J. Phys. Chem. 1993, 97, 1283-1285
1283
Normal Coordinate Analysis of the Vibrational Transitions in Benzil Vesna Volovhkt and Lidija Colombo' Ruder BoJkouiC Institute, University of Zagreb, P.O. Box 1016, 41000 Zagreb, Croatia Received: July 1, 1992
Normal coordinate analysis is performed for the benzil molecule. Force constants of phenyl rings are transferred from earlier studies on binuclear aromatic molecules. The existence of some low-frequency internal modes has been proved, thus eliminating the earlier explanations of the excess of the bands observed in the low-frequency Raman and FIR spectra of the benzil crystal.
Introduction In our previous paper,I we have reported Raman and infrared spectra of an oriented single crystal of benzil and its solutions. A high degree of resolution obtained by polarization analysis enabled us to record almost a complete internal spectrum and to propose a preliminary assignment based on the structural similarity with a benzophenone molecule studied recentlye2 Both molecules have two phenyl rings and the same symmetry (C2). Consequently, a large number of transitions in both spectra are originating from the vibrations of the phenyl rings, while the vibrations of the central part of the molecule will be specific for each of the two spectra. It is most likely that some of the latter vibrations in benzil will be of low frequency, and this part of the spectrum is crucial for understanding the dynamics of this interesting crystal. In fact, most of the studies performed on benzil so far, have dealt with lattice dynamics3 or the phase transition observed at 84 Ke4-I0 The internal spectrum was in almost all cases4.11J2recorded without further interpretation. Nevertheless, from the beginning of the study of the lattice dynamics of the benzil crystal in the high-temperature phase, it was noticed that the number of low-frequency bands observed in the Raman3 and in the infrared spectraBexceeds the number of lattice vibrations predicted by the group symmetry analysis. The proposed explanation of this feature was that the additional Raman band is a difference mode arising from two lattice modes: 69 cm-I - 39 cm-' = 30 cm-I. Based on earlier studies on different molecules of the binuclear aromatic type,2J3s14we presume that some internal modes could be in this spectral range. This assumption has been applied in our preliminary assignment1and is confirmed in the present work by the normal coordinate analysis, giving at the same time the vibrational character of these transitions.
Choice of Force Field The benzil molecule (C&C0)2 has 26 atoms which give rise to 72 internal vibrational modes. The symmetry of the molecule in thecrystalI5andin thegasphaseI6isCz(Figure la). Therefore, the internal spectrum spans the representation of 37 A and 35 B, both species being active in the infrared and Raman spectra. Due to its structural characteristics, the spectrum of the benzil molecule will possess in each symmetry species 27 vibrations of the phenyl ring and 4 modes connected with phenyl-C bond vibrations. The remaining 10 vibrations correspond to the vibrations of the central part of the molecule. The valence force field is defined by 84 internal coordinates, 12 of them being redundancies. The C2 symmetry separates all internal coordinates in 43 of the species A and 41 of the species B. A definition of the internal coordinates is given in Figure la. t Also a member of the Faculty of Chemical Engineering and Technology, University of Zagreb.
Figure 1. (a) Definition of the internal coordinates for benzil molecule. (b) Molecular structure of glyoxal.
The structural parameters used in the normal coordinate calculations were those obtained from the study of benzil in the gas phase.16 The experimental data were taken from the Raman and infrared spectra of solutions. The force field for phenyl rings was transferred from an earlier study on benzophenone2 and obtained in an overlay calculation on phenylalkynes.I3J4 This part of the molecular force field was kept fixed during the calculations, while the force field for the central part of the molecule was varied to reproduce the observed frequencies. Some starting values of the force field constants could be taken from the calculations on glyoxalI7JB(Figure lb) owing to the similar structural parameters of the O=C-C=O groups in both molecules. The final valuesof these force constants are listed in Table I.
