10063
J. Phys. Chem. 1994,98, 10063-10071
Planar Vibrations of Benzenoid Hydrocarbons. Comparison of Benzene Force Fields and Application of a Simple Predictive Model to Kekulene Koichi Ohno’ and Hideaki Shinohara Department of Chemistry, College of Arts and Sciences, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153, Japan Received: April 20, 1994; In Final Form: July 26, 1994@
A simple force field model (MOB) designed for predictive calculations of aromatic planar vibrations has been compared with recent theoretical and experimental force fields for benzene and applied to polycyclic aromatic hydrocarbons (PAHs). The rms frequency error for benzene is ca. 20 cm-l in the M 0 / 8 model, which is better than those for unscaled ab initio calculations in the Hartree-Fock level (ca. 100-130 cm-l), the MP2 method (ca. 50 cm-l), and local density functional (LDF) and coupled cluster singles and doubles (CCSD) methods (ca. 30 cm-l). The M O B model requires only topological connections of benzenoid rings for its application to any size of polycyclic benzenoid hydrocarbons. Without any knowledge except for the structure formula the M0/8 model was applied to kekulene (C4&4), and on this basis spectral intensities were calculated. The results were found to be in good agreement with available experimental data including IR, fluorescence, and phosphorescence spectra. The essential nature of the benzenoid force field was proved to be governed by the topology of the carbon network, which was effectively incorporated in the M0/8 model for describing highly correlated motions of CC bonds in conjugated systems.
I. Introduction Collective motions of nuclei in molecules have been described as molecular vibrati0ns.l Their frequencies and normal coordinates have been studied in connection with intramolecular force fields. Internal coordinates such as stretchings and bendings have been used on the basis of the valence concept. Since nuclear motions are shared among several internal coordinates for polyatomic molecules, interaction force constants need to be introduced. Thus in many cases, coupling terms for adjacent internal coordinates have been considered, whereas interactions between nonadjacent internal coordinates have been disregarded for the sake of simplicity. It must be stressed that the approximation decoupling nonadjacent coordinates is not valid for conjugated systems, since modification of n electron motions associated with a bond stretching arouses correlated motions of remote bonds via n electron delocalization. The CC-CC coupling terms for meta and para positions in addition to ortho positions have been proved to be indispensable for correct description of collective motions of CC bonds.2-10 In previous studies,8-10a simple force field model (MOB), which is a systematic extension of the earlier MO model of conjugated systems by Coulson and Longuet-Higgins,’ has been established and successfully appplied to vibronic problems for various polycyclic aromatic hydrocarbons (PAHs).12-15 In the present study, the M0/8 model is compared with recent t h e o r e t i ~ a l ’ ~and - ~ ~e~perimental~~.” studies for planar vibrations of benzene. Application of the M0/8 model to kekulene (C48H24) demonstrates that this simple force field approach is useful in analysis and prediction of vibronic properties of PAHs.
11. Method and Calculations A. The Force Field Model (MOB). The M0/8 model was designed to be applied as a predictive means to all kinds of planar benzenoid hydrocarbons of infinite size without any modification and extra knowledge except for topological con@
Abstract published in Advance ACS Abstracts, September 1, 1994.
