Low frequency internal modes of 1,2,4,5-tetramethylbenzene, tetramethylpyrazine and tetramethyl-1,4-benzoquinone INS, Raman, infrared and theoretical DFT studies.

Abstract

The results of inelastic neutron scattering (INS), Raman and infrared (IR) studies on 1,2,4,5-tetramethylbenzene (durene), tetramethylpyrazine (TMP) and tetramethyl-1,4-benzoquinone (TMBQ) in the solid state are reported. The observed frequencies are analyzed on the basis of DFT calculations. The low frequency region, below 400 cm(-1), related to the torsional and bending out-of-plane vibrations of the CH(3) groups, is of particular interest. The detailed analysis is possible due to the simulation of the INS spectra by using the auntie-CLIMAX program. It is shown that the observed low frequency INS bands are dramatically shifted, compared to the calculated ones, towards higher frequencies. Although one cannot exclude deficiencies of theoretical methods as applied to low frequency modes, it seems more probable the interpretation based on an existence of non-conventional CH(...)pi, CH(...)N, CH(...)O hydrogen bonds formed by the methyl groups in crystalline phases.

Full text

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Spectrochimica Acta Part A 63 (2006) 766–773
Low frequency internal modes of 1,2,4,5-tetramethylbenzene,
tetramethylpyrazine and tetramethyl-1,4-benzoquinone
INS, Raman, infrared and theoretical DFT studies
A. Pawlukoj´ ca,d, I. Natkanieca,e, G. Batorb, L. Sobczykb,∗,
E. Grechc, J. Nowicka-Scheibec
aJoint Institute for Nuclear Research, 141980 Dubna, Russia
bFaculty of Chemistry, University of Wrocław, Joliot-Curie 14, 50-383 Wrocław, Poland
cDepartment of Inorganic and Analytical Chemistry, Szczecin University of Technology, Piastow 12, 71-065 Szczecin, Poland
dInstitute of Nuclear Chemistry and Technology, Dorodna 16, 03-195 Warsaw, Poland
eH. Niewodnicza´ nski Institute of Nuclear Physics, Radzikowskiego 152, 31-342 Krak´ ow, Poland
Received 10 May 2005; received in revised form 10 June 2005; accepted 13 June 2005
Abstract
The results of inelastic neutron scattering (INS), Raman and infrared (IR) studies on 1,2,4,5-tetramethylbenzene (durene), tetram-
ethylpyrazine (TMP) and tetramethyl-1,4-benzoquinone (TMBQ) in the solid state are reported. The observed frequencies are analyzed
on the basis of DFT calculations. The low frequency region, below 400cm−1, related to the torsional and bending out-of-plane vibrations of
theCH3groups,isofparticularinterest.ThedetailedanalysisispossibleduetothesimulationoftheINSspectrabyusingtheauntie-CLIMAX
program. It is shown that the observed low frequency INS bands are dramatically shifted, compared to the calculated ones, towards higher
frequencies. Although one cannot exclude deficiencies of theoretical methods as applied to low frequency modes, it seems more probable
the interpretation based on an existence of non-conventional C H...?, C H...N, C H...O hydrogen bonds formed by the methyl groups in
crystalline phases.
© 2005 Elsevier B.V. All rights reserved.
Keywords: INS spectroscopy; Torsional modes; Tetramethyl derivatives
1. Introduction
As follows from the critical reviews, devoted to the appli-
cations of the INS technique in the molecular spectroscopy
[1,2], the region of low frequencies, corresponding to the
deformation modes with participation of the H-atoms, seems
to be of particular interest. This is due to the large incoherent
scattering cross-section of hydrogen and the high amplitudes
of these vibrations. The methyl derivatives became the sub-
ject of our interest, since they are characterized by the high
intensities of the CH3torsional and C CH3wagging modes.
The detailed studies on durene [3,4] seem to be a very good
∗Corresponding author. Tel.: +48 71 375 7237; fax: +48 71 328 2348.
E-mail address: sobczyk@wchuwr.chem.uni.wroc.pl (L. Sobczyk).
example, which has shown that the INS spectra can be useful
in the analysis of the internal and external molecular interac-
tions.Thesearchesforthemostusefulmodels,describingthe
behavior of the modes in condensed matter, appeared most
important. However, in our opinion, these models are not
sufficiently precise to predict the INS spectra in the low fre-
quencyregion.Ontheotherhand,asfollowsfromthereviews
[5,6],thetorsionalpotentialisrelatedtotherotationalbarrier
which rules the tunnel splitting.
