558
J. Phys. Chem. 1987, 91, 558-563
Polarized Raman Spectra of the Anthracene-Trlnitrobenzene Complex in the Lattice Vibrational Region Kikujiro Ishii,* Ken-ichi Sato, and Hideyuki Nakayama Department of Chemistry, Faculty of Science, Gakushuin University, Mejiro. Toshimaku, Tokyo 171, Japan (Received: June 17, 1986)
Polarized Raman spectra of the single crystals of the anthracene-l,3,5-trinitrobenzene complex and the correspondingcomplex with deuterium-substitutedanthracene were measured in the lattice vibrational region and between 88 K and rwm temperature. Eleven lattice bands were observed among the 12 bands expected by the symmetry consideration,and each band was assigned to the librational or translational lattice vibrations. This is the first report that gives substantial assignments to the translational lattice vibrations in molecular complexes. Brief discussion is given on the problem of the coupling between the vibrations on the donor and acceptor sublattices.
Introduction Raman spectra of charge-transfer (CT) complex crystals in the lattice vibrational region have recently drawn the attention of many workers. Some of those works have been carried out in connection with the phase transitions found for some tetracyanobenzene complexes.’ However, as will be described below, lattice vibrations in C T complexes arouse one’s more general interest, since C T complexes involve characteristic intermolecular interactions. We start from the experimental fact that the lattice energies of weak C T complexes are almost the same as those of the component substances.* This fact suggests that the intermolecular potentials and thus the force constants of the lattice vibrations in weak C T complexes are almost the same as the single-component molecular crystals. However, the ccntribution of the CT interaction to the force constant of each lattice vibration may depend on how much that mode modulates the C T interaction. There is a possibility that some vibrational modes would particularly be affected by the C T interaction and have large vibrational frequencies. Another phenomenon expected is the intensity enhancement of some Raman bands by the C T interaction. Raman intensity depends on the derivative of the polarizability along the vibrational ~oordinate.~It is naturally understood that strong Raman bands arising from the librational lattice modes are seen for the crystals of aromatic hydrocarbons. On the other hand, the intensities of translational Raman bands of molecular crystals are small, since their intensities are given by the indirect modulation of the crystal polarizability through the modulation of the local field.4 In C T complexes, however, the relative displacement of the donor and acceptor molecules modifies the C T interaction, which directly causes the change in the electronic polarizability. Translational modes in C T complexes thus potentially give enhanced Raman bands as compared with those in usual molecular crystals. Chen and Prasad5 discussed the lattice vibration of molecular complexes within the framework of the giant molecule model and the sublattice model. Beckman et aL6 observed 12 bands in the low-frequency Raman spectra of the anthracene-1,3,5-trinitrobenzene (hereafter A-TNB) complex. They suggested that five of those might arise from the intracharge-transfer modes proposed by Chen and Prasad5 on the basis that the temperature dependences of their intensities were different from those of other bands. The idea of the intracharge-transfer modes has a close relation (1) See for instance: (a) Macfarlane, R. M.; Ushioda, S. J. Chem. Phys. 1977, 6 7 , 3214. (b) Umemura, J.; Haley, L. V.; Cameron, D. G.; Murphy, W. F.; Ingold, C. F.; Williams, D. F. Spectrocfiim. Acta, Part A 1981, 37A,
835. (2) Suzuki, K.; Seki, S.Bull. Chem. SOC.Jpn. 1955, 28, 417. Metzger, R. M.; Arafat, E. S. J. Chem. Phys. 1983, 78, 2696. (3) See, for instance: Turrell,G. Infrared and Raman Spectra of Crystals; Academic: London, 1972. (4) Luty, T.;Mierzejewski, A.; Munn, R. W. Chem. Phys. 1978, 29, 353. (5) Chen, F. P.; Prasad, P. N . J. Cfiem. Phys. 1977, 6 6 , 4341. (6) Beckman, R. L.; Hayes, J. M.; Small, G. J. Chem. Phys. 1977,21, 135.