Discussion According to the previous considerations, the whole spectrum of the benzil molecule has been separated into two parts: vibrations
of the phenyl rings listed in Table I1and vibrational modes specific for the molecule of benzil presented in Table 111. It is worth mentioning that the same approach has been used by Solin and Ramadas: who are theonly authors to givea partial interpretation of the internal spectrum. Most of the phenyl vibrations, particularly the in-plane ones, have been correctly assigned in our previous paper.' The scarce and unreliable assignment proposed previously for the vibrations
0022-365419312097-1283%04.00/0 0 1993 American Chemical Society
1284 The Journal of Physical Chemistry, Vol. 97, No. 7, 1993
TABLE I: Force Constants for the Central Part of B e n d force 1
2
3 4
5
constant
KR KQ Ha Hs Ha
value
force
constant
valuea
H, H*
0.167 2.294 0.627 4.294 0.131
Diagonal 5.067 6 11.458 7 1.887 8 2.43 1 9 0.753 10
HM K, H,
Interaction 0.252 27 0.406 28 -0.514 29 0.612 30 2.160 31 -0.635 32 1.032 33 1.584 34 0.015 35 -0.560 36 0.686 37 -0.573 38 0.800 39 -0.210 40 0.277 41 -1.859
11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
-0.224 0.269 -0.162 -0.027 -0.105 0.231 -0,006 0.040 0.059 -0.05 1 -0.254 0.012 0.053 -0.007 -0.180
a Stretching force constants,mdyn A-1; stretching-bending interactions, mdyn rad-'; bending force constants, mdyn A rad-*.
TABLE II: Observed and Calculated Frequencies (cm-I) of the Phenyl Vibratioils in the Spectrum of the B e d Molecule symmetry
obsd
A
3078's 3063'~s 3054" 3036Ow 303Wm 1598vsp 1583h 1493 w 1451w 1324wp 1287wp 1177wp 1161 m d p 1073wp 1023sp 1OOOvsp 989 w 970vwdp 928vw 844vw 787mp 750mp 717mp 616mdp 644mdp 464mp 400wdp
a
calcd symmetry 3064 3063 3061 3061 3060 1601 1584 1490 1438 1334 1288 1176 1161 1083 1023 996 985 962 928 853 785 750 691 612 650 472 402
B
obsd
calcd assignment 20a 20b 7a 2 7b 8a 8b 19a 19b 3 14 9a 9b 18b 18a 12 5 17a 17b 1Oa
307Pvs 3064 3062's 3063 306 1 3027" 3061 301P 3060 1600vs 1601 1586m 1587 1490w 1490 1455m 1441 1330w 1334 1288 sh 1288 1179w 1176 1164w 1161 1079m 1082 1030m 1025 1005m 999 995vw 985 982vw 964 930m 931 855sh 852 723ms 717 750m 756 695s 687 620m 602 471 m 478 426vw 426 400w 391
1 11 4 6b 6a 16b 16a
Frquencies of the bands observed in the crystal.
