Orientational disorder in 1,2,3-trichloro-4,5,6-trimethylbenzene. A single crystal deuterium NMR study of the site populations and dynamics

Article abstract of DOI:10.1039/b008999k

Deuterium NMR measurements on powder and single crystal samples of 1,2,3-trichloro-4,5,6-trimethylbenzene (TCTMB) specifically deuterated at the central methyl group (TCTMB-d₃) are reported. The compound exhibits three solid phases: (I) A high

Full text of DOI:10.1039/b008999k

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Orientational disorder in 1,2,3-trichloro-4,5,6-trimethylbenzene.
A single crystal deuterium NMR study of the site populations and
dynamics
Thomas Brauniger,a Raphy Poupko,a Zeev Luz,*a Detlef Reichert,b Herbert Zimmermann,c
Heike Schmittc and Ulrich Haeberlenc
a W eizmann Institute of Science, Rehovot 76100, Israel
b Fachbereich Physik, Martin-L uther-Universitat Halle-W ittenberg, 06108 Halle, Germany
c A.G. Molekulkristalle, Max-Planck-Institut fur Medizinische Forschung, Jahnstrasse 29,
69120 Heidelberg, Germany
Received 8th November 2000, Accepted 27th February 2001
First published as an Advance Article on the web 11th April 2001
Deuterium NMR measurements on powder and single crystal samples of 1,2,3-trichloro-4,5,6-trimethylbenzene
(TCTMB) speciÐcally deuterated at the central methyl group (TCTMB-d ) are reported. The compound
3
exhibits three solid phases: (I) A high temperature phase, just below the melting point (400 to 499 K), of
unknown structure. (II) An intermediate monoclinic phase (268 to 400 K). (III) A low temperature triclinic
phase (\268 K). Earlier X-ray investigations of the latter two phases indicate that they are, respectively, well
ordered (Phase III at 173 K), and orientationally disordered, with the TCTMB molecules statistically aligned
along the six possible orientations of the benzene core (Phase II at 298 K). In contrast to these observations
the deuterium NMR results show a continuous growth, with temperature, of orientational disorder already in
Phase III. The transition to Phase II involves a discontinuous increase in the disorder, but a considerable
degree of order is retained in this phase even at high temperatures. This ordering reÑects the non-equal
population distribution of the molecular orientation in the crystal lattice sites. A quantitative analysis of the
deuterium NMR spectra provided detailed information on this distribution and its temperature dependence in
the solid phases of TCTMB. The deuterium NMR spectra also exhibit characteristic dynamic e†ects. As a
function of increasing temperature, four dynamic regions can be distinguished: (i) Below 15 K, the spectrum
exhibits features typical of coherent quantum-mechanical tunneling of the CD groups. (ii) Above 15 K, up to
3
about 170 K, there is fast classical (incoherent) reorientation of the methyl groups, but otherwise a rigid
molecular lattice. (iii) Between 180 and 250 K, the spectra exhibit dynamic lineshape changes reÑecting the
onset of six-fold jumps of the TCTMB molecules. (iv) Above 250 K the spectra correspond to a dynamically
averaged, but temperature dependent, quadrupolar splitting, reÑecting the changes in the orientational
distribution of the TCTMB molecules. This region includes the phase transitions, III to II and II to I. T
relaxation measurements over the entire temperature range yielded kinetic parameters for the molecular
1
six-fold jumps (k(260 K) \ 7 ] 106 s~1, *E \ 38.5 kJ mol~1), as well as for the incoherent methyl group
reorientation (k(25 K) \ 1 ] 109 s~1, *E \ 2.8 kJ mol~1).
central methyl group, C Cl (CH )(CD )(CH ) (TCTMB-d ). It
1
Introduction
6
3
3
3
3
3
was shown earlier3 by di†erential scanning calorimetry (DSC)
that TCTMB exhibits three solid phases, with transition tem-
peratures, 500 (melting), (401 ^ 3) and (260 ^ 3) K. The corre-
It is well known that mixed hexasubstituted benzenes of the
general formula C Cl (CH ) exhibit orientational disorder
6
n
3 6~n
in the solid state. This is a consequence of the fact that the van
der Waals radii of the chlorine and methyl groups are quite
similar, so that they can be interchanged without severely
a†ecting the packing energy of the crystalline lattice. Exten-
sive dielectric measurements were carried out on a variety of
chloro-methylbenzenes as early as 1940 by White et al.,1
which indicated that the disorder in these compounds is
dynamic, involving planar molecular reorientation. These
early Ðndings were conÐrmed by subsequent studies, using
sponding transitions for our TCTMB-d sample are shown in
3
the DSC thermogram in Fig. 1. They are essentially the same
as those of the isotopically normal compound. We will refer to
the three solid phases, in order of decreasing temperature, as
Phase I (400 to 499 K), Phase II (268 to 400 K) and Phase III
(\268 K), respectively. No studies on Phase I have been
published so far. The X-ray structures of Phases II and III
were investigated by Fourme and coworkers, at, respectively,
2984 and 173 K.5 Phase II was found to be monoclinic and
orientationally disordered, while Phase III is triclinic and
essentially ordered. The crystal structures of these phases are
very relevant for the interpretation of the present NMR
results and we therefore describe them in some detail in a
separate section (Section 2) below.
X-ray di†ractometry, proton T and wide line NMR spectros-
copy and calorimetry. A brief review summarizing the current
1
knowledge on the dynamic disorder in halogeno-
methylbenzenes can be found in a recent paper by Tazi et al.2
In this paper we present a deuterium NMR study of the
orientational disorder in 1,2,3-trichloro-4,5,6-trimethylbenzene
(TCTMB). For the measurements we used powder and single
crystal samples of TCTMB, speciÐcally deuterated at the
Already before the crystal structures of TCTMB were deter-
mined it was realized, on the basis of dielectric measurements,
that the molecules in the solid phases of this compound
DOI: 10.1039/b008999k
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903
This journal is ( The Owner Societies 2001
1891

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Fig. 1 DSC thermogram of the speciÐcally deuterated TCTMB
sample (TCTMB-d ). 9.6 mg of the material were used, with a heating
3
rate of 10 K min~1. The vertical dashed bars indicate the integration
range for computing the phase transition enthalpies.
undergo fast planar reorientation,1 implying the presence of a
degree of disorder even in the low-temperature Phase III.
These Ðndings were later conÐrmed and further investigated
by additional dielectric relaxation studies,3 as well as wide line
proton NMR6 and relaxation measurements.7 Although these
studies resulted in numerical estimates for the kinetic param-
eters of the molecular motions, neither the dielectric nor the
earlier NMR measurements could provide detailed informa-
tion on the nature of the disorder (population distribution)
and its dynamics at the molecular level. In the present work
we apply the method of single crystal deuterium NMR to
investigate the disorder in the solid phases II and III of
TCTMB. As will be seen, this method is ideal for such studies.
We show that the ““disorderedÏÏ Phase II is, in fact, partially
ordered, in the sense that the various molecular directions are
not equally populated and we determine the population dis-
tribution as a function of the temperature. Likewise, Phase III,
which is well ordered at low temperatures, becomes gradually
disordered on heating and we provide quantitative estimates
for this disorder. The dynamics of the disorder in both phases
corresponds to 60¡ jumps between the minima of the pseudo-
six-fold-symmetric potential in which the TCTMB molecules
are embedded. Analysis of the NMR results provides esti-
mates for the kinetic parameters of this process. Finally, we
also determined kinetic parameters for the three-fold incoher-
ent jumps of the methyl groups, at low temperatures, and
show that, below 15 K, this thermally activated process is
taken over by coherent quantum mechanical tunneling.
Fig. 2 Projections of the crystal structures of TCTMB in the mono-
clinic phase II and triclinic phase III, based on X-ray di†raction data
recorded at 2984 and 173 K,5 respectively. In the Phase II, all substit-
uents of the benzene rings are indicated by identical dark-dotted
spheres. In the Phase III, the methyl groups are indicated by small,
dark-dotted spheres, the chlorines by large, light-dotted spheres. (a),
(b) Projections of Phase II unit cell down the crystallographic a and
m
b
axes, respectively. M and M@ are monoclinically related molecules.
m
(c) Projection of the Phase III unit cell down the a* axis. b and c are
t
t
t
the axes of the primitive unit cell, bs \ b \ 2b and cs \ 2c are axes
2
The crystal structure of Phases II and III
t
t
m
t
m
of the (non-primitive) triclinic supercell. The arrows indicate the direc-
tion of polarization of the molecules. The molecules M and M@ are not
The X-ray structure of Phase II was determined by Fourme et
al.4 at 298 K. It was found to be monoclinic, belonging to the
symmetry related. (d) Two projections down the bs axis of the triclinic
t
supercell. The two projections correspond to the a and b forms of the
space group P2 /c with two symmetry related molecules, M
triclinic phase. The arrows are associated with the molecules of the
top layer in each domain. The two domains are related by two-fold
screw axes as shown. The ] and [ symbols at the center of the
1
and M@, per unit cell. The dimensions of this unit cell are:
a \ 8.22 A, b \ 3.88 A, c \ 17.16 A, with b \ 119.33¡.
m
m
m
m
molecules indicate relative displacements along bs . The molecules M
Projections of this unit cell down the a* and b axes are
t
m
m
and M@ in the same domain are not symmetry related, but the pairs
shown in Fig. 2(a) and (b), respectively. Since in this space
group four asymmetric units are expected per unit cell, it
follows that the molecules must occupy sites of inversion sym-
metry. However, as the TCTMB molecules lack such a sym-
metry, it must be assumed that they are orientationally
disordered such that on the average the lattice sites are
centrosymmetric. The molecular planes were found to lie
M(a), M@(b) and M(b), M@(a) are pairwise related by twofold screw
axes.
