hz. We have also
measured J TH from a rather poor spectrum of CT3H and CT2H2 dissolved in CDCl3 and obtained the values 13.32 Hz for CT3H and
13.5 Hz for CT2H2, numbers that are in agreement with the above
prediction from the earlier study. In our CDCl3 isotropic solvent
experiments the abundance of CT3H was greater than that of
CT2H2 which resulted in rather weak lines for the CT2H2 spectrum
and a less reliable value for J TH . Here we shall take J TH ¼ 13:34 Hz
for all isotopologues and shall ignore any potential isotopologue
dependence of J TH .
While it would be possible to attempt to sort out the signs of
the dipolar couplings obtained in 5CB by attempting various fittings to the three independent DGbm parameters of the theory presented above, it is more appealing first to examine the 3H NMR
spectrum of the tritiated methanes obtained in the liquid crystal
1132. In this case an earlier study of the deuteriated methane isotopologues in 1132 gave fitted values for the three independent
DGbm parameters, and these values can be used to predict the
DTH and DTT values for the tritiated analogues. These values are
then used to produce a predicted 3H spectrum with no adjustable
parameters. The result of this prediction is compared with the
experimental spectrum in Fig. 2. In the calculation the relative isotope chemical shifts and relative weightings are set equal to those
obtained below for the 5CB spectrum. While this experimental
spectrum is inferior to that obtained for 5CB (Fig. 3), it is seen that
the agreement between experimental and calculated spectra is
excellent. The experimental and calculated couplings with their
signs are summarized in Table 1.
We now turn to the 5CB spectrum. As a first attempt, we set the
signs of the dipolar couplings to be the same as predicted for the
Table 2
Experimental dipolar couplings and chemical shiftsa of tritiated methanes in 5CB as
well as DGbm parameters obtained from a weighted least-squares fit to these
experimental dipolar couplings plus dipolar couplings calculated from these fit
parameters.
CH3T
DTH
DGb1
(105 erg/cm)
0:008 0:012
DGb2
(105 erg/cm)
1:308 0:039
DGb3
(105 erg/cm)
0:208 0:020
Drigid calc
Dnon-rigid calc
Dtotal calc
Dexperimental
6.8704
1.6292
5.2412
5:028 0:025
CH2T2
DTH
0.0055
12.5942
DTT
0.2777
2.2354
0.2721
10.3588
0:07 0:04
10:588 0:026
CHT3
DTH
DTT
5.9724
6.3702
1.1884
1.0673
4.7840
5.3029
4:758 0:020
5:253 0:014
CT4
DTT
–
0.1002
0.1002
0
a
The tritium resonance frequencies are: CH3 T ¼ 46:6 Hz, CH2 T2 ¼ 30:9 Hz,
CHT3 ¼ 15:3 Hz and CT4 ¼ 0 Hz.
1132 spectrum. The dipolar couplings and chemical shifts are then
obtainable from the spectrum, and are given in Table 2. The fit to
the experimental spectrum is shown in Fig. 3, where the individual
calculated spectra are also displayed shifted vertically to aid
recognition.
The isotope effect on the triton chemical shifts is displayed in
Fig.
4.
We
note
an
upfield
isotope
effect
of
15:55 0:25 Hz ¼ 0:0243 0:0004 ppm per triton. The isotope effects observed for the tritiated isotopologues of dihydrogen are
0.064 ppm between T2 and HT and about 0.019 ppm between T2
and DT, with T2 being upfield in both cases [5].
In Fig. 3 the relative intensities of the calculated spectra for
CT3H and CT2H2 are adjusted to fit simultaneously the peaks at
11.0 and 19.6 Hz (from CT3H) and the peak at 14.9 Hz (from
CT2H2). This fit gives the relative mole fraction of CT3H/
CT2H2 = 1.375. If we assume statistical tritiation, this ratio predicts
the mole fraction of the five isotopologues to be: CT4 ¼ 0:2056,
CT3 H ¼ 0:3989, CT2 H2 ¼ 0:2902, CTH3 ¼ 0:0938 and CH4 ¼
0:0114. These numbers, which represent 67.3% tritiation, have
been used for the relative intensities of the calculated spectra in
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E.E. Burnell et al. / Chemical Physics Letters 486 (2010) 21–26
Fig. 4. Experimental chemical shifts in ppm (shift increases downfield) of tritiated
methanes in 5CB.