for the central part of the molecule was the real challenge t o perform normal coordinate analysis of this molecule. The 18 specificvibrations of the benzil molecule, given in Table 111, can be separated into 3 groups of vibrations involving predominantly 2 phenyl-C bonds, 2 C 4 groups, and the C O - C O ' bond. Three of the Ph-C vibrations in each symmetry class are the substituent-dependent modes of the monosubstituted benzenes. Two of the lowest frequencies in this group describe torsions of the Ph-C bonds. The remaining two groups of vibrations, as already mentioned, can be compared with the vibrations of the glyoxal molecule.17-18 The C 4 stretching frequencies in benzil are somewhat lower than those in glyoxal, although the bond lengths in both molecules
Volovgek and Colombo are very close (Table IV). This could be due to the strain which exists in the molecule of benzil.I5 The C - 0 in-plane bendings remain in the same frequency range as these transitions in glyoxal with A-B or ag-b. splittings of the same order of magnitude. A very large splitting obtained for the C = O out-of-plane bending modes of A and B species has no counterpart in the spectrum of glyoxal. It is interestingthat theC-H out-of-planebendingmodes in glyoxal exhibit a relatively large ag-bu splitting too. The last group of the specific transitions in benzil could be described by the vibrations of the two halves of the molecule (O-C-Ph) moving against each other. Such movement is most pronounced in the CO-CO' stretching mode assigned to the very polarized band at 1052 cm-I. As a consequence of the similarity in the Co-Co' bond lengths in b e n d and glyoxal molecules, the frequencies and the force constants are close in both calculations (Table IV). The rest of the transitions in this group are the vibrational modes with calculated frequencies below 100 cm-I. Two of them are of the A species, and one is the B species. In the Raman spectrum of the solution, we observed,by thedifference technique,' a spectral feature which was interpreted as two bands at 69 and 56 cm-I. It should be mentioned that in solution both A and B symmetry species are active in the Raman and infrared spectra. On the other hand, we have not recorded the FIR spectrum of the solution below 100 cm-I nor has it been reported in the literature. As already mentioned, in the spectrum of the crystal below 100 cm-I, there are three Raman modes instead of the two predicted by the factor group theory,3and there are four infrared active modes instead of the three predicted by the factor group analysis.8 At this point, it is worth remembering that from the correlation among the molecular symmetry group (Cz), the site symmetry (CZ),and the factor group (D:), it follows that each molecular vibration of species A will have AI and E components in the crystal spectrum AI modes being active in the Raman spectrum only. The molecular B vibrations give rise to crystal modes A2 and E, A2 vibrations being active only in the infrared spectrum. Thus, we suppose that the exceding A and B modes correspond to the low-frequency internal vibrations of the benzil molecule and propose assigning them to the low-frequency bands observed in the Raman spectrum of solution, where both A and B species are active. From the atomic displacements and the potential energy distribution (PED), it follows that the only lowfrequency B mode representsrotational movementsof both phenyl rings around axes normal to the ring's planes. We assigned it to the observed band at 69 cm-I. Among the two calculated vibrational modes of species A, we assigned the lower one (54 cm-I) to the second observed Raman band at 56 cm-I. From the atomic displacements and PED, this is the torsional mode of the CO-CO' bond. Compared to the equivalent mode in glyoxal (127 cm-I), it could appear that the frequency in benzil is too low, but the frequency of the same mode in deuterated glyoxal (1 18 cm-I) indicates the high degree of dependence of this vibrationalfrequency on the mass substituted at theendofthebond. Thesecondcalculatedmodein Asymmetry is a complex movement of both oxygen atoms and phenyl rings. Whether this modecorrespondstoone ofthe twoobserved Raman bands or whether it is a mode which has not yet been observed is difficult to say now. In fact, all these modes should undergo strong crystal field effects and exhibit more or less important frequency shifts in the crystal spectrum. Unfortunately, the normal coordinate analysis of the lattice vibrations of benzil has not yet been performed. Therefore, at the present stage of the investigationsof the vibrational spectrum of benzil, it is difficult to conclude which of the low-frequency bands observed in thecrystal spectrumcorresponds to the internal modes and which to the external modes. To solve this problem completely, it would be necessary to perform normal coordinate
Vibrational Transitions in Benzil
The Journal of Physical Chemistry, Vol. 97, No. 7, 1993 1285
TABLE IIk Specific Vibrational Modes of the Benzil Molecule (Frequencies in cm-I) symmetry B
symmetry A vibrational mode 13 15 1 Ob
Ph-C C=O C=O C=O
torsion str i.p. bend. 0.p. bend. C - C str C - C torsion rocking of phenyl rings
obsd
calcd
1211mdp 310 vw 263 m
1208 320 26 1 132 1685 413 169 1050 55 70
1685 s p 415 mp 165 m dp 1052 m p 56 w
PED 4 3 R + 24@+ 21T 776 537 272 586 404 292 567 326 88Q 338 + 233 132 1286 797 32a 63r 338 + 16T 64u 59M 1106 557 18u
+ + +
+ + + +
TABLE Iv: Comparison between Structural Parameters (A), Force Constants (mdya/A), and Frequencies (cm-1) of Benzil and Glyoxal Molecules CO=O co-CO’ Q KO YO r K, vr benzil
1.210
11.458
glyoxal
1.207
12.760
1732 1745ag b,
1.523
4.294
1052A
1.525
4.278
1065a,
calculations including both the internal and the external modes of crystalline benzil.