nection of hexagonal rings.8,10Although the detail of this model has been reported, the outline is summarized as follows. The potential functions are described in the quadratic form. Internal coordinates are classified into four types: CC stretchings, CH stretchings, CCC bendings, and CCH bendings. Highly correlated motions of n electrons associated with CC bond stretchings are taken into account by the perturbation theory for conjugated n electron systems developed by Coulson and Longuet-Higgins. Semiempirical treatments lead to the following expression for CC stretching force constants:8.10 F,,(CC)
=fl
+f2(Pi - Po) +f3(IIii - no)for i = j
and F,(CC-CC)
=
f3n,for i
f
j
Here, Pi is the bond order for the respective CC bond i, PO is the bond order (BO) for benzene, IT, is the bond-bond polarizability (BBP) with respect to a couple of CC bonds i andj, and no is the diagonal element of the BBP matrix for benzene. BOs and BBPs can be evaluated by Huckel-MO calculations. f1, f2, andf3 are the potential parameters. Other potential parameters included in the M0/8 model are as follows: f4,diagonal CH stretching force constant;f5, diagonal CCC bending force constant; f5 diagonal CCH bending force constant; f7,off-diagonal CC-CCC interaction force constant; andfs, off-diagonal CC-CCH interaction force constant. The force field parameters were optimized previously8,l0by leastsquares adjustment of calculated frequencies to observed fundamental frequencies for perhydro and perdeutero species. Standard parameter values for all benzenoid hydrocarbons (MO/ 8ST) were obtained as averaged values of individually optimized parameters for benzene, naphthalene, anthracene, pyrene, and triphenylene:1°J4f1 = 6.821, fz = 5.450,f3 = 3.646,h = 5.072, fs = 0.928, f6 = 0.504, f7 = 0.430, and fg = 0.199. B. Normal Coordinate Calculations. For the purpose of predictive calculations, reference geometrical structures of benzenoid rings are assumed to be pure hexagons with the
0022-3654/94/2098- 10063$04.50/0 0 1994 American Chemical Society
Ohno and Shinohara
10064 J. Phys. Chem., Vol. 98, No. 40, 1994 TABLE 1: Comparison of CC Stretching Force Constants for Benzene (mdynldi) (3)' Net0 Scrocco force (1)" (2)* (4)dDuinker (5)' Scherer Califano Mills Kydd constant Whiffen RR/2 RR(0) RR(m) RR@)
6.616 0.939 -0.913 -0.040
6.727 0.829 -0.470 0.279
6.456 0.784 -0.336 0.312
6.822 0.434 -0.434 0.725
6.714 0.487 -0.446 0.621
(6Y Ohno
(7)g Pulay
(8)hOzkabak
Foggarasi Boggs
Goodman
6.654 0.744 -0.474 0.338
6.578 0.710 -0.407 0.425
6.616 0.728 -0.419 0.383
force constant
(9)' I-F STO-3G
(10)lI-F 4-21P
(1lYHF 4-21G
(12)kHF 6-311++ G(d,p)
(13yMP2 4-2 1G
(14)' MF?? 6-311G (d,p)
LDF
CCSD
RW2 RR(0) W m ) RR(P)
8.661 1.360 - 1.063 0.903
7.137 0.917 -0.641 0.638
7.695 0.925 -0.618 0.651
7.678 0.960 -0.707 0.636
6.618 0.65 1 -0.360 0.396
7.172 0.583 -0.337 0.291
6.952 0.651 -0.381 0.307
7.105 0.790 -0.542 0.484
force constant
naphthalene
RR/2 RR(0) RR(m)
(15)'
(16)"'
(17)" M0/8
(18)" M018
(19)" M0/8
pyrene
triphenylene
(20)o M018
(21Y M018NAFT
(22Y M018ST
(23)' Ohno PFB
LDF CCSD
6.722 0.741 -0.472 0.338
6.712 0.691 -0.441 0.315
6.810 0.721 -0.460 0.329
7.207 0.820 -0.523 0.374
6.863 0.743 -0.474 0.339
6.821 0.744 -0.474 0.339
6.616 0.727 -0.441 0.382
7.029 0.721 -0.462 0.396
anthracene
(24)'
RR@) Reference 3 1. Reference 4. Reference 6. Reference 34; valence force field given in Table VII (calculation 11, Table VLII). Reference 36. f Reference 8; M018 optimized for benzene C& and c96 (method Y8, Table 5). 8 Reference 16; set 11 adapted to experiments with three scale factors. This set was obtained from modification of the 4-21P results listed as (10). I, Reference 20; the benchmark values which were slightly modified from the earlier values by Ozkabak and Goodman in ref 25. I Reference 16; ab initio SCF (HF) calculations without scale factors. Reference 17; ab initio HF and MP2 calculations without scale factors. Reference 20; ab initio HF and MP2 calculations without scale factors. ' Reference 22; local density functional (LDF) calculations employing a triple-f basis set with triple polarization on hydrogen and