to our interest in the Raman spectra of molecular complexes described above. The models considered by Chen and Prasad will be discussed later. A-TNB is one of the typical weak C T complexes.’ The crystal consists of the one-dimensional arrays of anthracene and TNB molecules.8 Factor-group analysis3 indicates that 12 lattice vibrations are Raman active, among which three translational vibrations of TNB are included. If the 12 Raman bands observed for A-TNB previously6 were the bands expected by the factorgroup analysis, there is a possibility that the intensities of the three translational modes are enhanced by the presence of the C T interaction. However, the previously reported Raman spectra are not separated into the components of the different polarizations and no concrete assignment was given to the observed bands. In this paper, we report the polarized Raman spectra of the single crystals of A-hlo-TNB and A-dlo-TNB. Assignments of the bands in the lattice vibrational region are empirically given on the bases of the calculated moments of inertia and of the isotope effects on the band frequencies. Some bands were found to show anomalous isotope effects and are suggested to arise from the expected translational modes. Discussion is given on the difference between the spectra reported here and those by Beckman et aL6 The gradual phase transition in the region 80-159 K, which was also reported by them, was not confirmed in our work.
Experimental Section Anthracene-hlo and TNB were purchased from Tokyo Chemical Industry Co. Anthracene-hlo was purified successively by recrystallization from benzene in the presence of maleic anhydride, azeotropic distillation with ethylene glycol, and zone-refining. TNB was purified by recrystallization from ethanol and then by vacuum sublimation. Anthracene-dlo was purchased from Aldrich Chemical Co. and purified by zone-refining. Three methods of single-crystal preparation were tried for the anthracene-hlo complex. Needle-like crystals obtained by recrystallization from chloroform were usually thin and were not suitable for the polarization measurement along the crystal axes other than the needle axis. The crystals obtained by the Bridgman method seemed to contain many imperfections. Finally we got some brilliant orange single crystals of about 2 X 2 X 3 mm3 by the plate-sublimation method.g The crystal axes were identified by X-ray diffraction with the oscillating-crystal method. Single crystals of the anthracene-dlo complex were obtained by recrystallization from chloroform. We tried plate sublimation also but could not continue it until good crystals were obtained because of limitation of the material. The crystal used for the measurements were clear needle crystals with hexangular cross (7) See, for instance: Foster, R. Organic Charge-Transfer Complexes; Academic: London, 1969. (8) Brown, D. S.;Wallwork, S. C.; Wilson, A. Acta Crystallogr. 1964, 17, 168
(9) Karl, N . In Crystal Growth, Properties, and Applications; Freyhardt, H. C., Ed.; Springer-Verlag: Berlin, 1980; Vol. 4, p 1 .
0022-3654/87/2091-0558$01.50/00 1987 American Chemical Society
Raman Spectra of Anthracene-Trinitrobenzene
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987 559
TABLE I: Results of the Factor-Group Analysis: Number of Lattice Vibrational Modes
A, anthracene sublattice acoustic optical, trans optical, rot T N B sublattice acoustic optical, trans optical, rot A-TNB complex acoustic optical, trans optical, rot
B,
A,
B,
0
0
0
0 3
1 2
2 1
0
0
3
0
element of Raman tensor
1 1
0 2 2
0
0
1 4
2 5
a’a’, bb cc, a’c
a’b bc
1
2
0
0
1
2
1 3 1
2 3 2
a Figure 1. Illustration of the crystal structure of A-TNB (ref 8). There is a similar column at the C face center.
incident and scatterid light by the sapphire windows of the cryostat.