Fig. 3 (as well as in Fig. 2) where the agreement with the experimental spectrum is very satisfactory.
Next we perform a weighted least-squares fit of the DGbm values to the dipolar couplings. The values obtained, as well as comparison between experimental and calculated couplings, are given
in Table 2. The agreement is excellent, an indication that the correct relative signs for the DTT and DTH have been chosen. In addition, this is strong evidence that the theory applies in general for
the tritiated isotopologues, as well as to couplings in a new liquid
crystal, 5CB.
A spectrum was also obtained for the tritiated isotopologues as
solutes in EBBA. The predicted spectrum in this case is obtained in
the same manner as for the 1132 case, using the parameters from
the older study of the deuteriated isotopologues along with the
theory presented earlier. In this case the spectrum is of such poor
quality that little can be said.
5. Conclusions
The unexpected observation that methane (CH4) dissolved in
uniaxial nematic liquid crystals showed a dipolar splitting, while
the deuterated methanes ðCHn D4n ; n ¼ 0—3Þ showed both dipolar
and quadrupolar splittings has remained a mystery for a long time.
It was not until a quantum–mechanical theory by Snijders et al.
was developed that these splittings could be understood in detail.
This theory invoked an interaction between vibrational and reorientational solute motion where the twofold degenerate vibrational
bending mode, and the threefold degenerate bending and stretching modes of methane played a key role. Since the precise mechanism that causes the interaction between solute and solvent is
unknown, the three relevant quantities DGð@bij =@Q m Þ DGbm ðm ¼ 1—3Þ were used as fitting parameters. This theory has
been tested for all the protonated and deuterated methanes and
was found to be very successful. Fitting parameters DGbm in a number of nematic liquid crystals were obtained.
Once this theory was developed, the implications for solute
molecules other than methane soon became obvious. Especially
when one wants to derive detailed and accurate structural information of solutes from liquid-crystal NMR, the contribution to
the dipolar couplings arising from the vibration–reorientation
25
mechanism, that completely dominates in methane, may still be
significant, although not dominant, in other less symmetrical solutes. This may lead to uncertainties in structures that are much larger than previously assumed and much larger than the accuracy
with which dipolar couplings can be measured experimentally
would suggest [23]. It is therefore important to confirm the theory
underlying the vibration–reorientation interaction beyond a shadow of doubt.
For this purpose we studied the tritiated isotopologues
CHn T4n ðn ¼ 0—3Þ in a number of nematic liquid crystals. In addition to tritium chemical shifts, information about dipolar splitting
was also obtained. In the nematic phase EBBA only poorly resolved
spectra were measured. Much better results were obtained in the
solvent 5CB, a nematic phase not employed in previous studies
on protonated and deuterated methanes. The theory developed before was used by just inserting the tritium mass and magnetogyric
ratio. The tritium spectra could be reproduced very well by fitting
theoretical to experimental couplings with three adjustable
parameters DGbm .
Experiments in the liquid-crystal solvent 1132 led to tritium
spectra of reasonable quality. For this particular solvent the three
DGbm parameters had been derived for the protonated and deuterated species, and they were transferred without change. The predicted dipolar couplings in combination with the indirect
couplings led to predicted tritium spectra that, without any adjustable parameters, could essentially be superimposed on the experimental ones.
The fact that the quantum-mechanical theory developed for the
protonated and deuterated methane isotopologues also offers a virtually perfect prediction of all our observed dipolar splittings in the
tritium-substituted species is convincing proof that the concept of
vibration–reorientation interaction is eminently valid. The same
theoretical description can therefore be used when solutes of symmetry less than tetrahedral are studied in liquid-crystal solvents.
Acknowledgements
The authors wish to express their gratitude for many years of
close collaboration with Annalaura Segre (deceased 25 April
2008) and Jaap G. Snijders (deceased 13 August 2004). We wish
to dedicate this Letter to their memory. EEB acknowledges the Natural Sciences and Engineering Research Council of Canada for
financial support.
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