double polarization on carbon. Reference 23; coupled cluster singles and doubles (CCSD)calculations using a generally contracted, correlation consistent valence triple-; basis set (3 18 functions in 234 contractions). Reference 8; transferred from the M018 parameters individually optimized for naphthalene or anthracene. Reference 10; transferred from the M018 parameters individually optimized for pyrene or triphenylene. p Average values of the individually optimized M018 parameters for naphthalene, anthracene, pyrene, and triphenylene. This set is the average of (17)-(20). '?Reference 10; average values of the individually optimized M0/8 parameters for benzene, naphthalene, anthracene, pyrene, and triphenylene, and this set of the M018 parameters is denoted as MOWST (standard set of M018 parameters). This set is the average of (6) and (17)-(20). Average values of Ohno's (6) and Pulay, Fogarasi, and Boggs's semiempirical results. Average values of the LDF (15) and CCSD (16) theoretical results. J
following parameters: CC distance = 1.397 (A) and CH distance = 1.084 (A), and all the valence angles are 120". Wilson's GF matrix method' is used for normal coordinate calculations. Cyclic redundancies are eliminated by transforming the secular equation into a symmetric form according to Miyazawa's method.26 In our program,27geometrical structures are generated automatically from a set of simple input data specifying the topological connection of benzenoid rings. No other data are required except for isotope substitutions. C. Vibronic and Infrared Intensity Calculations. FranckCondon factors and vibronically induced intensities are calculated by a semiempirical approach reported previously. Distorted geometries are generated from reference geometries and Cartesian displacements obtained from normal coordinate calculations by the M0/8 model. Vibronic coupling strengths are estimated numerically from variations of transition moments and transition energies by CI calculations. Dipole moment derivatives are estimated numerically from variations of molecular dipole moments. Dipole moments are calculated by SCF-MO 111. Comparison of Benzene Force Fields
A. CC Stretching Force Constants. Table 1 compares experimental and theoretical CC stretching force constants for benzene. W 2 , RR(o), RR(m), and RR@) denote diagonal and ortho, meta, and para interaction force constants for CC stretchings. Other potential parameters were not included in Table 1 in order to clarify the most important differences. Brief historical highlights in six decades of extensive studies on benzene force constants can be seen from the selected sets in Table 1. Listed values from set (1) to set (8) in Table 1 are CC force constants obtained with the aid of experiments. Set (8),
determined by Ozkabak and Goodman25 in 1987 (slightly modified in 1991):O is now considered as a benchmark force field which includes no intuitive constraints in the potential model, whereas sets (1)-(7) involve some constraints. It was Whiffen's force field (1)31in 1955 that removed many of the ambiguities present in Crawford and Miller's pioneering work3* in 1949, which was based on extensive studies made by Ingold and c o - w ~ r k e r sin~ 1936-1946. ~ Successive studies on benzene and its derivatives by S ~ h e r e r ~in- ~1962-1964 revealed the importance of conjugation effects of the aromatic ring and the correlation of the relative signs for the CC-CC interaction constants in connection with the KekulC structures; 0rrho:meta: para = (+):(-):(+). Neto, Scrocco, and Califano (NSC)6 optimized a valence force field model for benzene, naphthalene, and anthracene in 1966. The results by NSC (3) were found to be similar to the force field by Scherer (2).4 In 1968 Duinker and Mills (DM)34 performed detailed studies using accurate frequencies determined by Brodersen and L a n g ~ e t hfor ~~ benzene and its deuterated analogs. The DM force field involves the Kekul6 constant constraining the ratios of interaction constants; RR(o):RR(m):RR(p)= 1:-1:l. In the final results by DM (4) the constraint to the RR@) was released. After the DM