““polar disorderÏÏ.8 Moreover, the X-ray results4 also indicate
that these arrows are equally distributed along the six direc-
tions of the pseudo-hexagonally-symmetric TCTMB molecule,
corresponding to complete planar disorder. Below we will
demonstrate that this is actually not the case.
nearly parallel to the a c crystal planes, with their normals
m m
subtending an angle of 21.8¡ with the b axis. The average
m
inversion symmetry implies that if we associate with each
TCTMB molecule an arrow pointing from the center chlorine
atom to the center methyl group (CD in TCTMB-d ), these
arrows will be statistically pointing ““upÏÏ and ““downÏÏ
throughout the lattice. We refer to this type of disorder as
The X-ray structure of Phase III was determined by
Fourme and Renaud5 at 173 K. They found this phase to be
triclinic, belonging to the space group P1. The transition from
the monoclinic Phase II to this phase involves almost no
3
3
1892
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903

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change in the position of the molecules or in the orientation of
their planes (i.e., the directions of the normals to the molecular
planes remain essentially the same as in the monoclinic phase).
Rather, the transition involves, predominantly, the setting-in
of orientational order: At the temperature at which the X-ray
measurements were performed, the directions of the arrows
associated with each molecule are Ðxed and each lattice site
has a well deÐned polarization (preferred directions of the
from the a and b domains, it is not possible to construct a
genuine monoclinic supercell.) In each domain, adjacent M
(M@) molecules in the stack along the b axis are related by
inversion centers. Since molecules related by inversion are
magnetically equivalent, we expect in
a single crystal
2H-NMR spectrum, for a general direction of the magnetic
Ðeld, signals from four types of molecules, which are pairwise
related by monoclinic symmetry. Accordingly, we shall
analyze the NMR results of Phase III in the framework of
monoclinic symmetry. We must keep in mind, however, that
this pseudosymmetry is based on the assumption of a sta-
tistical distribution of a and b domains in the crystal. As we
shall see this is not always so.
For later reference we summarize in Table 1 relevant X-ray
data on the molecular orientations in Phases II4 and III.5
These data (unit vectors along molecular bond directions) are
given in the standard orthogonal system (SOS), abc*, which is
common to the monoclinic cell and triclinic supercell.
arrows). A projection of the triclinic unit cell down the a* axis
t
is shown in Fig. 2(c). It can be patterned on the monoclinic
Phase II lattice by shifting the origin by 1b along
2 m
b
and setting a \ a , b \ 2b , c \ Jb2 ] c2 , with a \
m
t
m
t
m
t
m
m
t
arctan(c /b ), b \ arccos[(c /o c o)(a /o a o)], c \ p/2. This unit
m
m
t
t
t
t
t
t
cell has twice the volume of the monoclinic unit cell, with four
molecules; two of type M, related by an inversion center, and
two of type M@, also related by inversion. The two types of
molecules are, however, not symmetry related anymore, as
they are now polarized in di†erent orientations.
For certain purposes it is convenient to deÐne a triclinic
supercell with lattice dimensions, as \ a , bs \ 2b , cs \ 2c
3
Experimental
t
m
t
m
t
m
and as \ cs \ p/2, bs \ b . A projection of this cell down the
t
t
t
m
as* axis is also shown in Fig. 2(c). This non-primitive cell has
t
3.1 Material and crystal growth
twice the volume of the triclinic primitive cell (four times the
volume of the monoclinic unit cell) and contains eight mol-
ecules. It has, however, the advantage of having two right
angles and, as discussed by Fourme and Renaud,5 allows
treatment of this phase within the simpler framework of
monoclinic symmetry. The parameters of this supercell at 173
K are: as \ 8.12 A, bs \ 7.62 A, cs \ 34.25 A, with bs \
Two deuterated isotopologues of TCTMB were prepared, viz.,
TCTMB perdeuterated in the three methyl groups (TCTMB-
d ) and TCTMB speciÐcally deuterated in the center methyl
9
group (TCTMB-d ). They were obtained by chlorination of
3
the corresponding deuterated trimethylbenzenes (TMB-d
12
and TMB-d ). In a typical experiment 20 g of distilled TMB
3
t
t
t
t
119.33¡. These dimensions are somewhat smaller than
expected from the relations given above and from the values
determined for the monoclinic Phase II at 298 K. The di†er-
ence is ascribed to thermal contraction.
were dissolved in 220 ml petrol ether (bp \ 60È95 ¡C) and 200
mg of iodine were added. A slow stream of chlorine gas was
passed through the solution for about 2 h, resulting in
decoloration and warming of the reaction mixture. The
mixture was then allowed to cool and kept in ice overnight,
yielding after Ðltration, a Ðrst crop of 3 g TCTMB. The Ðltrate
was then subjected to a second chlorination until no further
heating of the reaction mixture was detected. Cooling as
above and Ðltering yielded another crop of 6 g TCTMB. The
combined harvest was recrystallized twice from ethanol (with
a few drops of chloroform added), yielding 6 g of white
TCTMB crystalline needles.
Another projection of the triclinic supercell, now down the
bs axis is shown in the upper diagram of Fig. 2(d) (labeled
t
““a-domainÏÏ). As pointed out by Fourme and Renaud,5 the P1
unit cell can appear in two lattice forms related to each other
by a two-fold screw axis parallel to b . The two forms are
t
referred to as a and b and a projection of the corresponding b
form is also shown in Fig. 2(d). In principle crystals can crys-
tallize as pure a or pure b forms, but in reality mixed crystals
are usually obtained, with a statistical distribution of the two
forms.9 On a mesoscopic level these crystals consist of a
mosaic of a and b domains separated by domain walls where
the molecular polarization switches from that of one form to
the other. Inspection of Fig. 2(c) and (d) shows that such a
mixed crystal contains two sets of symmetry non-related mol-
ecules. One set consists of the M molecules in the a domains,
M(a) and the M@ molecules in the b domains, M@(b). The other
set consists of the M@(a) and M(b) molecules. Within each set
the primed and unprimed molecules are related by twofold
screw axes. (Note, however, that the translation part of the
screw operation which transforms a into b is di†erent from
that which transforms b into a. Therefore, by combining cells
TMB-d was prepared from the isotopically normal com-
12
pound by catalytic exchange with D O, using 10% Pt/C. The
2
mixture was kept in a stainless steel pressure vessel at 300 ¡C
for one week. The deuterated TMB was isolated and the pro-
cedure repeated two more times using fresh D O and Pt/C.
2
After distillation, 90% of the TMB was recovered as TMB-
d
, with 96È98% deuterium enrichment at the methyl
12
groups, as determined by NMR and mass spectrometry.
Trimethylbenzene speciÐcally deuterated in the center
methyl group, C H (CH )(CD )(CH ) (TMB-d ) was prepared
by
(DMBA),
6
3
3
3
3
3
a
three-step synthesis from 2,6-dimethylbenzoic acid
involving reduction to deuterated 2,6-
dimethylbenzylalcohol-d , bromination to the corresponding
2
Table 1 Polar angles, h, /, (in degrees) of the substituent bond directions, 1, 2 and 3, and of the normal to the molecular plane, o, for the M and
M@ molecules in the Phases II (at 298 K4) and III (at 173 K5) of TCTMB as obtained from X-ray di†raction (see Fig. 2). The angles refer to the
abc* SOS. The molecules in the upper part of the Table are related to the corresponding ones in the lower part, by monoclinic symmetry, i.e. by a
180¡ rotation about b (h ] p [ h, / ] p [ /)
Mol.