Results and Discussion i. Factor-Group Analysis and Moment of Inertia. Before presenting the results, we summarize some data that help us in discussing them. The A-TNB crystal is monoclinic with the space group C2/c (Z = 4).* A part of the unit cell is shown in Figure 1. There is a similar column of molecules at the C face center related to the column at the origin of the unit cell by the glide plane. Anthracene molecules occupy the sites with C, symmetry, and T N B molecules reside on the twofold axes. The results of the factor-group analysis3are shown in Table I, where the number of vibrational modes is indicated for the primitive unit cell with Z = 2. The axis a’used for indicating the Raman tensor elements is the one that is perpendicular to the ’ plane. As shown in the table, three translational modes and h e rotational modes are Raman active in the complex. Within the zeroth approximation that the anthracene and TNB sublattices are assumed independent of each other, the Raman-active translational modes are localized on TNB. The moments of inertia of the molecules were calculated as shown in Table 11. The principal axes of the moment of inertia of each molecule almost coincide with the symmetry axes of the free molecules (see the structures of Table 11), although their symmetries are lowered to those of the crystal sites. The axes of the librations in the crystal may by no means coincide with the axes of the moment of inertia. However, these data are helpful in roughly estimating the relative ratio of the frequencies of the librational modes. We therefore will refer to the librational modes by using the symmetry axes of the free molecules as the indices. When deuterium is substituted into anthracene, the librational bands of anthracene are expected to shift to the small-frequency sides. On the other hand, Raman bands of T N B would not be affected by this if the two sublattices were independent of each other. In thc last column of Table I1 are shown the relative shifts by the deuterium substitution expected in the harmonic approximation. Since vibrations of anthracene and T N B may mix together in reality, the vibrations assigned mainly to TNB may also be affected more or less by the deuterium substitution. Thus the deuterium shift of TNB bands provides the measure of the degree of mixing of the anthracene and T N B vibrations. ii. Spectra of the hlo Complex at Room Temperature. Spectra of A-hlo-TNB at room temperature around 297 K are shown in
TABLE I 1 Calculated Moment of Inertia and Expected Deuterium-Substitution Effect on the Assumptions of Independent Lattice and Harmonic Oscillation
n
I
0zN
rot axis anthracene-hlo anthracene-dlo anthracene-h anthracene-dlo anthracene-hlo anthracene& TNB TNB TNB
X X
Y
Y Z Z X
Y Z
I
moment of inertia, amu A2 240 280 1120 1230 1340 1480 860 1000 1860
(WD/WH)
-1
-8.3% -4.5% -4.9%
sections of 1-2 mmz. The needle axis was identified to be the c axis by X-ray diffraction. Another crystal axis used in the polarization measurement was identified to be the b axis by comparing the spectra with those of the anthracene-hlo complex. Measurements were carried out with an N E C GLG5700 25mW He-Ne laser and a JASCO CT-25ND monochromater. A conventional photon-counting system was used with a Hamamatsu R943-02 photomultiplier. Low-temperature measurements were carried out with an Oxford DN1704 cryostat in which the specimen was placed in the temperature-controlled dry nitrogen atmosphere and the temperature was measured with a calibrated alumekhromel thermocouple. In the polarization measurements, special care was devoted to preventing the depolarization of the TABLE 111: Raman Frequencies of the b
Complex at Room Temperature
obsd freq band 1 2 3 4
5 6 7 8’ 9 10 11 126
(a’a’)
31
(bb)
30
A”*
B.s (cc)
36
(a’c)
(bc)
(bar)
(16)
15 30
(28) 37 53
62
(64)
65
63 68
(70)
(96)
96
90 119 143
freq and symmetry 15 30 31 36 53 63 68 90 96 119 143
B, B, A, A,
B, A*
B, B, A, B, A,
A,, B, “Observed only at the lowest temperature in our experiment. bAssigned to a mode that involves mainly an intramolecular vibration of TNB.
Ishii et al.
560 The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
TABLE I V Raman Frequencies (em-') of the h l o and dlo Complexes at 88 K and the Relative Shift by Deuterium Substitution
band symmetry
final
hl0
4 0
complex 15.0
complex
re1 shift, % '
15.0
0
33.1 42.2 58.3 69.8 74.0 91.6 99.6 101.7 123.6 149.6
-6 -2 -2q -1., -2.6
32.2 35.2 42.9 59.9 70.7 76.0 91.9 98.1 106.9 131.4
149.1
assignt rot(T,Z) rot(A,Z) rot(A,Z) rot(T,X) rot(T,Y) rot(A,Y) rot(A,Y)
-O., +l.5
-4+ -5.9 +O.,
trans(T,Y) trans(T,X) rot(A,X) rot(A,X) a
'Assigned to a mode that involves mainly an intermolecular vibration of TNB. 0
80 160 Wave number /cm-'
Figure 2. Polarized Raman spectra of the hlo complex at room tem-
perature.