In our strategy, accepted in this paper, we have chosen for
comparisonthreedynamicallysimilarmolecules(ofthesame
D2hsymmetry) containing four CH3groups in the phenyl
ring.Themoleculesarecharacterizedbydifferenteitherintra
or intermolecular interactions in the crystalline lattice. The
packing of the molecules is very well known for 1,2,4,5-
1386-1425/$ – see front matter © 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.saa.2005.06.030

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tetramethylbenzene(durene)[4],tetramethylpyrazine(TMP)
[7,8] and tetramethyl-1,4-benzoquinone (TMBQ) [9]. In
analysis of the solid state of durene, one can distinguish the
interaction between methyl groups and ?-electrons of the
phenyl rings (non-conventional C H–? hydrogen bonds),
while in the cases of TMP and TMBQ, there are inter-
actions via C H...O and C H...N hydrogen bonds. One
should stress here that these interactions are considered as
blue-shifting hydrogen bonds. In contrast to conventional
hydrogen bonds, the C H...Y bridges are characterized by
an increase of the stretching ν(C H) frequency. Although
one cannot exclude other lattice effect upon the dynamics
of CH3 groups, it seems that the direct contacts between
the C H bonds and the proton accepting centers are the
main factors affecting this dynamics. It is now commonly
accepted approach based on theoretical and experimental
arguments, to treat such contacts as unconventional hydro-
gen bonds. There is a rich literature devoted to various
aspects of C H...Y interactions, as follows from reviews
[10–12].
Inthispaper,wewilltrytoshowtheeffectoftheunconven-
tionalhydrogenbondsonthefrequenciesoftheCH3torsional
and C CH3wagging modes. The values of the frequencies
obtained experimentally for the crystalline state will be com-
pared with those modeled by using the DFT calculations.
This comparison yields sufficiently good data with respect to
the structure optimization and dynamics [13].
One should emphasize that the INS technique yields
the best information enabling the correct assignment of the
observedINSpeakstocorrespondingmodesrecognizedfrom
the DFT calculations. Our approach, presented in this paper,
we treat as a first step in recognition of the unconventional
hydrogen bonds by analyzing the dynamics of CH3groups
in a given environment. For more complete recognition, we
decided to compare the INS results with those based on
Raman and infrared (IR) spectra.
2. Experimental and calculations
The compounds of 98% purity from Aldrich were used
without additional treatments.
NeutronscatteringdatawerecollectedatthepulsedIBR-2
reactorinDubnausingtheinvertedtime-of-flightspectrome-
ter NERA-PR [14] at 20K. The spectra were converted from
neutron per channel to the S(Q,ω) function density of states.
For energies between 5 and 100meV, the relative INS reso-
lution was estimated to be ca. 3%.
The IR spectra were recorded at room temperature in the
KBr discs or in Nujol as well as in Fluorolube (low frequen-
cies)suspensionsusingeitherKBrorCsIwindowsonaFT-IR
Bruker IFS 113v spectrometer with a resolution of 2cm−1.
The Raman spectra of powder samples were recorded on a
Nicolet Magna 860FT Raman Spectrometer. Nd:YAG laser
was the exciting source, with a power of ca. 200mW. The
back scattering geometry was applied. The resolution was
set up for 2cm−1. Five hundred and twelve scans were mea-
sured.
The structure optimization and frequencies as well as IR
intensitiesandRamanactivitiesofthemoleculesstudiedwere
calculated by using the GAUSSIAN 98 program [15] on the
B3LYP level with 6–31 G(d,p) basis set.
Thecorrespondingmodesweredefinedbymeansofinter-
nalcoordinatesaccordingtoPulayetal.[16].Massweighted
normal vibrational coordinates were used to calculate the
INS spectral profiles by the auntie-CLIMAX program [17]
adaptedwithauthorspermissiontoparametersoftheNERA-
PR spectrometer.
3. Results and discussion
Calculated and experimental INS, IR and Raman fre-
quencies for three investigated compounds are compared in
Tables 1–3. From the collected data, it clearly follows that in
the Raman and IR spectra, only few modes are recorded.