Phase
Subst. 1
Subst. 2
Subst. 3
o
M
M(a)
M(b)
II
III
III
111.5, 340.9
110.4, 341.1a
110.9, 342.1
51.8, 335.0
50.9, 333.8
51.3, 334.2a
170.3, 9.4
168.8, 11.6
168.9, 15.9
85.0, 68.8
83.9, 68.8
83.3, 69.6
M@
II
III
III
68.5, 199.1
69.6, 198.9a
69.1, 197.9
128.2, 205.0
129.1, 206.2
128.7, 205.8a
9.7, 170.6
11.2, 168.4
11.1, 164.1
95.0, 111.2
96.1, 111.2
96.7, 110.4
M@(b)
M@(a)
a Polarization direction of the molecule at low temperatures.
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903
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Table 2 E†ective orientations of the goniometer axis, h, /, in the
abc* SOS used in the analysis of the twinned Crystal A
4
Results and discussion
4.1 Deuterium NMR spectra of a powder sample
Molecule
Major twin
Minor twinb
As a preliminary study of the TCTMB system we Ðrst record-
ed the deuterium NMR spectra of a powder sample of
M
M@a
103.0, 285.5
77.0, 254.5
77.0, 74.5
103.0, 105.5
TCTMB-d over a wide temperature range, covering all three
3
a E†ective orientation of the goniometer axis for the M@ molecule,
obtained from the corresponding entries for M by 180¡ rotation about
the crystallographic b axis (h ] p [ h, / ] p [ /). b E†ective orienta-
tion of the goniometer axis for the minor twin, obtained from the
corresponding entries for the major twin, by 180¡ rotation about the
crystallographic a axis (h ] p [ h, / ] 2p [ /).
solid phases. Examples of such spectra are shown in Fig. 3. In
the low temperature range of Phase III, below 130 K, the
spectrum is characteristic of a rigid powder due to a nearly
axially symmetric quadrupolar tensor, g \ 0.07, o lWCD3X o \
Q
38.5 kHz, where lWCD3X \ 3QWCD3X is the major quadrupolar
splitting and QWCD3QX, is the major principal component of the
4 ZZ
ZZ
quadrupole coupling tensor, deÐned in the usual manner,
QWCD3X \ e2qWCD3XQ/h. The low temperature spectrum in Fig. 3
ZZ
is consistent with rapidly reorienting methyl groups, but
benzyl bromide and Ðnally debromination. A solution of 50 g
otherwise static TCTMB molecules. For this situation lWCD3X
DMBA in dry ether was added to 20 g LiAlD in ether and
Q
4
is expected to be 1S3cos2q [ 1TlCD \ [1lCD B [40 kHz,
the mixture reÑuxed for several hours. The mixture was then
2
Q
3 Q
where lCD is the major quadrupole splitting of an aliphatic
hydrolyzed, Ðrst with D O, then with H SO and subse-
Q
2
2
4
deuteron (D120 kHz) and q is the angle between the CÈD
quently extracted with ether. After evaporation of the solvent
and distillation of the residue, 37 of 2,6-
bond direction and the C symmetry axis of the CD group,
g
3
3
which we assumed to be tetrahedral. Hence, for TCTMB-d at
dimethylbenzylalcohol-d were recovered. The sample was
3
2
130 K, lWCD3X \ 3QWCD3X \ [38.5 kHz, where the angular
redissolved in ether, and 27 g of PBr were slowly added. The
Q
4 ZZ
3
brackets in the superscript indicate averaging over the methyl
mixture was stirred for several hours at room temperature and
group rotation, and Z is parallel to the CÈCD bond direc-
then reÑuxed overnight. After cooling the mixture was poured
onto ice and three times extracted with ether. The solution
was then washed with H O and dried over Na SO . After
3
tion.
Between 130 and about 260 K, the spectrum broadens and
eventually coalesces to a much narrower powder pattern, with
2
2
4
evaporating the solvent, 52 g of 2,6-dimethylbenzylbromide-d
2
an average quadrupole splitting of o Sl T o \ 17 kHz (where we
were recovered. In the Ðnal step of the synthesis the latter
Q
have suppressed the SCD T superscript) and a relatively large
3
product was added to a solution containing 18 g LiAlD in
4
asymmetry parameter, g ^ 0.55. These results reÑect the
ether and the mixture reÑuxed for 8 h. After work up, 28 g of
planar reorientation of the TCTMB molecules, i.e. their six-
fold jumps between the various possible orientations of the
benzene core at the lattice sites. The magnitude of the major
the desired TMB-d were obtained. From NMR and mass
3
spectrometry, the deuteration level of this product was found
to be 98%.
quadrupolar splitting is nearly one half of lWCD3X, indicating
Single crystals of TCTMB were grown in vacuum sealed
Q
that it corresponds to the direction normal to the molecular
tubes, using
furnace.
a
BridgemanÈStockberger crystal-growing
plane and that its sign is therefore positive, i.e. Sl T \ ]17
Q
kHz. This value is somewhat smaller than 1lWCD3X, most likely
2 Q
due to fast out-of-plane wobbling of the molecules, which
3.2 NMR measurements and goniometry
further averages out the quadrupolar interaction. The fact that
the biaxiality of SQT is strongly temperature dependent,
implies that the planar motion is not six-fold symmetric, i.e. in
the jump model, not all orientations are equally popu-
lated.10,11
The deuterium NMR measurements were performed on two
spectrometers: (i) The Heidelberg home-built spectrometer,
operating at a deuterium frequency of 72 MHz, using a single
pulse detection (p/2 pulse width, 3.0 ls). It was predominantly
used for sub 100 K measurements. (ii) A Bruker CXP300
spectrometer, controlled by a Tecmag pulse programmer, with
a deuterium frequency of 46.1 MHz and using quadrupole
echo detection (p/2 pulse width 2.5 ls, echo delay 15 ls). Both
spectrometers were equipped with a goniometer probe, allow-
ing rotation of the crystal about an axis perpendicular to the
magnetic Ðeld. The deuterium 2D exchange spectrum was
acquired on a Varian Inova 400 (deuterium frequency, 61.4
MHz).
The melt-grown crystals were cleaved and cut to suitable
size (D4 ] 4 ] 8 mm3), and then Ðxed on PVC rods using
epoxy glue. The orientations of the goniometer rod in the
crystal SOS were determined by optical goniometry and sub-
sequently Ðne-tuned by Ðtting the NMR rotation spectra. For
protection, the crystals were housed in standard thin-walled 5
mm glass tubes. The single crystal measurements were made
on two specimens, labeled A and B. Most measurements were
performed on Crystal A, which happened to be twinned with a
major and a minor component. The two components shared
the crystallographic a axes, but had antiparallel b axes. This
crystal had the goniometer rod glued at a general orientation
in its SOS. The polar angles of the goniometer in this crystal
are summarized in Table 2. The second crystal, B (not
twinned), was used for relaxation measurements at low tem-
peratures and for acquiring spectra in the tunneling regime. It
had the goniometer rod glued parallel to its b axis.
Fig. 3 Deuterium NMR spectra of a powder sample of TCTMB-d
3
as a function of the temperature, as indicated on the left. The corre-
sponding phases are indicated on the right hand side of the Ðgure.
1894
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Above 260 K the spectrum remains sharp and its overall
width stays essentially unchanged with Sl T decreasing from
Q
17 kHz at 260 K to 16 kHz at 420 K. This slight decrease in
Sl T is probably caused by a small increase in the wobbling
Q
amplitude of the molecules. On the other hand, over the same
temperature range of the measurements the asymmetry
parameter gradually reduces from 0.55 to less than 0.2 (see
Fig. 4), indicating a continuous change of the populations
associated with the di†erent orientations of the TCTMB mol-
ecules. Yet, although we qualitatively understand well the
powder spectra over the entire temperature range of the mea-
surements, it is not possible to derive from them quantitative
data. The dynamic spectra in Phase III are a superposition of
subspectra belonging to two symmetry inequivalent sites, M
and M@. Their simulation would require ten adjustable param-
eters (two independent populations and three jump rates for
each site), which is quite unfeasible to implement. Even the
averaged-out spectra in Phase II, where the molecules M and
M@ are equivalent, cannot be quantitatively analyzed in terms
of the orientation distribution of the molecules. This is so
because Sl T is Ðxed by the model so that there is only one
Q
measured parameter, i.e. g, while there are two independent
populations to determine. Also, no discontinuity in the line-
shape is observed in the Phase III to Phase II transition,
although a discontinuity is expected on the basis of the DSC
and X-ray results. We therefore resort to single crystal experi-
ments in order to get more quantitative information on the
solid phases of TCTMB.