'E
i
\
c(a'a')b
88K
3
n 801
Bg
'
11
9
1
Ag
s c
.-fn
I
120
'9"
0
0,
I
.-
C
c(ba')b
C
m
5
401 r
a
1 I
0
40
I
I
1
80
120
160
Wave number /cm-'
Figure 3. Polarized Raman spectra of the hlo complex at 88 K.
Figure 2 for all the polarizations. Observed peak frequencies and their average are collected in Table 111 for each vibrational mode. Vibrational modes belonging to the A, and B, representations are considered to appear respectively in the top four spectra and the bottom two spectra in Figure 2. The orthonormality between the spectra belonging to the different irreducible representations seems almost good, thus the experimental setup is considered to have been appropriate for the polarization measurement. However, the small depolarization of the incident light seems to have occurred owing to the nonideality of the shape of the specimen. The strong 68-cm-' B, band in the (bc) spectrum is thus considered to have leaked into the (cc) spectrum, pulling the apparent peak of the 63-cm-I A, band to the high-frequency side. The frequency of the 30-cm-' band seen in the (ba') spectrum is almost the same as the 3 1-cm-' A band. Although one might consider that this 30-cm-' band hadappeared by the leakage of the 31-cm-l A, band into the (ba') spectrum, the temperature variations of the spectra which will be described later showed that these two bands arise from different modes. In the last column of Table 111, the irreducible representation of each band is given. iii. Spectra of the hlo Complex at 88 K and the Temperature Dependences of the Frequencies and Intensities. The temperature dependence of the spectra of the h I ocomplex was measured with the c(a'a')b:A, and c(ba')b:B, polarizations. The spectra at 88 K are shown in Figure 3. Thirteen bands were observed in the region below 200 cm-' and are numbered as shown in Figure 3 and Table IV. The temperature dependences of the band frequencies are illustrated in Figure 4. Each band shows almost a linear temperature dependence in the whole region of the measured temperature, which suggests that there is no phase transition in this region. For bands 1-1 1, the variations of the frequencies are larger
, 100 200 Temperature /
300
K Figure 4. Temperature dependences of the Raman band frequencies of the hlo complex; solid circles, A, modes; open squares, B, modes.
as the peak frequencies are larger. This is understandable if the thermal expansion of the crystal is almost isotropic and the potential curve of each lattice vibration is similarly affected by it. Thus bands 1-1 1 are attributed to the lattice vibrational modes. Bands 12 and 13 are, however, distinguished from other bands, since they show smaller temperature dependences than bands 9-1 1. Therefore, bands 12 and 13 are inferred to come from the intramolecular vibrations. It should be noted that the intramolecular vibrations of TNB are observed at 133 and 160 cm-' for the TNB crystal.1° They have been attributed respectively to an out-ofplane vibration of the NOz groups and to an in-plane CN deformation mode. The coupling of such low-frequency intramolecular vibrations with the lattice vibrations is considered to cause small but definite temperature dependences of the vibrational frequencies. A small leak of the A, spectrum is seen in the B, spectrum in Figure 3. Namely, the shoulder at the high-frequency side of band 2 in the B, spectrum seems to come from band 3 in the Ag spectrum. Band 11 in the ABspectrum also seems to leak at the corresponding position in the B, spectrum, but the assignment of this band in the B, spectrum is uncertain at this stage. Band 8 is very weak and was observed only at 88 K. We believe that this is a real signal since we observed the corresponding band in the spectrum of the dlo complex. The temperature dependences of the peak heights are shown in Figure 5 for some bands that showed conspicuous changes. These are normalized by the height of the 754-cm-I E" band of the TNB intramolecular vibration" which is Raman active both in the (a'a') and (ba') spectra of the crystal. Other bands that are not included in Figure 5 showed smaller changes in their peak (IO) Shurvell, H. F.; Norris, A. R.;Irish, D.E. Can. J , Chem. 1969,47, 2515.