Due to either selection rules or extremely low intensities,
some of the modes are not active both in Raman and IR spec-
tra. In contrast, practically all modes below 1000cm−1are
well reflected in the INS spectra. Even more, modes in the
region of the lowest frequencies are just highly intense in
these spectra. This confirms a general principle character-
izing advantages of this technique. Some minor differences
between the INS and IR or Raman frequencies observed for
TMPandTMBQmaybeduetoseveralreasons.Oneofthem
isthelimitedresolutionoftheINSspectrometers(inourcase
3%). The other important factor consists in that the IR and
Raman spectra were measured at room temperature, whereas
the INS one at low temperatures. The assignment of particu-
lar frequencies to given modes was based on the observation
of atomic motions owing to the GAUSSIAN program [15]
and the % PED calculations [18]. In tables only, these con-
tributions are indicated which dominate in a given mode. In
calculations, none of the harmonic frequency scaling factors
was introduced. As it has been shown [19], none of such fac-
tors reflect sufficiently well the spectral pattern in the low
frequency region in the solid state. As it can be seen from the
results collected in this paper, the modes with the lowest fre-
quencies, particularly with participation of the CH3groups’
rotation, show a particular behavior.
We have checked the influence of the basis set on the cal-
culated frequencies, especially in the low frequency region.
Application of the larger basis set with inclusion of diffusion
function,B3LYP/6-31++G**leadsinthecasesofdureneand
TMP to very similar results. The differences do not exceed a
few cm−1for the analyzed ν1–ν7modes, whereas the higher
frequencies are identical. Moreover, in the case of TMBQ,
the extended basis set leads to even lower values in the low
frequencyregion(thedifferencereaching20cm−1),sothatto
larger discrepancy between the calculated (for the gas phase)
and experimental (in the solid state) INS modes.

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A. Pawlukoj´ c et al. / Spectrochimica Acta Part A 63 (2006) 766–773
Table 1
Calculated and experimental frequencies for 1,2,4,5-tetramethylbenzene
(durene)
Approximate
assignments
Calculated
B3LYP/6-31G**
Experimental
INSIRRaman
ν1, ring torsion
ν2, CH3 tors.
ν3, CH3 tors.
ν4, CH3 tors.
ν5, CH3 tors.
ν6, ring torsion
ν7, ring torsion
C CH3 bend.
C CH3 bend.
C CH3 bend.
C CH3 wagg.
Ring def.
C CH3 wagg.
Ring def.
C CH3 bend.
C CH3 wagg.
Ring def.
C CH3 wagg.
C CH3 str.
C CH3 str.
C Hwagg.
C Hwagg.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
C CH3 str.
C CH3 str.
C Hbend.
C Cstr.
C Hbend.
C Cstr.
CH3 bend. sym.
CH3 bend. sym.
CH3 bend. sym.
CH3 bend. sym.
C Cstr.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
C Cstr.
C Cstr.
C Cstr.
114
136
138
140
162
188
267
288
296
307
349
438
463
514
529
595
670
724
754
820
881
899
1004
1017
1024
1044
1051
1053
1071
1077
1093
1215
1230
1300
1313
1341
1414
1422
1433
1435
1437
1491
1491
1499
1505
1506
1506
1511
1517
1549
1615
1676
115
187
197
162
169
190
283
288
296
300
359
441
459
515
530
597
679
727
753
820
885
899
1004
1017
1024
1044
1051
1053
1071
1077
1094
n.a. n.a.
–
–
–
–
191
273
–
294
–
356
434
447
509
–
n.a. n.a.
–
–
742
–
866
–
999
–
1023
–
–
–
–
n.a.
–
n.a.
–
–
1268
1381
1394?
n.a.
1445
1375
n.a.
–
1455
–
1460
–
–
–
–
1502
–
–
–
1567
1622
The DFT optimized structures of investigated molecules
are consistent with those determined by the X-ray diffraction
studies. As shown in Tables 4–6, the differences of minor
importance do not exceed generally accepted correctness if
one takes into account that the calculations are related to
Table 2
Calculated and experimental frequencies for tetramethylpyrazine
Approximate
assignments
Calculated
B3LYP/6-31G**
Experimental
INSIRR
ν1, ring torsion
ν2, CH3 tors.
ν3, CH3 tors.
ν4, CH3 tors.
ν5, CH3 tors.
ν6, ring torsion
ν7, ring torsion
C CH3 bend.
C CH3 bend.
C CH3 bend.
C CH3 wagg.
C CH3 wagg.
Ring def.
C CH3 bend.
Ring def.
C CH3 wagg.
C CH3 str.
C Nstr.