approach, presented a slightly modified version (5)involving 17 parameters in 1969. Apart from these experimental models (1)-(51, a simple valence force field model (6) was proposed by Ohno8 in 1978 on the basis of molecular orbital (MO) theories developed by Coulson and LonguetHiggins.ll A systematic reduction in the numbers of parameters within the constraint of the MO theory yielded the M0/8 model (originally referred to as the method I/8 model8). In 1981 Pulay, Fogarasi, and Boggs (PFB)16 reported two sets of scaled quantum mechanical (SQM) force field models on the basis of ab initio SCF calculations. Set I1 by PFB involves nine scale
J. Phys. Chem., Vol. 98, No. 40, 1994 10065
Planar Vibrations of Benzenoid Hydrocarbons
TABLE 2: Comparison of Experimental and Calculated Frequencies for Planar Vibrations of Benzene (cm-l) sym and HFc HFd6-311++ MP2' MP2' M0/8h M0/8h M018' M0/8' Wi1son"no. exptlb 4-21G G(d,p) 4-21G TZ2P+f LDP CCSDS Naph Anth Pyrene Triph AI, 1 A z 3~ E z 6~ E z 8~ E z 9~ B1,12 Bz, 14 Bzu 15 El, 18 E1,19
rms error
993 1350 608 1601 1178 1010 1309 1150 1038 1484
1078 1543 698 1765 1323 1148 1365 1237 1137 1659 130.6
1070 1491 662 1774 1280 1090 1335 1180 1128 1629 103.0
992 1434 645 1600 1247 1069 1322 1237 1056 1533 52.1
1018 1374 608 1637 1195 1039 1461 1178 1074 1515 54.6
1004 1314 602 1610 1150 993 1379 1125 1039 1462 29.4
1012 1391 613 1672 1207 1025 1304 1166 1071 1528 33.9
991 1366 605 1600 1177 971 1299 1189 1027 1474 18.8
986 1358 604 1610 1169 972 1329 1184 1024 1473 19.0
995 1357 590 1607 1174 948 1312 1191 1032 1471 24.8
1027 1318 598 1597 1150 946 1299 1168 1021 1438 31.6
M0/8STi 997 1352 604 1605 1168 968 1306 1183 1026 1467 18.6
Reference 37. Reference 20; rounded-off values of harmonic frequencies reported by Goodman,Ozkabak, and Thakur. Reference 17. Reference 20. e Reference 21. f Reference 22. 8 Reference 23. Reference 8. Reference 10. factors among which three scale factors are used for the CC stretching force constants; in the PFB model (7) only one degree of freedom is left for theoretical constraint between RR(m) and RR@). It is worthy of note that semiempirically determined CC force constants by Ohno (6) and also those by PFB (7) are in good agreement with the corresponding constants for the benchmark force field by Ozkabak and Goodman (8); average values of Ohno's (6) and PFB's (7) ( W 2 = 6.616, RR(o) = 0.727, RR(m) = -0,441, and RR@) = 0.382) are in excellent agreement with the benchmark values (8) reported a decade later. Nonempirical CC stretching force constants are also listed in Table 1, (9)-(16). Results of ab initio SCF(HF) calculations using different basis sets are shown in Table 1, (9)-(12). Although basis set dependence is not conspicuous for split valence sets (10)-(12), the STO-3G results (9) are considerably different from the others. Pulay, Fogarasi, and Boggs16 obtained the 4-21P force constants (lo), and they modified these values with scale factors to determine the set II SQM values mentioned above (7). Nonempirical CC stretching force constants in the HF level by Guo and Karplus (GK)17 and also by Goodman, Ozkabak, and Thakur (GOT)20indicate that the HF calculations give ca. 15% larger values for the diagonal constant and 3070% larger values for interaction constants. Inclusion of electron correlation effects at the second-order Mdler-Plesset (MP2) perturbation theory considerably decreases the disparity of ab initio CC force fields from the experimental OG field (8). Although the smaller basis MP2 results (13) by GK seemed satisfactory, the larger basis MP2 results (14) by GOT became rather disappointing. Stimulated by the unfortunate trend involved in the MP2 calculations, different correlation approaches have been made by Btrces and Ziegler (BZ)22 and also by Brenner, Senekowitsch, and Wyatt (BSW).23 The local density functional (LDF) calculations by BZ (15) and the coupled cluster singles and doubles (CCSD) calculations by BSW (16) gave improved nonempirical CC force constants. In view of the remaining disparity (10-30%) involved in the LDF and CCSD results (15) and (16), further efforts need to be