Raman Spectra of Anthracene-Trinitrobenzene 1
6
100
Y
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987 561 6
1
Anthracene
x
200 300 Temperature/ K
Figure 5. Temperature dependences of peak heights of some Raman bands of the hlo complex. Peak heights were normalized by that of the
750-cm-l band of the TNB intramolecular vibration in each spectrum.
a'(cc)b
A
Ag
~
I 0
&
'
I
I
TNB
I
I
80 160 Wave number /cm-'
Figure 7. Raman spectra of anthracene, A-TNB, and TNB measured with compacted powder samples. X,Y,and Z indicate the assignments of the librational modes in the anthracene crystal (ref 11). 9
0
80
11
160
Wave number /cm-'
Figure 6. Polarized Raman spectra of the dlocomplex at 88 and 291 K. See the text as to the small arrow in the B, spectrum at 88 K.
heights. Although the data points in Figure 5 are scattered around the curves for the guide to the eye, the peak-height evolution of each band seems monotonous in the measured temperature region. The changes of the peak heights may attributed to the gradual changes of the molecular orientations in the crystal. iv. Spectra of the d l o Complex and Deuterium-Substitution Effects. The temperature dependence of the spectra of the d l o complex was measured with the a'(cc)b:A, and a'(bc)b:B, polarizations. The spectra at 88 and 291 K are shown in Figure 6. Note that the 291 K spectra are very similar to the roomtemperature spectra of the h l ocomplex with the corresponding polarizations (see Figure 2). By a survey of the frequencies of the bands and the comparison with those of the hlo complex, it was found that there are good correspondences between the spectra of the h l o and d l ocomplexes. The bands of the d l ocomplex were thus numbered similarly to the case of the hlo complex. Peak frequencies and the relative shifts by the deuterium substitution a t 88 K are collected in Table IV. A small band seen in the 88 K B, spectrum in Figure 6 around 120 cm-I (indicated by a small arrow) shows just the same temperature dependence and the same deuterium shift as band 11 seen in the A, spectrum (see also Figure 3 for the hlo complex). Therefore, we believe that these bands seen in the spectra with different polarizations arise from the identical mode. Its symmetry assignment is difficult. However, since the deuterium shift of this band is as large as band 10 (B,), this mode is inferred to be the A, counterpart of the factor-group-splitted pair of anthracene librations. Almost all the bands are affected by deuterium substitution. However, note that they seem to be classified into three groups
by the magnitude of the relative deuterium shifts, namely, group 1 with the shift as large as -5%, group 2 from -3 to -l%, and group 3 of about zero or positive. Magnitudes of these shifts reflect how much the anthracene vibrations contribute to each vibrational mode and help us to assign the Raman bands. v. Assignment of Each Band. As it has been described so far, 11 lattice vibrational bands were found in the frequency region below 140 cm-I. In assigning these bands to the substantial molecular motions, we first base our arguments on the assumption that the crystal field in the A-TNB complex is not so different from that in the single-component crystals of aromatic compounds. The results of the factor group analysis (Table I) are kept in mind during the following discussion. Calculation of the moment of inertia told us that the relative deuterium shifts of anthracene are large for the librations around the X axis and smaller for the ones around the Y and 2 axes (Table 11). From the factor group analysis, three pairs of anthracene librations are Raman active in the complex (Table I). Figure 7 shows the spectra of anthracene, A-TNB, and T N B measured with the compacted polycrystalline samples at 88 K. Three pairs of doublets are seen in the anthracene spectrum. They are obviously assigned to the factor-groupsplitted librations around the three principal axes of anthracene molecules." The spectrum of T N B is, on the other hand, very complicated. It is because the crystal structure of,TNB is a very complicated one with 16 molecules in the unit cell.'* The spectrum of the complex is explained by the superposition of its single-crystal spectra with all the polarizations. When these spectra are compared, it is noticed first that the strong band 7 (B,) of the complex may be attributed to one of the librations of anthracene around its Y axis. This assignment is reasonable since this mode apparently is accompanied with the largest change in the polarizability. In the vicinity of this band, there must be an A, band assigned to the same molecular libration. Band 6 (A,) is the most probable candidate for this, although its deuterium shift is a little smaller than band 7 . Band 4 (A,) has also a possibility, but the magnitude of the factor group splitting with band 7 seems too large in this case. Similarly band 9 (A,) is excluded. The deuterium shift of band 9, +1.5%, also excludes the possibility that it is a librational mode of anthracene. The librations of anthracene around the X and Z axes are expected respectively in the high-frequency region around 130 (1 1) Suzuki, M.; Yokoyama, T.; Ito, M. Spectrochim. Actu, Part A 1968, 24A, 1091. (12) Choi, C. S.;Abel, J. E.Acta Crystullogr., Sect. B: Srrucr. Crystallogr. Cryst. Chem. 1972, 828, 193.