Before describing the single crystal measurements, we
brieÑy report on a 2D-exchange experiment12 performed on a
Fig. 5 Top: A deuterium 2D-exchange spectrum of a powder sample
of TCTMB-d , at 195 K; mixing time q \ 200 ms, 40 t increments,
perdeuterated powder sample of TCTMB-d . This experiment
9
allows identiÐcation of the nature of the process, i.e. whether it
9
m
1
32 scans per increment, 10 s recycle time. Bottom: Simulated spec-
involves discrete jumps (60¡/120¡, or other angles), or planar
di†usion. The former will yield a 2D pattern with well deÐned,
jump-angle dependent ellipsoidal ridges, while the latter will
merely result in partial smearing of the main diagonal ridge.
In the top part of Fig. 5, is shown such an experimental spec-
trum, recorded at 195 K with a mixing time of 200 ms. At this
temperature there is already signiÐcant exchange broadening,
resulting in severe signal loss. Nevertheless, clear ridges corre-
sponding to 60¡ jumps, as may be deduced by comparison
with simulation (bottom part of Fig. 5) are observed.
Although this result is anticipated from the X-ray structure, it
lends support to the jump model used in the interpretation of
the dynamic spectra.
trum, using symmetric three-fold jumps (120¡), kq A 1, Sl T \ 40
m
Q
kHz, 1/T \ 2000 s~1.
2
4.2 Deuterium NMR of Crystal A in the monoclinic Phase II
In Fig. 6 are shown deuterium NMR spectra of TCTMB-d ,
3
obtained from Crystal A in the monoclinic Phase II at 370 K,
Fig. 6 Top: Schematic representation of the twinning of Crystal A;
the crystallographic a axis is common to both twins, while the b axes
are antiparallel. Bottom: Deuterium NMR spectra of Crystal A in the
monoclinic Phase II at 370 K, for several orientations of the magnetic
Ðeld (goniometer angle c). The solid and open triangles indicate,
respectively, signals due to the major and minor twin.
Fig. 4 Plots of the asymmetry parameter, g (bottom), and the quad-
rupole splitting, Sl T (top), of the TCTMB-d deuterons, derived from
Q
3
powder spectra of the type shown in Fig. 3, as a function of the tem-
perature.
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903
1895

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for a number of goniometer orientations, c. As discussed
above, in this phase, in a general orientation of the magnetic
Ðeld, two doublets are expected due to the CD groups in the
3
two monoclinically related molecules, M and M@. In e†ect (see,
for example, the spectrum for c \ 173.5¡), two main doublets
(labeled with solid triangles), and two minor ones (open
triangles) of almost one half the intensity of the former, are
observed. This doubling of the number of peaks was traced
back to twinning, with a major and a minor twin. By inspec-
tion of the rotation pattern we found that the two twins share
a common a axis, while their b axes are antiparallel, as shown
at the top of Fig. 6. To interpret the spectra we Ðrst plotted
the line positions as a function of c, identiÐed the various fam-
ilies of ““harmonicsÏÏ using a computer sorting algorithm13
and Ðnally applied the SUPERFIT program14 to derive the
quadrupole coupling tensors, SQT. The best-Ðt rotation pat-
terns so obtained are shown in the upper diagram of Fig. 7,
where the full and dotted lines correspond, respectively, to the
major and minor twins of the crystal. In computing the SQTs
we made use of the method of Tesche et al.15 for monoclinic
crystals, where a single rotation experiment suffices to derive
the quadrupole coupling tensor. This method is based on the
fact that the rotation pattern of a monoclinically related mol-
ecule, say M@, can count as a second rotation experiment on
M, but with a goniometer axis related to the original one by
the monoclinic symmetry (180¡ rotation about b). This
method can be extended to other types of symmetries, for
example local molecular symmetry.8 In the present case, for
the Ðnal analysis of the rotation patterns we have extended
the single rotation method to the twin symmetry of Crystal A.
The situation now amounts to acquiring simultaneously rota-
tion spectra from two crystals; the rotation pattern of, say,
M(minor) can be considered as an extra experiment on
M(major) with a goniometer axis related to the original one
by a 180¡ rotation about the (common) crystallographic a axis
(see Fig. 6). A similar relation exists between M@(minor) and
M@(major). The polar angles of the e†ective goniometer axes
for the four types of molecules in the twinned Crystal A are
given in Table 2.
Fig. 7 Rotation patterns of Crystal A in the monoclinic Phase II
(370 K) and in the triclinic Phase III, before (15 K) and after (264 K)
the dynamic averaging of the quadrupole coupling tensor. The full
and dotted lines correspond, respectively, to the major and minor
twin. The lines of the major twin are identiÐed with the molecules in
the unit cell accord ing to the notation of Fig. 2. The vertical dashed
line corresponds to the c value where the magnetic Ðeld crosses the ac
plane.
Similar to the powder, the spectrum of the single crystal is
also temperature dependent, as reÑected by the shifts of the
line positions. Examples of spectra at di†erent temperatures,
within Phase II, and associated rotation patterns (actually
only those for the minor twin) are shown in Fig. 8. The tem-
perature e†ect is quite signiÐcant and reÑects the changes in
SQT due to shifts in the population distribution in the various
sites. We have analyzed the rotation patterns over the entire
temperature range of Phase II as described above, and the
results for the principal values of SQT and their principal
directions (h and / in the SOS), are summarized in Table 3(a).
The orientations quoted in the Table are for molecule M.
Those for M@ can be obtained by a 180¡ rotation about the
crystallographic b axis (h ] n-h, / ] n-/). The identiÐcation
of the M and M@ tensors with the M and M@ molecules was
Fig. 8 Right: Deuterium NMR spectra of Crystal A at several temperatures in the monoclinic phase for a Ðxed goniometer angle (c \ 133.5¡).
The stars and crosses mark the signals of the monoclinically related molecules, M and M@, of the minor twin, that are plotted on the left. Left:
The full rotation patterns for the signals marked on the right, for the indicated temperatures.
1896
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Table 3 The principal values SQT (in kHz) and principal directions d (h, /, in the SOS), of the TCTMB-d SQT tensors, at the indicated
ii
ii
3
temperaturesa,b
T /K
Mol.
SQT
d
SQT
d
SQT
d
xx
xx
yy
yy
zz
zz
(a) M molecules in the monoclinic phase
270
280
300
320
340
360
370
[17.52
[17.35
[16.58
[14.38
[15.25
[14.65
[14.39
26.5, 168.1
23.7, 169.7
21.0, 170.3
18.7, 172.5
17.2, 172.4
15.2, 173.1
13.9, 174.1
[5.3
64.1, 335.3
66.9, 335.7
69.6, 336.3
72.0, 336.2
73.3, 336.9
75.4, 337.1
76.7, 337.3
22.82
22.90
22.79
20.60
22.49
22.42
22.33
84.9, 67.8
84.9, 67.9
85.3, 68.0
85.1, 67.8
85.6, 68.2
86.0, 68.1
86.1, 68.2
[5.55
[6.21
[6.22
[7.24
[7.77
[7.94
(b) M(a) and M(b) molecules in the triclinic phase
255
258
261
264
M(a)
M(b)
M(a)
M(b)
M(a)
M(b)
M(a)
M(b)
[15.69
[23.81
[14.93
[22.77
[14.20
[21.64
[13.53
[20.50
90.2, 337.1
[7.40
1.12
5.6, 249.2
44.4, 326.6
8.0, 290.6
45.1, 328.6
13.3, 310.6
46.6, 329.7
26.7, 324.7
48.1, 330.0
23.09
22.69
23.12
22.04
23.03
21.89
22.93
21.95
84.4, 67.0
81.1, 65.1
84.3, 66.2
82.1, 66.6
84.1, 66.2
82.6, 66.8
84.2, 66.3
82.9, 66.4
133.0, 344.2
95.6, 336.8
134.1, 344.3
101.9, 337.5
44.3, 164.4
115.9, 339.1
42.7, 164.2
[8.19
0.73
[8.83
[0.25
[9.40
[1.45
a The principal directions of the monoclinically related molecules are obtained by a 180¡ rotation about the crystallographic b axis. b The
estimated errors of the principal values and directions are, respectively, ^0.2 kHz and ^0.4¡.
based on the assumption that the directions of the major prin-
normal to the molecular plane and y completing the set to
a right-handed system. We refer to this coordinate system as
the averaging axis system (AAS). Also, we assume that the
QWCD3Xs are axially symmetric with QWCD3X \ QWCD3X \ s and
cipal axes (d in Table 3(a)) must coincide with those of the
zz
corresponding normals to the molecular planes (o in Table 1).
Likewise, the signs of the quadrupole tensor components in
Table 3(a) are based on the assumption that the major com-
i
A
ZZ
ponent, SQT , must have the same sign as the perpendicular
zz
component of QWCD3X, and is therefore positive, as discussed
for the powder spectrum. The principal values of SQT are also
plotted as a function of the temperature in Fig. 9. These
results are fully consistent with those for the powder (Fig. 4).