made before settling nonempirical force fields for benzene. As the MO/8 model has a universal nature for all benzenoid hydrocarbons, CC stretching force constants for benzene can be obtained from those for other molecules. Transferred values to benzene CC force constants from individually optimized sets for naphthalene (17),8 anthracene ( 1 Q 8 pyrene (19),1° and triphenylene (20)'O are also shown in Table 1. All of these results (17)-(20) are comparable with best semiempirical, (6) and (7), empirical, (€9,and theoretical, (15) and (16), results. Average force constants for the M0/8 model from naphthalene, anthracene, pyrene, and triphenylene (MOBNAPT) listed in
Table 1, (21), are nearly the same as the optimized values for benzene (6). These results give a confirmation of the universal nature of the M0/8 model for benzenoid hydrocarbons. Table 1, (22), lists the CC force constants for the standard set of the M0/8 model (M0/8ST)l0 which are derived from a simple average of individually optimized values for benzene, naphthalene, anthracene, pyrene, and triphenylene. The MOBST set (22) is very similar to the experimental OG set (8), the average of Ohno's (7) and PFB's (8) semiempirical sets (23), and the average of the theoretical LDF (15) and CCSD (16) sets (24). B. Planar Mode Frequencies. Table 2 lists a comparison of experimental and calculated frequencies for planar vibrations of benzene. CH stretching modes are omitted from the table because of very similar frequencies and minor importance. Calculated frequencies for empirically optimized force fields are not included in Table 2, although they give much better agreement with experiments. Ab initio SCF(HF) and MP2 calculations become popular for nonempirical studies of molecular vibrations. Calculated frequencies for the HF level are ca. 10% higher than the observed values. Root mean square frequency errors for HF calculations are ca. 130-100 cm-', as can be seen from Table 2. This is far from the spectroscopic quality of ca. 1 cm-'. Although a scale factor of 89% is recommended by the Gaussian the suitable factor may depend on the molecule to be studied and also on the employed basis sets. Most appropriate values of scale factors also strongly depend on the mode type. A sophisticated choice of scale factors is not compatible with the purpose of predictive calculations. MP2 calculations considerably reduce rms frequency errors without scale factors; rms errors for the MP2 results are ca. 1/2 of those for the HF results in Table 2. This is a consequence of the second-order vibronically induced electron correlation effects which push down the ground state potential surface with respect to the upper surfaces. It is however tragic that the rms error increases in spite of the extension of the basis sets from 4-21G to TZ2Pff. A considerably mode-specific error is involved in the MP2 calculation with a large basis set including tiple-c plus double-polarization functions plus f functions (Mpu TZ2P+f);21 the frequency is 152 cm-l higher than the observed one. This is far from satisfactory, although the MP2/TZ2P+f calculation gives the v6(ezg) frequency in exact agreement with the observation. Recent calculations considering electron correlation effects by BBrces and Ziegler (BZ)22and also by Brenner, Senekowitsch, and Wyatt (BSW)23further decreased rms frequency errors to ca. 60% of the MP2 results. The maximum errors of these methods are, however, still highly mode-specific; the LDF results by BZ yielded 70 cm-' higher frequency for Y14(b2u),
Ohno and Shinohara
10066 J. Phys. Chem., Vol. 98, No. 40, 1994 TABLE 3: Relative Infrared Intensities of the el. Bands for Benzend ~~
~
MNDOC AM1 PM3 6-31G 6-31G(d) 6-31G+(d, p) exptlb
118
119
I20
0.5909 0.0004 0.0077 0.0854
0.1678 0.1820 0.1700
0.0580
0.1644 0.1739 0.2207
1.0000 1.oOoo 1.oOoo 1.oOoo 1.oOoo 1.0000 1.0000
0.1325 0.1251
0.2002
a Cartesian displacements were obtained from the MOWST normal coordinates. Dipole moment derivatives were calculated numerically. Infrared intensities were normalized for the CH stretching mode (mode 20 by Wilson's numbering). Reference 18.