562
The Journal of Physical Chemistry, Vol. 91, No. 3, 1987
cm-l and in the low-frequency region around 50 cm-l. They must show larger deuterium shifts. Bands 10 (B,) and 11 (A,) are therefore safely assigned to the factor-group pair of the modes mainly coming of the librations of anthracene around the X axis. Similarly band 3 (A,) is assigned to the libration around the Z axis. There must be the partner of this band in the B, spectrum, and it must show a large deuterium shift. Band 2 could be this, although it was not observed in the spectra of the d l o complex for which the B, spectrum was measured with the different polarization from the h l ocomplex. The fact that bands 2 and 3 similarly increase their intensity largely as the temperature is elevated (Figure 5) supports the above inference. For TNB, three rotational modes and three translational modes are expected to be Raman active (Table I). According to the calculation of the moment of inertia, the largest one is that around 2 axis of TNB. Therefore, it would be the libration of T N B around this axis, if a separated band is observed in the lowest frequency region. It is also known by checking the symmetry that this librational mode belongs to the B, representation. Thus band 1 (B,) is assigned to the libration of T N B around the 2 axis. Of the remaining two librations of TNB, one is expected to be observed in the A, spectra and the other in the B, spectra. The moments of inertia indicate that those librations would appear in the midregion of the lattice spectra and have similar frequencies. Then, the pair of bands 4 (A,) and 5 (B,) or the pair of band 8 (B,) and 9 (A,) can be the candidates for them. The comparison of the moments of inertia of T N B around its X and Y axes with that of anthracene around the Yaxis suggests that the T N B X and Y librations would be observed at the frequencies higher than the anthracene Y libration. Thus bands 8 and 9 might be attributed to the T N B X and Y librations, but there remains a question why band 8 is so weak if it was a librational mode. This discussion will be continued later. Three translational modes of TNB are Raman active. Among those, a B, mode involves the translational movement of T N B along the stacking axis (c axis) of the complex (a sandwich mode), and the other two modes are an A, and a B, mode in which TNB molecules move along the directions almost perpendicular to the stacking axis (sliding modes). N o datum has been reported so far on the frequency of such a translational vibration in C T complexes. We presume, however, that the two sliding modes have similar frequencies and the sandwich mode has a different, probably much larger frequency, because the interaction between the molecules is considered strong along the stacking axis. If this is the case, the sandwich mode may be found separately at a higher frequency, and two sliding modes may be found with frequencies similar to each other. Thus, the two sliding modes are assigned to the pair of bands 4 and 5 or the pair of bands 8 and 9. We now return to the data of the deuterium substitution effect (Table IV). The effects on bands 4 and 5 are respectively -2% and -2.7%, while those on bands 8 and 9 are respectively -0.3% and +le,%. It is inferred that the mixing of the TNB modes with the anthracene librational modes is larger for the librations than the translations. Thus, bands 4 and 5 are tentatively assigned to the T N B librations and bands 8 and 9 to the T N B translations. These assignments are reasonable from the viewpoint of the band intensities. The direction of each movement, X or Y, is determined by the irreducible representations of the observed band as shown in the last column in Table IV. The deuterium shifts of bands 4 and 5 are as large as those of bands 6 and 7 which are attributed to the anthracene librations. This would be understood if one notes that the TNB X and Y librations mix not only with the anthracene Y librations but also with its X librations which are expected to show large deuterium shifts. This is because the anthracene X and Y molecular axes are inclined from the TNB X and Y axes (see Figure 1). An empirical sum rule found for the deuterium shifts of the naphthalene-PMDA complex1) seems to hold also in A-TNB. Namely, the sum of the deuterium shifts of bands 4,6, and 11 (A, modes) and that of bands 5,7, and 10 (Bgmodes) is roughly the same and comparable with the sum of the expected (13) Ishii, K.; Kurihara, M.; Nakayama, H., in preparation.