In particular, Sl T and g of the powder match, respectively
Q
3SQT and (SQT [ SQT )/SQT , of the single crystal
4
zz
yy
xx
zz
results (note the use of lower case subscripts for the average
tensor components). The latter include, however, also the
orientation of the average tensors, which is crucial for the
population analysis to be described in the next section.
4.3 Population analysis in Phase II
As discussed in the above section, the measured quadrupole
tensors in Phase II, SQT, are averages over the various orien-
tations (directions of the associated arrows) of the TCTMB
molecules in the lattice. Thus,
SQT \ ; P QWCD3X
(1)
i
i
where P is the fractional population of orientation i and
i
QWCD3X is the corresponding quadrupolar tensor of the (rapidly
i
reorienting) methyl group. In the present section we analyze
the SQTs and their temperature dependence in terms of the
fractional populations of the molecules at the various orienta-
tions. To do so we derive an expression for SQT based on eqn.
(1), and then compare it with the experimental results at each
temperature.
For TCTMB there are six possible molecular orientations
(arrows) at a crystal site, which we label 1, 2, 3, 1@, 2@ and 3@
(see top of Fig. 10). However, since the orientations 1È1@, 2È2@
and 3È3@ are pairwise related by inversion symmetry, they are
also pairwise magnetically equivalent, QWCD3X \QWCD3X, and
Fig. 9 Top: Schematic potential energy diagram for the three-fold
(six-fold) planar jumps of the TCTMB molecules in the monoclinic
Phase II. The inserted numbers are the Ðtted enthalpies (kJ mol~1)
and degeneracies (eqn. (9)) for the corresponding sites. Bottom: The
principal values of the quadrupole coupling tensor, SQT. t is the
i
i{
their fractional populations are identical, p \ p . Thus, in
i
i{
angle between the direction associated with SQT , and the direction
eqn. (1), the summation runs from i \ 1 to 3 and the P s now
xx
i
of substituent 1 (x-component of the AAS) as deÐned in Fig. 10. Both
stand for the population sums, P \ p ] p . To use eqn. (1)
i
i
i{
quantities are plotted as a function of the temperature in Phase II and
the upper temperature region of Phase III (respectively, right and left
of the vertical dashed line at 268 K). The open and solid symbols in
Phase III refer to molecules M(a),M@(b), and M(b),M@(a) respectively.
Note the di†erent t-scale for the two phases.
correctly, the various QWCD3Xs must be written in a common
i
coordinate system. We choose this to be the principal axis
system (PAS) of orientation 1 of molecule M, as deÐned in the
upper part of Fig. 10, with x along the 1-direction, z along the
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Inserting in eqn. (1) yields
([1 ] 9P )
1
1
s
8
SQAAST \
3J3 (1 [ P [ 2P )
1
2
0
2
3J3 (1 [ P [ 2P )
0
1
2
(5 [ 9P )
0
(6)
1
0
[4
To compute the P s the tensor of eqn. (6) must be compared
with the experimentally determined tensor (Table 3(a), Fig. 9).
As above, both tensors must be written in the same coordinate
system, and we again choose the AAS, i.e., we need to trans-
form the experimental SQT from its PAS (Table 3(a)) to the
AAS.
i
Inspection of the results in Table 3(a) shows that the magni-
tude of the major component of SQT, SQT , is essentially
zz
independent of the temperature (D22.5 kHz) and similar to
the perpendicular component of QWCD3X (QWCD3X \ [1s). Also,
M
2
its orientation (h, / D 85¡, 68¡) does not change with the tem-
perature and is essentially parallel to the molecular plane
normal, i.e. along z of the AAS (cf. Table 1). Thus, only a
single (passive) rotation about the molecular normal axis is
needed to transform the experimental SQT from its PAS to the
AAS,
SQAAST \ R(t)SQTR(t)~1
Fig. 10 Top: Labeling of the substituent orientations of the TCTMB
molecule. The labels apply to molecule M of the monoclinic cell of
Phase II and to the molecules M(a) and M(b) of the triclinic supercell
of Phase III. Bottom: The calculated fractional populations, P , P
1
SQT cos2 t ] SQT sin2 t
xx
yy
\ ([SQT ] SQT )sin t cos t
xx
yy
0
1
2
and P in the monoclinic Phase II and the upper temperature range
3
2
of Phase III (respectively, right and left of the vertical dashed line at
([SQT ] SQT )sin t cos t
xx yy
0
0
268 K). In the latter phase the open symbols refer to the M(a),M@(b)
molecules, while the solid symbols to the M(b),M@(a) molecules. The
dotted lines are calculated using eqn. (9) and the thermodynamic
parameters given at the top of Fig. 9.
SQT sin2 t ] SQT cos2 t
(7)
xx yy
0
SQT
zz
where t is the angle between the eigenvector associated with
SQT (Table 3(a)) and the x direction in the AAS. The experi-
xx
mental values of t, so obtained, are included in Fig. 9. Finally,
QWCD3X \ [1s, so that
to determine the populations, we compare the tensors of eqn.
M
2
(6) and eqn. (7) element by element and (recalling that &P \
1) extract the following expressions,
1 2
1
i
QAAS \QWCD3X \ s
[1
2
.
(2)
1
1
1
9
C
C
8
D
[1
2
P \
1 [
(SQT cos2 t ] SQT sin2 t)
xx yy
1
2SQT
zz
The corresponding tensors of orientations 2 and 3 in the AAS
are obtained by a ““passiveÏÏ rotation16 of their respective PAS
coordinates into the PAS of orientation 1,
1
2
8
D
P \
1 [ P ]
([SQT ] SQT )sin t cos t
xx yy
2
1
6J3 SQT
zz
QAAS \ R(e )QPASR(e )~1
(8)
P \ 1 [ P [ P
i
i
i
i
3
1
2
1
2
(3 cos2 e [ 1) [3 cos e sin e
[3 cos e sin e (3 sin2 e [ 1)
0
where we substituted s \ [2SQT . Inserting the experimen-
s
2
zz
\
(3)
tal values of t and of the components of SQT (Table 3(a)),
0
yields the populations, P , plotted in the bottom part of Fig.
0
0
[1
i
10.
where
It may be seen that these plots do not obey a simple Boltz-
mann behavior based on enthalpy alone, as reÑected in the
fact that the three populations do not approach a common
high-temperature asymptotic value of 1/3. Clearly, entropy
factors a†ect the population distribution and accordingly we
Ðt the population curves to the more general equation
1 2
cos e
sin e
0
0
1
R(e) \ [ sin e cos e
(4)
0
0
and e is ]60¡ for substituent 2 and [60¡ for substituent 3 (cf.
Fig. 10). This gives
[exp(T *S [ *H )/RT ]
i
i
P \
i
; [exp(T *S [ *H )/RT ]
[1
1 2
[3J3
0
i
i
s
8
QAAS \
[3J3
5
0
n exp([*H /RT )
2
i
i
\
(9)
0
0
[4
; n exp([*H /RT )
i
i
[1
1 2
where n \ exp(*S /R) is a measure of the site degeneracy.
Setting, arbitrarily, the enthalpy and degeneracy of orientation
1, to *H \ 0 and n \ 1, we obtain the values inserted at the
top of Fig. 9. This insert also includes a schematic potential
3J3
0
i
i
s
8
QAAS \
(5)
3J3
5
0
3
1
1
0
0
[4
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energy diagram, based on the population analysis results. It
shows that orientations 1 and 3 have similar local potential
minima, while orientation 2 is less stable and appears to be
more highly degenerate.
An important conclusion from this analysis is that Phase II
has no complete planar disorder, as suggested by the X-ray
results.4 Rather, a population di†erence between the di†erent
orientations is maintained even at high temperatures. As the
temperature is lowered, orientation 2 becomes depleted, while
the populations of orientations 1 and 3 increase. It is tempting
to ascribe this increase in polarization as a pretransition e†ect,
as if the system anticipates the polarization in Phase III. We
discuss this point in the next section. As will be seen, this
anticipation is only partly fulÐlled.
4.4 Deuterium NMR and population analysis in the triclinic
Phase III
As discussed in Section 2, the transition from the monoclinic
Phase II to the triclinic Phase III, although Ðrst order, does
not involve displacements of the molecules or any major
change in their tilt. According to the X-ray results the tran-
sition involves predominantly the setting-in of spontaneous
polarization. The two originally symmetry related molecules,
M and M@ of Phase II now become inequivalent, in the sense
that they polarize in di†erent orientations and to di†erent
degrees. Thus, upon transition to Phase III, the signals associ-
ated with the M molecules of Phase II split into a pair of
symmetry unrelated signals, M(a) and M(b), while those of M@
yield the pair M@(a) and M@(b). From the discussion of Section
2, it also follows that the pair M(a), M@(b) is monoclinically
related and likewise the pair M(b), M@(a).