91130
171
171
190
190
211
280
300
313
313
382
463
491
536
543
616
688
736
n.an.a
–
n.a
120
122
140
156
196
274
282
303
303
381
476
484
531
537
617
680
727
n.a
–
–
198
–
273
307
307
379
455
478
528
556
n.a.
678
n.a.
712
722
C CH3 wagg.
C CH3 str.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
CH3 rock.
C CH3 str.
775
820
991
1002
1013
1028
1051
1069
1070
1080
1137
775
824
754
800
–
–
988
1007 1005
–
–
1045
n.a.
–
1068
1144
n.a.
1181
1200
1222
Ring def.
C Nstr.
C CH3 str.
C H3 bend. sym., C Nstr.
C H3 bend. sym., C Cstr.
C H3 bend. sym.
C H3 bend. sym.
C Cstr., C H3 bend. sym.
C Nstr., C H3 bend. sym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym., C Nstr.
C Cstr.
C Nstr.
1234
1263
1317
1399
1416
1416
1429
1448
1451
1481
1492
1493
1494
1499
1507
1508
1512
1603
1609
1196
1255
1332
1284
–
1358
1372
1382
1389
14051378
–
–
n.a.
–
n.a.
1410
1440
–
1459
–
1544
free molecules. Very good agreement between the experi-
mental and DFT calculated structural parameters for durene
was already reported [4].
In the present paper, we focus our attention on the anal-
ysis of seven modes of the lowest frequencies, which are
visualised in Fig. 1.
InthecaseofTMP,themodesν2,ν3,ν4andν5correspond
tothealmostneattorsionalvibrationsofCH3groups(rotation

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A. Pawlukoj´ c et al. / Spectrochimica Acta Part A 63 (2006) 766–773
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Table 3
Calculated and experimental frequencies for tetramethyl-1,4-benzoquinone
Approximate
assignments
Calculated
B3LYP/6-31G**
Experiment
INS
IR Raman
ν1, ring torsion
ν2, CH3 tors.
ν3, CH3 tors.
ν6, ring torsion
ν4, CH3 tors.
ν7, ring torsion
ν5, CH3 tors.
C CH3 wagg.
C CH3 bend.
C CH3 bend.
C CH3 bend.
C CH3 wagg.
C CH3 bend.
Ring def.
C CH3 wagg.
C Obend.
Ring def.
C CH3 str.
C CH3 wagg.
Ring def.
C Obend., CH3 rock.
C Owagg.
C Owagg.
CH3 rock., C Cstr.
C CH3 str.
C CH3 str., C Cstr.
CH3 rock., C Cstr.
CH3 rock.
CH3 rock.
CH3 rock., C Cstr.
CH3 rock.
CH3 rock.
CH3 rock., C Obend.
CH3 rock., C CH3 str.
C CH3 str.
C CH3 str.
C CH3 str.
C CH3 str.
CH3 bend. sym.
CH3 bend. sym.
CH3 bend. sym.
CH3 bend. sym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
CH3 bend. asym.
C Cstr.
C Ostr.
C Ostr.
C Cstr.
65
75
85
120
145
172
134
189
196
163
212
304
306
315
342
367
427
439
441
444
545
550
630
688
718
795
846
893
998
998
–
n.a.n.a.
–
n.a.
–
–
108
109
114
117
205
303
304
314
322
366
420
435
440
444
546
552
621
686
717
785
840
893
1000
1000
1021
1040
1049
1066
1069
1116
1146
1155
1277
1314
1347
1414
1417
1420
1421
1490
1491
1492
1496
1504
1504
1519
1520
1672
1708
1725
1726
n.a.
–
–
298
–
–
–
355
419
–
429
439
544
n.a. n.a.
621
–
697
793
816
865
971
971
986
–
1028
n.a.n.a.
–
–
–
–
1122
1259
–
–
1339
1376
1375
–
–
–
–
n.a.
1440
–
n.a.
1458
–
1631
1637
1649
around the C3axis), while modes ν1, ν6and ν7correspond
to the out-of-plane C CH3 bending vibrations with some
contributions of the ring deformation. In the case of TMBQ,
the ranging of these modes, as can be seen in tables, is a little
different.