Ishii et al. shifts of the anthracene X and Y librations. vi. Comparison with the Results of Beckman et al. Beckman et aL6 measured Raman spectra of the A-TNB crystals between 12 and 300 K. They observed 12 bands below 160 cm-’ at 12 K. Since they did not get the polarization data, they did not give substantial assignments to the observed bands. From the positive shifts by the deuterium substitution, they claimed that the bands observed at 124 and 131 cm-’ at 15 K were anomalous. These bands seem to correspond to our band 11 (A,) observed at 131.4 cm-’ at 88 K. To be noted is that, in contrast with their results, the deuterium shift of our band 11 is -5.9%, which is very reasonable in assigning this band to an X libration of anthracene. Apparent correspondences of the frequencies are seen respectively between their bands 1, 9, 11, and 12 and our bands 1, 10, 11, and 12. However, the correspondences between the bands in the region from 30 to 100 cm-l are poor. One of the reasons for this might be that Beckman et al. measured the spectra without determining the orientation of the specimen and observed the superpositions of the spectra of various polarizations. They also reported that some of the bands showed anomalous temperature dependences of the relative ratio of the intensities in the temperature range between 80 and 150 K. However, as described before, we obtained results of almost monotonous changes in the band intensities between 88 K and room temperature when we normalized the spectra by using as the standard an intramolecular mode observed in both the A, and B, spectra. It should be pointed out that the relative intensities between the Raman bands with different polarizations are sometimes affected very much by small changes in the experimental conditions such as the orientation of the specimen. vii. CT Interaction and Lattice Vibration. Vibrational spectra of molecular crystals are characterized by the similarity to the spectra of the isolated molecules. It is true for the intramolecular vibrations in single-component molecular crystals. For molecular complexes, the shift in the vibrational frequencies on complex formation can sometimes be regarded as the indicator of the strength of the intermolecular intera~ti0n.l~However, such shifts are very small in almost neutral complexes like A-TNB. As for the lattice (or intermolecular) vibrations, spectra are naturally different from complex to complex, since the environments of the molecules in the crystal are different. However, it should be emphasized that the frequencies of the vibrational modes which are mainly attributed to the vibrations of one of the component molecules seem not widely different from complex to complex. An example of this is seen in the result reported in this paper that the librational frequencies of anthracene in A-TNB are not so different from those in A-PMDA15 or the anthracene crystal.”. This also indicates that the intermolecular force in C T complexes mainly comprises the van der Waals-type forces when the degree of the charge transfer is small. The C T interaction may play important roles in determining the relative configuration between the donor and the a ~ c e p t o r but , ~ it does not seem to contribute largely to the total potential energy of a molecule in the crystal. This conclusion is not in favor of the expectation described in the Introduction. Probably we must evaluate the intermolecular potential energy in detail to discuss the contribution of the C T interaction. Chen and Prasad5 proposed an idea of a giant molecule as the limit of the strong coupling between the vibrations on the donor and acceptor sublattices. Their discussion is correct in most places, but one must be careful in some respects in applying their idea to the case of C T complexes. First, crystals of C T complexes are usually composed of columns made with infinitive stacks of donor and acceptor. No particular pair of donor and acceptor molecules can be regarded as a giant molecule. Second, especially for the librational mode, the relative configuration of the donor and the (14) See, for instance: Bozio, R.; Peck, C. In The Physics and Chemistry of Low Dimensional Solids; Alcacer, L., Ed.; D. Reidel: Dordrecht, 1980; p 165. (15) Tokura, Y . ;Koda, T.Solid State Commun. 1981, 40, 295.
J . Phys. Chem. 1987, 91, 563-570
563
Conclusion
Figure 8. Schematic illustration of the in-phase coupled libration (the low-frequency branch) of the donor and acceptor sublattices.