In Fig. 11 (top) are shown two spectra of Crystal A, record-
ed just above (270 K) and below (260 K) the II % III phase
transition temperature (268 K). The magnetic Ðeld orientation
was such that the monoclinically related molecules are mag-
netically inequivalent. Hence, two well resolved doublets are
observed (for the major twin) in Phase II and four barely
resolved doublets in Phase III, as expected from the above
discussion. Such ““narrow-linedÏÏ spectra as shown in the 260
K trace of Fig. 11, are observed only over a very limited tem-
perature range of Phase III, from 268 K down to about 255
K. Below this temperature, the system enters the dynamic
NMR regime: The lines Ðrst broaden and, on further cooling,
narrow again. Below 180 K, a new high-resolution spectrum
emerges (see the 160 K trace in Fig. 11), where the molecular
reorientation is frozen out, but not the reorientation of the
methyl groups. The spectrum then remains essentially
unchanged down to about 15 K. We will delay the discussion
of the dynamic e†ects to a later section. Here we limit our-
selves to the two regimes of extreme fast and extreme slow
molecular reorientation in Phase III.
In the upper temperature range (255 to 268 K) there is a
rapid six-fold jump process of the TCTMB molecules between
unequally populated orientations, leading to average biaxial
tensors, as in Phase II. Since, however, in Phase III the mono-
clinic pair M(a),M@(b) is symmetry unrelated to the M(b),M@(a)
pair, two di†erent tensors reÑecting the di†erent population
distribution in the two type of sites are expected. To deter-
mine the populations, four rotation experiments, at di†erent
temperatures in the range 255 to 268 K, were performed. One
such rotation pattern, corresponding to 264 K, is shown in the
middle part of Fig. 7. Following the identiÐcation of the
monoclinically related pairs (pairwise crossing when the mag-
netic Ðeld traverses the ac plane), the analysis proceeded as for
the Phase II spectra. The results, so obtained, are summarized
in Table 3(b) and in Fig. 9. The identiÐcation of the quadru-
polar coupling tensors of the two inequivalent pairs with the
crystal sites M(a),M@(b) or M(b),M@(a) cannot be done in an
unequivocal fashion. This is so, because the molecular plane
Fig. 11 Selected deuterium NMR spectra of Crystal A. Top: Spectra
recorded at a Ðxed orientation of the magnetic Ðeld (c \ 133.5¡) at the
indicated temperatures. The peak labeling refers to the molecules of
the major twin. Bottom: Spectra recorded at 15 K for a number of
crystal orientations, as indicated. The crosses and stars label M@(b)
and M(a) molecules of the major twin.
normals of the symmetry unrelated molecules, e.g. M(a) and
M(b) are essentially parallel and can therefore not be used for
their identiÐcation. We shall shortly return to this problem,
and meanwhile adopt the assignment of Table 3(b) and Fig. 9.
Once the SQTs of the two pairs of sites were determined, we
calculated the orientation populations, as described for the
monoclinic Phase II. The situation here is, however, some-
what more subtle. In the triclinic phase the molecules do not
occupy sites of inversion symmetry. Consequently p need not
i
be identical to p so that, in principle, there are six popu-
i{
lations for each crystal site. It may be seen, however (see Fig.
2), that in the triclinic lattice, down the b axis, the molecules
t
are alternately related by inversion symmetry, so that within a
unit cell, p \ p . Since the NMR spectra of inversion related
i
i{
sites are identical, we can only detect their sum P \ p ] p ,
i
i
i{
and the problem reduces again to that of the monoclinic
Phase II (eqn. (8)). The results so obtained are plotted in Fig.
10, together with those for Phase II. We thus see that Phase
III is also disordered, at least in its upper temperature range
with unequal populations for the various substituent direc-
tions.
At low temperatures (\100 K) this phase indeed becomes
fully polarized with only one orientation populated for each
site. This follows from the analysis of rotation patterns record-
ed in this temperature range. One such rotation pattern,
recorded at 15 K, is shown at the bottom of Fig. 7. An identi-
cal rotation pattern was obtained at 100 K. Analysis of these
results gave the principal values and principal directions sum-
marized in Table 4. The resulting tensors correspond essen-
tially to static molecules with rapidly reorienting methyl
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Table 4 Principal values QWCD3X (in kHz) and principal directions d (h, /, in the SOS) of the QWCD3X tensors for the M(a) and M(b) molecules in
ii
ii
the triclinic phase, as determined from rotation experiments at 15 K. Also given are the directions of the CÈCD bonds (in the rows labeled Z)
3
and the normals to the molecular planes (rows labeled Y ), as determined from X-ray data at 173 Ka
i
Mol.
QWCD3X
d
(NMR)
d
(X-ray)
db
ii
ii
ii
Z
X
Y
M(a)
M(a)
M(a)
[53.60
28.26
25.34
109.5, 334.9
19.6, 339.0
91.3, 65.4
110.4, 341.1
È
83.9, 68.8
5.9
È
8.2
Z
X
Y
M(b)
M(b)
M(b)
[53.28
27.68
25.60
52.6, 329.2
39.3, 170.1
79.6, 67.2
51.3, 334.2
È
83.3, 69.6
4.1
È
4.4
a The estimated error of the principal values is ^0.4 kHz, and of the major principal direction ^0.4¡. b Angle between corresponding directions,
obtained from the NMR and X-ray results.
groups, QWCD3X. The directions associated with their major
monoclinic pair of doublets, as well as in the two doublets of
the minor twin (not labeled in the Ðgure). These anomalies are
not always readily detected, because most spectra su†er from
excessive line overlap. For the spectra shown in Fig. 11, we
can safely rule out experimental artifacts, such as saturation,
and we believe that the e†ect is real. We recall that the
pseudo-monoclinic symmetry of Phase III stems from the
assumption of equal number of a and b domains in the
sample. This assumption is, however, not required by any
symmetry or thermodynamic consideration. It is likely that
for melt-grown crystals, as used in our NMR measurements,
the distribution of the a and b domains is not statistical,
leading to the observed intensity di†erence.
principal components (parallel to the CÈCD bond) are now
3
along substituent 1 for the M(a),M@(b) pair and along substit-
uent 2 for the M@(a),M(b) pair (cf. Table 4). These directions
were found to be the polarization directions in the X-ray
study (see Table 1). In fact, we matched the experimental SQTs
to the molecular sites by identifying their major principal
directions with those of the X-ray polarizations.
We now return to the population results in the high tem-
perature range of Phase III (Fig. 10). Referring Ðrst to the
open symbols, we note that the most populated orientation
for this type of molecules is P (diamonds) and that, over the
1
narrow range where measurements could be carried out, P
1
keeps increasing with decreasing temperature, at the expense
of the populations of orientations 2 (circles) and 3 (squares). It
is therefore natural to associate these results with those mol-
ecules in the crystal, which according to the low-temperature
X-ray measurements are polarized along the 1-direction.
Hence, the assignment of the open symbols to the M(a),M@(b)
molecules (see Fig. 2 and Table 1). The situation for the solid
symbols is more complex. By elimination, we identify them
with the M@(a),M(b) molecules, which according to the X-ray
results are, at low temperatures, polarized along the 2-
4.5 Dynamic e†ects: Line broadening and T relaxation
1
In the temperature range 180 to 260 K, the deuterium NMR
spectra of TCTMB-d exhibit line broadening e†ects, reÑec-
3
ting the molecular six-fold jumps within the lattice sites. In
Fig. 12 (left) two sequences of experimental spectra, for the
single Crystal A (top) and for a powder sample (bottom) are
shown. The spectra exhibit characteristic dynamic features
that in principle could be simulated by standard dynamic
NMR methods. The application of these methods to the
present problem is, however, quite demanding. As already
indicated the simulations require a total of ten adjustable
parameters (three rate constants and two fractional popu-
lations for each site). Nevertheless, we made a crude attempt
to simulate the spectra by assuming, (a) k \ k \ k \ k
direction. Indeed, P of the solid symbols (Fig. 10) increases
2
on lowering the temperature, however, the plots also show
that P is larger than P and it also increases with tem-
1
2
perature, at least over the narrow range of measurements. We
must therefore assume that in some temperature range within
Phase III, P of the M@(a),M(b) molecules passes through a
1
maximum and then decreases on further cooling. This behav-
12
23
13
(where k is the rate constant for the jump from orientation j
ior is not consistent with a regular Boltzmann equation, which
predicts a monotonic change in population with temperature.