Table 4
Structural parameters of 1,2,4,5-tetramethylbenzene (durene)
Calculated B3LYP/6-31G**
Coordinates Experiment [4] 1.5K
C C(H)
C C
C C(H3)
C(H) C C
C C(H) C
C C C(H3)
C(H) C CH3
1.398
1.408
1.510
118.6
122.9
121.1
120.3
1.389, 1.403
1.410
1.506, 1.512
118.0, 119.2
122.7
120.2, 123.2
118.8, 116.7
Bond length (˚A), angles (◦).
Table 5
Structural parameters of tetramethylpyrazine (TMP)
Calculated B3LYP/6-31G**
Coordinates
Experimenta[7] (K)
100300
C C
C N
C CH3
C N C
C C N
N C CH3
C C CH3
1.409
1.340
1.507
118.6
120.7
117.2
122.1
1.409
1.327
1.507
118.0
120.7
117.2
122.0
1.378
1.350
1.505
118.3
120.9
117.5
121.4
Bond length (˚A), angles (◦).
aCorrelated for librational effects.
For all seven modes, as the data in Tables 1–3 show, more
or less dramatic difference between calculated and ascribed
to them INS frequencies appear. The assignment seems to be
unequivocalasithasbeendonebasedonsimulatedINSspec-
tra with clear arrangement of the peak intensities resulting
from the amplitudes of the H-atom movements. In Figs. 2–4,
thecomparisonsofexperimentalINSspectrawiththosesim-
ulated by CLIMAX program together with Raman and IR
spectra are presented.
The agreement for INS spectra seems to be excellent if
one omits the region related to the lattice phonons, which are
not taken into account in calculations. In the experimental
regime applied for tetramethyl derivatives, the region below
400cm−1isdistinguishedwherethepeaksarehighlyintense
and well shaped.
We would like to emphasize here once more the advan-
tages of the INS technique as applied to studies on the low
frequency modes with participation of H-atoms. The modes
Table 6
Structural parameters of 2,3,5,6-tetramethyl-1,4-benzoquinone (TMBQ)
Calculated B3LYP/6-31G**
Coordinates
Experiment [9] 300Ka
C O
C C
C C
C CH3
O C C
C C C
C C C
C C CH3
C C CH3
1.216
1.321
1.478
1.503
120.6
119.8
120.2
116.7
123.0
1.232
1.341
1.492
1.514
120.2
119.7
120.2
116.9
122.9
Bond length (˚A), angles (◦).
aAveraged in accordance with molecular symmetry mmm.

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Fig. 1. Visualisation of seven modes of the lowest energies corresponding to the neat CH3torsional vibrations and combination of C CH3wagging and ring
torsional vibrations.
in the region 100–200cm−1are most intense in the INS
spectra. Particularly, expressive seems to be the comparison
in Figs. 2–4 with Raman and IR spectra which look indi-
gent?
Havingnodoubtswithrespecttotheassignmentofexper-
imental INS peaks, the question arises about the sources of
such dramatic differences between experimental and calcu-
lated frequencies. Certainly, the reason for that can consist
in deficiencies of the theoretical methods. Expressing some
reservation with respect to the methods applied to the tor-
sional modes in a detailed analysis, Scott and Radom [20]
emphasized simultaneously that among various theoretical
methods that used in this paper can be included to the best
ones.
Simultaneously, they showed that for the low frequency
modes, the scaling factor is very close to unity. The reason

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771
Fig. 2. Calculated (a) and experimental (b) INS spectra of durene in the fre-
quency range below 600cm−1compared with Raman (c) and IR (d) spectra.
of imperfectness of the theoretical simulation methods, as
appliedtothelowfrequencymodes,canresultfromtheirhigh
anharmonicity. However, it is well known that in such cases,
the experimental frequencies are lower than the calculated
ones and the scaling factor is then much lower than unity.
Therefore, it seems that, although one cannot exclude some
errorinDFTcalculationsbyusingtheGAUSSIANprogram,
this cannot be the reason of such tremendous discrepancies.
Wesuggest—andthiscanbeconsideredasamainpointofthe
present paper—the molecular interactions in the crystalline
lattice are the main reason for them.
OneshouldstressherethatdetailedINSexperimentaland
ab initio HF and DFT theoretical studies on normal alkanes
showed very good coincidence of calculated and experimen-
talCH3torsionalfrequency[21].Inthiscase,theCH3groups
arenotengagedininteractionsotherthanofthevanderWaals
type.