Conclusion The aim of the present study was to prove that the excess of Raman and infrared bands observed in the lattice mode spectral range of benzil is the molecular vibrational modes. Therefore, normal coordinate analysis was performed for the free molecule using the experimentaldata obtained in solution. Good agreement between calculated and observed frequencies points out that the force field used was sufficiently precise to describe the dynamics of the benzil molecule. It has been proven that this molecule has vibratioal modes of very low frequency. Considering the large interest which has been demonstrated so far in the dynamics of the benzil crystal, it is obvious that a normal mode analysis for the crystal is an utmost necessity. As a first step in such an endeavor, the present study has contributed to the achievement of this aim.
+ +
+ + +
+ 19u
obsd
calcd
PED
1215 m 192 s 335 m 158 w 1680 s 648 vs 880 vs
1213 192 337 155 1676 645 888
47R 23T 20@ 64~+45~+17p+146 308 25$ I 5 3 717 31M 92Q 428 273 + 166 13a 306 + 308 + 17p 15T
69 w
82
+
+ + +
+ +
+ +
50a+34$+31Q+lIR
Acknowledgment. This work was supported by the Ministry of ScienceTechnology and Informatics of the Republic of Croatia (Grant 1-03-066). References and Notes (1) Colombo, L.; Kirin D.; Volovkk, V.; Lindsay, N.E.; Sullivan, J. F.; Durig, J. R. J . Phys. Chem. 1989, 93, 6290. (2) Volovkk, V.; BaranoviC, G.; Colombo, L.Specrrochim. Acra A, in press. ( 3 ) Claus, R.; Hacker, H. H.;SchrBtter, H. W.; Brandmiiller,J.;Hausiihl, S. Phys. Rev. 1969, 187, 1128. (4) Solin, S. A.; Ramadas, A. K. Phys. Rev. 1968, 174, 1069. ( 5 ) Figui8re. P.; Szwarc, H. Mol. Cryst. Liq. Cryst. 1976, 35, 1. (6) Odou, G.; More, M.; Warin, V. Acta Crystallogr. 1978. ,434, 459. (7) Sapriel, J.; Boudou, A.; Perigaud, A. Phys. Rev. B 1979, 19, 1484. (8) Wyncke, B.; Brehat, F,;Hadni, A. Ferroelectrics 1980, 25. 617. ( 9 ) Moore, D. R.;Tekippe, V. J.; Pamadas,A. K.;Toledano, J. C. Phys. Rev. B 1983. 27, 7676. (10) Lefebvre, J.; More, M.; Zielinski, P.;Odou, P. In Dynamics of Molecular Crystals; Lascombe, J., Ed.;Elsevier: Amsterdam, 1986; p 193. (11) Stenman, F. J. Chcm. Phys. 1969, 51, 3141. (12) Claus, R.; Schratter, H. W.; Brandmiiller, J.; Haussiihl, S. J . Chem. Phys. 1970.52, 6448. (13) BaranoviC, G.;Colombo, L.; Skare, D. J . Mol. Smcr. 1986, 147, 275. (14) BaranoviC, G.;Colombo, L.; FuriC, K.; Durig, J. R.; Sullivan, J. F.; Mink, J. J . Mol. Srruct. 1986, 144, 58. (15) Brown, C. J.; Sadanaga, R. Acra Crysrallogr. 1965. 18, 158. (16) Quang, S.; Hagen, K. J. Phys. Chem. 1987.91, 1357. (17) Pietilg, L.-0.; PalmB, K.; Mannfors. B. J . Mol.Spectrosc. 1985,112, 104. (18) Pietili, L.-0.; Palm4 K.; Mannfors, B. J . Mol. Spectrosc. 1986,116, 1.