A way out of this dilemma is to assume that the packing
potential in which the TCTMB molecules are embedded, is
temperature dependent, e.g. by the gradual changes in polar-
ization with the temperature. It would be interesting to
conÐrm this assumption by measuring the populations over
the entire range of Phase III. Unfortunately, this is not pos-
sible by the technique described above, because of the smear-
ing out of the signals due to dynamic line broadening.
ij
to orientation i), (b) identical rates for the two symmetry unre-
lated molecules and (c) a Boltzmann equation for the popu-
lations of the form,
P \ n exp([E /RT )/Z
(10)
i
i
i
where Z is the partition function. The parameters, n and E
i
i
for each orientation were determined from two sets of popu-
lations at the high and low temperature limits of the simula-
tion range. At the high temperature end (260 K) the
Before concluding this section we wish to comment on
some line intensity peculiarities, observed in the low-
temperature region of Phase III. Examples of such spectra of
the twinned Crystal A, are shown at the bottom of Fig. 11.
These spectra, which include the peak assignments, were
recorded at 15 K, for several c values. Close inspection of the
spectra reveals that pairs of doublets, which are related by the
pseudo-monoclinic symmetry, do not have identical inten-
sities. For example, it may be seen in the c \ 132¡ trace that
the intensity of the doublet due to the M@(b) molecules of the
major twin (crosses) is quite di†erent from that of the M(a)
molecules (stars). Similar anomalies are observed for the other
experimental P s from Fig. 10, were taken, while at the low
temperature end (100 K), the populations of the polarized
i
orientations (P [M(a)], P [M@(b)] and P [M@(a)], P [M(b])
1
1
2
2
were chosen to be 0.90, and all other P s were set to 0.05. The
i
latter assumption is consistent with the restriction that the
line broadening cannot exceed the order of P Æ SQT. Using
i
these assumptions and an exchange independent linewidth of
1/T * \ 5000 s~1, the simulated lineshapes shown on the
2
right-hand side of Fig. 12, were obtained. Although the
spectra reproduce many of the experimentally observed fea-
tures, the Ðt is far from perfect, clearly due to the over-
simpliÐed model used. An Arrhenius plot of the ““best-ÐtÏÏ rate
1900
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903

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Fig. 13 Longitudinal relaxation times, T , of the deuterons in
1
TCTMB-d as a function of the temperature. The high-temperature
3
results (open squares) were obtained on a powder sample and corre-
spond to the shoulders (at low temperatures, horns) at l \ ^17 kHz
(magnetic Ðeld perpendicular to the molecular planes). The low-
temperature results were obtained on Crystal B. The open and solid
diamond symbols correspond, respectively, to molecules M(a),M@(b)
and M(b),M@(a). The various lines are calculated using equations given
in the text and the appropriate kinetic parameters shown in Table 5.
clear T minimum at around 320 K. No discontinuity is
1
observed at the phase transition. The T relaxation around
1
this minimum is clearly dominated by the planar six-fold
(actually, three-fold) jumps of the TCTMB molecules and can
be analyzed using suitable relaxation equations. To simplify
the analysis we assume identical populations and equal jump
rates, k, between all orientations. In view of our earlier dis-
cussion, these are, admittedly, very crude assumptions, but
they are acceptable in the temperature range of the analysis
and they make the problem tractable. Under these conditions
Fig. 12 Left: Experimental deuterium NMR spectra of Crystal A at
a goniometer angle of c \ 160¡ (four upper traces) and of a powder
sample of TCTMB-d (four bottom traces), at the indicated tem-
3
peratures. Right: Simulated spectra calculated, using assumptions
described in the text and the indicated rate constants for planar three
fold molecular jumps.
the deuterium relaxation rate in the TCTMB-d molecules
3
becomes,17
constants yields the kinetic parameters shown in the Ðrst row
of Table 5.
Complementary dynamic information can be derived from
relaxation data. The deuterium longitudinal relaxation times
1
A
q
B
c
\ (2plWCD3X)2
(11)
Q
T
1 ] 4u2 q2
1
0 c
where q \ 1/3k. Fitting eqn. (11) to the high temperature
results of Fig. 13, and assuming an Arrhenius temperature
c
of TCTMB-d were measured on two specimens; a powder
3
sample in the temperature range 160 to 400 K, and a single
dependence for k, the kinetic parameters shown in the second
row of Table 5 were obtained. As may be seen they are quite
close to those estimated from the lineshape Ðtting.
crystal (Crystal B), in the range 10 to 55 K. The results for
both samples are plotted in Fig. 13. We defer the discussion of
the low temperature data to a later section. The T results of
the powder sample correspond, at the higher temperature
These results are also of the same order of magnitude as
estimated earlier by several other groups. For example, the
proton NMR linewidth measurements by Brot et al.6 show a
characteristic dispersion at around 223 K, which has been
interpreted as due to molecular reorientation. Using the
experimental results in this paper, we estimate the rate con-
stant entered in the third row of Table 5. The activation
energy shown in the same line, was derived from a subsequent
1
range, to the outer shoulders (parallel features) of the spectra,
at around ^17 kHz, which at lower temperatures turn into
the perpendicular horns of the powder pattern. These results
thus apply to those molecules in the powder whose plane
normals lie parallel to the external magnetic Ðeld. They cover
the temperature range of the two phases III and II, with a
Table 5 Kinetic parameters for the reorientational jumps and of the incoherent methyl group reorientation in solid TCTMB
Dynamic mode
Method
E /kJ mol~1
k/s~1 (T /K)
Ref.
a
Planar reorientation
2H, lineshape
41.0
5 ] 106 (260)
7 ] 106 (260)
9 ] 104 (223)b
B108 (300)d
3 ] 105 (226)
Èe
this work
this work
6
7
1
3
2H, T
38.5 ^ 0.5
40.0a
52.0c
Èe
1
1H, linewidth
1H, T
1
dielectric relax.
dielectric relax.
42.7c
Methyl reorientation
2H, T
2.8 ^ 0.3
1 ] 109 (25)
Èe
this work
7
1
1H, T
1
2.1
a From the Thesis of I. Darmon (Paris, 1969), quoted by Chezeau et al.7 b Estimated from the midpoint of the dispersion curve. c A distribution of
correlation times was assumed in the analysis. d Estimated from the T minimum. e Not given.
1
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903
1901

View Article Online
where, as before, q \ 1/3k, and
c
g \ sin2 2h(cos2 Ë ] cos2 2Ë)
1
] sin4 h(sin2 Ë ] 1 sin2 2Ë)
4
[ 8(sin3 h cos h sin3 Ë cos Ë)cos 3r
g \ 4 sin2 2h(sin2 Ë ] 1 sin2 2Ë)
2
4
] sin4 h(1 ] 6 cos2 Ë ] cos4 Ë)
] 8(sin3 h cos h sin3 Ë cos Ë)cos 3r
(13)
Fig. 14 A deuterium NMR spectrum of Crystal B at 12 K. The
upper trace is plotted at an 8-fold gain in order to enlarge the
““tunneling peaksÏÏ at the outer wings of the spectrum.
In these equations, h is the angle between the CD bond and
the methyl C axis, (h \ 70.53¡, the tetrahedral angle), and Ë/r
3
are the polar/azimuthal angles of the magnetic Ðeld in the
principal axis system of the methyl group. Since the azimuthal
orientations of the methyl deuterons are unknown, we
neglected the r-dependent term (which contributes at most
analysis of these wide line measurements, as quoted by
^20% to T ).17 Substituting the above quoted values of Ë and
Chezeau et al.7 Proton relaxation-time measurements by the
1
h, we obtain the following values for g and g , for the two
latter group7 gave a characteristic T minimum at 290 K,
1
2
1
sites, M(a),M@(b): g \ 0.675, g \ 5.70; M@(a),M(b): g \
which was also ascribed to planar molecular reorientation.
1
2
1
1.485, g \ 2.19. Using these coefficients and Ðtting the experi-
From these data they derived the activation energy listed in
the fourth row of Table 5. It is interesting that the authors,
not being able to quantitatively Ðt the relaxation data to a
single rate constant, concluded that the motion involves a dis-
tribution of correlation times. This probably reÑects the ine-
quivalency of the various sites, as discussed above. Finally, we
mention the dielectric relaxation data of White et al.1 and of
Brot et al.,3 (Ðfth and sixth row of Table 5), who also claim
that the process involves a distribution of correlation times. It
is remarkable that despite the crudeness of the models used in
the interpretation of the various experiments, the resulting
kinetic parameters are pretty similar.
2
mental data of Fig. 13 to eqn. (12), yielded similar kinetic
parameters for the two independent molecules. In the Ðnal
analysis we performed a common Ðt to both sets of data and
the results are given in the penultimate row of Table 5. The
result for the activation energy is in agreement with that of
Chezeau et al.,7 obtained from proton relaxation experiments
(see last entry in Table 5).