AsithasbeenmentionedinSection1,theCH3groupscan
form the non-conventional hydrogen bonds of the C H...?,
C H...N and C H...O types. It is commonly known [22]
that in conventional hydrogen bonds with participation of,
e.g. O H groups, a large blue-shift of the bending δ(OH)
vibrations takes place. Particularly, the out-of-plane γ(OH)
vibrations are shifted spectacularly toward higher frequen-
Fig. 3. Calculated (a) and experimental (b) INS spectra of TMP in the fre-
quency range below 600cm−1compared with Raman (c) and IR (d) spectra.
cies.Inouropinion,thebehaviorofthetorsionalandbending
CH3vibrations in the crystalline lattice is strictly related to
such interactions. Because the force constants of the CH3
torsionalvibrationsaremuchsmallerascomparedwithanal-
ogous γ vibrations in conventional hydrogen bonds, very
strong influence on these frequencies can evoke even much
weaker interactions such like in non-conventional hydrogen
bondswithC Hgroups.Thedetailedquantitativeanalysisat
the present stage of studies is not possible. Four CH3groups
donotpossessthesameenvironmentandtheresultingmodes
haveacomplexnatureasallgroupsareengagedinallmodes.
Comparing three investigated compounds, we can state
that the smallest differences between calculated and experi-
mental frequencies are observed for durene and the largest
ones for TMBQ. From the point of view of the non-
conventionalhydrogenbonds,itseemsreasonable.Certainly,
theCH–?contactsareweakest.Itisdifficult,however,topre-
dict how in concrete conditions, the C H...N and C H...O
bridges will behave. In the case of TMBQ, each of the car-
bonyl group oxygen atoms can form two bridges and the
network of bridges is broader than that in TMP so that more
C Hbondscanbeengaged,asitcanbeseeninthecrystalline
lattice.

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A. Pawlukoj´ c et al. / Spectrochimica Acta Part A 63 (2006) 766–773
Fig. 4. Calculated (a) and experimental (b) INS spectra of TMBQ in the fre-
quency range below 600cm−1compared with Raman (c) and IR (d) spectra.
In corroboration of the concept presented in this paper,
the non-published results, collected for complexes of hex-
amethylbenzene [23], can be used. In this case, one observes
also a marked discrepancy between calculated and experi-
mental CH3torsional frequencies. In the case of the complex
withtetracyanoethylene,wheretheCH3groupspossessmuch
more freedom, the experimental frequencies (in the solid
state) are very close to those calculated for the gas phase.
However, one cannot exclude that the charge transfer causes
some decrease of the rotational barrier too.
4. Conclusions
The analysis of modes related to torsional vibra-
tions of the CH3 groups in tetramethylpyrazine, 1,2,4,5-
tetramethylbenzene (durene) and tetramethyl-p-benzoqui-
nonepossessingthesamesymmetry,allowsustodistinguish,
among seven low frequency modes, four ones, into which
neat CH3torsional vibrations contribute. These modes are
practically not visible in IR and Raman spectra due to either
selection rules or extreme low intensities. In contrast to IR
and Raman spectra, these modes are characterized by high
intensitiesinthespectraofinelasticneutronscattering(INS).
The compounds studied in this paper are very good example
of advantages of this technique in studies of low frequency
modes with participation of hydrogen atoms (large cross-
section of nuclei and large amplitudes of vibrations).
The experimental INS spectra are very well reproduced
by using the auntie-CLIMAX program based on calculated
scaledfrequenciesbymeansoftheGAUSSIANprogramand
taking into account the resolution of the spectrometer. The
experimental frequencies (positions of peaks) appeared, as a
rule, higher than the calculated ones that can be interpreted
either in terms of the limitations of standard DFT calcu-
lations or by assuming interactions of the CH3 groups in
the crystalline lattice. These interactions can be treated in
termsoftheunconventionalhydrogenbondsoftheC H...N,
C H...O and C H...? type. The influence of the unconven-
tionalhydrogenbondsonthetorsionalCH3vibrationswould
beanalogoustotheconventionalhydrogenbonds,whichlead
to blue-shifting of the bending δ and γ vibrations. The anal-
ysis of the packing show that the strongest interactions take
place in TMBQ and the weakest ones in durene that could be
expectedfromthecomparisonofexperimentalandcalculated
frequencies for the compounds studied.
Acknowledgments
A partial financial support by the Polish Ministry of
Science and Informatics (Grant 4 T09A 05125) and the
Plenipotentiary Representative of Polish Republic in JINR
is acknowledged. Thanks are to Dr. B.Czarnik-Matusewicz
for fruitful discussion.
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