acceptor is changed even in the low-frequency branch (in-phase mode) resulting from the coupling between the two sublattices. This situation is illustrated in Figure 8. In other words, no pair of donor and acceptor molecules can be regarded as a rigid body irrespective of the strength of the coupling. The fact that most of the lattice modes in A-TNB are more or less affected by the deuterium substitution of anthracene indicates that there is nonnegligible coupling between the vibrations on the anthracene and T N B sublattices. Similar results have been ~ J ~the other hand, there reported for some C T c ~ m p l e x e s . ~ JOn are some molecular complexes in which the vibrations of the two sublattices seem almost independent of each It would be worth noticing that, for the complexes of the latter case, the intermolecular electronic interaction between the two sublattices seems very weak and no indication of C T absorption has been observed. Thus, by the quantitative study of the intermolecular potential in molecular complexes, the contribution of the C T interaction to the total intermolecular force would be clarified in future. We observed 11 bands among the expected 12 lattice vibrational bands of A-TNB. Two of them, at least, are considered to be the modes mainly comprising the translational movements of TNB. We assigned bands 8 (B,) and 9 (A,) to those. So far as we know, no translational Raman-active lattice mode has been observed and assigned for aromatic molecular crystals. The present results of A-TNB might be a novel example in which the intensities of the translational Raman bands are enhanced by the presence of the C T interaction. P.; Prasad, P. N. Chem. Phys. 1976, 16, 175. (17) Chen, F. P.; Prasad, P. N. Chem. Phys. Lert. 1977, 47, 341. McCaffrey, R. R.; Prasad, P. N. Chem. Phys. 1981, 63, 13. (16) Chen, F.
Polarized Raman spectra in the lattice vibrational region were measured on single crystals of the charge-transfer complex anthracene-TNB and the corresponding complex of deuteriumsubstituted anthracene. We succeeded in making good single crystals of the anthracene-hlo complex by the plate sublimation method, which enabled us to measure the spectra with all the polarizations at room temperature and to determine the irreducible representations of most of the observed bands. Temperature dependences of the Raman spectra were measured with some polarizations on anthracene-hlo and anthracene-dlo complexes between 88 K and room temperature. Comparison of their spectra a t low temperature gives the magnitude of the deuterium-substitution effect for each lattice mode. The frequency and intensity of each band change almost monotonously against temperature, which suggests that there is no phase transition in the temperature region studied. Empirical assignment of each band was made with the aids of the deuterium-substitution effect and the data of the moment of inertia. Eleven bands are assigned respectively to one of the 12 lattice modes expected by the factor-group analysis. Among those, nine are assigned respectively to one of the rotational modes of anthracene or TNB, and the remaining two are assigned to the translational modes of TNB. This is the first report in which the assignments are made on the translational lattice bands in the Raman spectra of charge-transfer complexes. One of the translational bands is as strong as the rotational bands, which suggests that the charge-transfer interaction between the donor and the acceptor enhances the intensity of this band. The observed deuterium shifts indicate that there are nonnegligible couplings among the vibrations of the two sublattices. One might conclude by this that the donor and acceptor molecules behave as a giant molecule. However, there remains the freedom of the rotations of the donor and acceptor molecules even in the in-phase branch of the coupled vibration of the two sublattices. Therefore, one would misunderstand what is going on in the crystal if one should consider the donor-acceptor pair vibrating in the in-phase modes as a rigid molecule. Acknowledgment. This work was partly supported by a Grant-in-Aid for Scientific Research (No. 454132) of The Ministry of Education, Science and Culture of Japan. Registry No. A-hlo-TNB, 1700-13-6;A - C ~ , ~ - T N105457-92-9 B,
Correlated Electronic States of the LiH Molecule Studied with the Polarization Propagator B. Weiner and Y. Ohm* The Quantum Theory Project, Department of Chemistry, University of Florida, Gainesuille, Florida 3261 1 (Received: March 1 1 , 1986)
The polarization propagator technique with an antisymmetrized geminal power reference is briefly outlined in its spin singlet restricted form and applied to the study of the XIZ+and the ALE+states of LiH at various internuclear separations. Emphasis is put on a pictorial and qualitative description of the quite complex correlated electronic states, which show the expected charge distributions in the bonding region as well as at separation.
Introduction It is well-known and appreciated that the orbital picture of chemical bonding is only a first approximation to the true quantum mechanical description. Although its use is an invaluable tool of the practical chemist it can often lead to quantitatively wrong 0022-3654/87/2091-0563$01.50/0
results and sometimes even to qualitatively incorrect models of molecular structure. The orbital picture is based on the independent particle approximation (IPA) where the electrons are considered to move independently of each other in an average potential. In order to explicitly include correlation effects, more sophisticated quantum chemical methods must be used. However, 0 1987 American Chemical Society