On the basis of the above kinetic results we would expect
the deuterium spectrum of TCTMB-d to start broadening on
3
cooling below 20 K, due to the freezing out of the thermally
activated methyl group reorientation. In fact, this does not
happen. Instead the spectra acquire a new structure, manifest-
ed in the appearance of typical tunneling peaks. A spectrum,
recorded at 12 K, where such extra peaks are clearly observed,
is shown in Fig. 14. In the present work we have not attempt-
4.6 Classical reorientation and coherent quantum-mechanical
tunneling of the methyl groups
ed a quantitative analysis of the TCTMB-d tunneling
3
Below 100 K the deuterium NMR lineshape of the TCTMB-
spectra. Qualitatively, however, they clearly indicate that
d
crystals remains essentially unchanged on further cooling
below about 15 K, the CD groups decouple from the lattice
thermal bath and enter a regime of coherent tunneling. From
the overall spread of the spectrum and the low intensity of the
extra tunneling peaks, we may conclude that the tunneling fre-
3
3
down to about 15 K. Below this temperature new lines appear
in the spectrum, that indicate the onset of coherent quantum-
mechanical tunneling.18 Well before this temperature range, at
around 170 K, the T relaxation time begins to shorten due to
quency in TCTMB-d is higher than the deuterium quadrupo-
1
3
slowing down of the classical, incoherent, reorientation of the
CD groups. In the present section we brieÑy address these
two phenomena.
le interaction, indicating that the CD groups can rotate fairly
unhindered.19
3
3
On the right-hand side of Fig. 13 are plotted T results
1
obtained on a single crystal (Crystal B) of TCTMB-d , in the
3
temperature range 10 to 55 K. The goniometer axis for this
5
Summary and conclusions
crystal was mounted along the crystallographic b axis, so that
for all rotation spectra the magnetic Ðeld lies in the ac plane.
Hence, all spectra consist of just two doublets, due to the two
sets of crystallographically inequivalent molecules, M(a),M@(b)
This work demonstrates the power of deuterium single crystal
NMR spectroscopy as a complementary tool for X-ray crys-
tallography. We have applied this method to quantitatively
study the population distribution (otherwise referred to as
orientational disorder) and the jump rates between di†erent
orientations in the solid phases of TCTMB. The high tem-
perature monoclinic phase was found by an earlier X-ray
investigation4 to be orientationally disordered, which was
ascribed to the pseudo-hexagonal symmetry of the TCTMB
molecules. The NMR method is extremely sensitive to the
population distribution between di†erent orientations and in
the present study we found a considerable deviation from
equal distribution (planar disorder). On cooling within the
monoclinic phase, the population distribution becomes more
polarized, as if the system senses the low temperature triclinic
phase, which from the low temperature X-ray measurements
of Fourme and Renaud5 at 173 K, is expected to be highly
ordered. It is interesting that these authors realized, mainly on
and M(b),M@(a). For the T relaxation measurements, the
1
orientation of the magnetic Ðeld was such that it subtended
27.1¡ and 79.3¡ with the CÈCD bonds of the M(a),M@(b) and
3
M@(a),M(b) molecules, respectively. The two T curves in Fig.
1
13 correspond to these two types of molecules. Both sets of
data pass through a minimum at, respectively, 30 and 24 K.
These results reÑect the slowing down of the reorientation of
the CD groups and can be used to derive kinetic parameters
3
for this process. The general equation for the T relaxation of
1
a deuterium, with axially symmetric quadrupole splitting, lCD,
Q
undergoing three-fold jumps between equally populated sites
is,17
1
(2plCD)2
C
q
q
D
Q
c
c
\
g
] g
(12)
1
2
1 ] 4u2 q2
T
8
1 ] u2 q2
1
0 c
0 c
1902
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903

View Article Online
the basis of the observed temperature factors, that the order-
ing at this temperature is not complete, and concluded that
the molecules are probably not fully polarized above 100 K.
Our deuterium NMR results are consistent with this view and
indicate that the disorder increases continuously on heating
towards the monoclinic phase. Thus, the transformation from
a perfectly ordered triclinic phase to a disordered monoclinic
phase is a very gradual process, spanning a wide temperature
range. The actual transition takes place between two partially
ordered phases, and is consequently only weakly Ðrst order. It
does not involve any major structural changes of the lattice
but merely a relatively small, discontinuous change in the
molecular polarization.
The phenomenon of transition between partially ordered
phases probably also occurs in other mixed chloro-
methylbenzenes. Clearly, the packing potential of these mol-
ecules is not perfectly hexagonal and depends not only on the
shape of the isolated molecule, but to a large extent also on
the arrangement of the neighboring molecules in the lattice.
Consequently a wide range of order/disorder can be expected
(classical) process is replaced by quantum mechanical coher-
ent tunneling. Although we have not quantitatively studied
this regime in the present work, we could demonstrate the
presence of tunneling by identifying its characteristic features
in the deuterium NMR spectrum.
Acknowledgement
This work was supported by the German-Israeli Foundation,
G.I.F. Project No. I-558.218.05/97 and by the G.M.J. Schmidt
Minerva Center for Supramolecular Architecture.
References
1
A. H. White, B. S. Biggs and S. O. Morgan, J. Am. Chem. Soc.,
1940, 62, 16.
M. Tazi, J. Meinnel, M. Sanquer, M. Nusimovici, F. Tonnard
and R. Carrie, Acta Crystallogr. Sect. B, 1995, 51, 838.
C. Brot and I. Darmon, J. Chem. Phys., 1970, 53, 2271.
R. Fourme, M. Renaud and D. Andre, Mol. Cryst. L iq. Cryst.,
1972, 17, 209.
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2
3
4
in the solid phases of the C Cl (CH )
compounds, from
5
6
6
n
3 6~n
perfect order to perfect disorder. The present system, at high
temperatures, is close to the latter situation. It is remarkable,
however, that already sixty years ago,1 it was suggested that
the disorder in TCTMB is not complete, in order to account
for anomalous dielectric relaxation e†ects observed in this
7
8
9
J.-M. Chezeau, J. H. Strange and C. Brot, J. Chem. Phys., 1972,
56, 1380.
T. Brauniger, R. Poupko, Z. Luz, P. Gutsche, C. Meinel, H. Zim-
mermann and U. Haeberlen, J. Chem. Phys., 2000, 112, 10858.
Actually, the existence of two domain types with a statistical
(equal) distribution in the triclinic phase was inferred by Fourme
and Renaud from the overall monoclinic symmetry (with dou-
bling of the b and c repeats) of the 173 K di†raction pattern. The
a and b domains are, in fact, derivative structures of the mono-
compound. An example of
a highly ordered chloro-
methylbenzene is the isomeric compound, 1,3,5-trichloro-2,4,6-
trimethyl benzene, where X-ray measurements2 indicate that,
although the molecules undergo rapid in-plane reorientation,
they exhibit complete orientational order. Thus, in this case,
the packing energy of the lattice well discriminates between
chlorine and methyl substituents.
clinic space group P2 /c. A general discussion of ““derivative
1
structuresÏÏ in terms of space group hierarchies has been given by
M. J. Buerger, J. Chem. Phys., 1947, 15, 1.
Another virtue of the NMR method is its usefulness in the
study of molecular rate processes over extremely wide
dynamic ranges. The pretransition region in both the mono-
clinic phase on cooling and in the triclinic phase on heating
extends over a very wide temperature interval, over which
there is a monotonic increase in the rate of the molecular
reorientation, from about 103 s~1 at 180 K to 1013 s~1 at
400 K.
Finally, we mention the ability of the single crystal deute-
rium NMR method to characterize the dynamics of the
methyl group. For TCTMB, above 15 K, the dominating
process is the thermally activated reorientation, which we
10 J. Hirschinger and A. D. English, J. Magn. Reson., 1989, 85, 542.
11 D. Reichert and H. Schneider, Z. Phys. Chem., 1995, 190, 63.
12 C. Schmidt, B. Blumich and H. W. Spiess, J. Magn. Reson., 1988,
79, 269.
13 A. Heuer, J. Magn. Reson., 1990, 89, 287.
14 W. Schajor, PhD Thesis, University of Heidelberg, 1983.
15 B. Tesche, H. Zimmermann, R. Poupko and U. Haeberlen, J.
Magn. Reson. A, 1993, 104, 68.
16 K. Schmidt-Rohr and H. W. Spiess, Multidimensional Solid-State
NMR and Polymers, Academic Press, London, 1994, pp. 444È
448.
17 D. A. Torchia and A. Szabo, J. Magn. Reson., 1982, 49, 107.
18 A. Detken, P. Focke, H. Zimmermann, U. Haeberlen, Z. Olejnic-
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19 M. Prager and A. Heidemann, Chem. Rev., 1997, 97, 2933.
studied by T relaxation. Below 15 K, this incoherent
1
Phys. Chem. Chem. Phys., 2001, 3, 1891È1903
1903