TABLE 4: Excited Electronic States of Kekulene symmetry calcdlcm-l calcdlnm" obsdlnmb s6 30 434 328.6 326 Ss 'Ezg 28 699 348.4 351 S4 lE~g 27 162 368.2 367 S3 I B l u 26 123 375.6 389 SZ 25 028 399.5 SIl B 2 u 24 593 406.6 (453)' TI 3 B ~ , 15 086 662.9 (585)d a Present calculation by the semiempirical SCF-MO CI method in refs 14 and 15. Observed wavelengths for singlet states estimated from the absorption spectrum of kekulene in 1,2,4-trichlorobenzeneat room temperature in ref 39. Observed wavelength estimated from the fluorescence spectrum in ref 39. Observed wavelength estimated from the phosphorescence spectrum in ref 39.
whereas the CCSD frequencies by BSW gave 71 cm-' higher value for ~ g ( e 2 ~ ) . Since the MOB model is size-consistent with respect to the number of benzenoid rings, any set of potential parameters should be transferrable to all size of benzenoid hydrocarbons. This property of the M0/8 model can be seen from the calculated benzene frequencies by individually optimized sets of parameters for naphthalene (MOWNaph), anthracene (MO/ 8Anth), pyrene (M0/8Pyrene), and triphenylene (MOBTriph). It is satisfactory for predictive calculations that potential parameters determined by different molecules are applicable to other molecules without modification; rms errors for benzene by the M0/8 model with parameters of different molecules are ca. 20-30 cm-'. It is of note that a rms error of 18.6 cm-' has been obtained for benzene by the MOBST parameter set, which is considered as the standard set for all benzenoid hydrocarbons.1° The largest error for benzene frequencies by MOBST is -42 cm-l for v12(blu), which is better than the maximum disparity of ca. 70 cm-l for the LDF and CCSD results and ca. 150 cm-' for the MP2 results. Transferability of the MOBST set to various molecules was studied previously;lorms errors were found to be ca. 13-27 cm-'. Thus, the M0/8 model with the standard choice of the parameter values is expected to be applicable to all benzenoid hydrocarbons in a satisfactory level of frequency errors (ca. 20-30 cm-l), which is better than the currently most sophisticated unscaled theoretical methods considering electron correlation effects with fairly large basis functions. C. Infrared Intensities. Table 3 lists experimental and theoretical estimates of infrared intensities for benzene. Semiempirical (MNDOC, AM1, PM3) and ab initio SCF dipole moment calculations with Cartesian displacements obtained from the MOBST normal coordinates yielded infrared intensities. Present results can be compared with ab initio SCF calculations made by Goodman, Ozkabak, and Wiberg (GOW).18 Thepresent results for ab initio calculations with several types of conven-
tional basis sets are found to be very similar to respective results obtained by GOW for the same basis sets. In the case of semiempirical MO calculations, relative IR activities depend seriously on the methods. In particular, the lowest frequency mode Y18 shows marked disparities; the calculated activity of the CH bending mode ( ~ 1 8 ) is overestimated by the MNDOC method, whereas it is underestimated by the AM1 and PM3 methods. On the other hand, ab initio MO results are more satisfactory, although basis set effects are important.
IV. Kekulene A. Electronic States. The molecular structure of kekulene was studied by Staab and c o - w ~ r k e r s .Electronic ~~ states of kekulene are considered to be similar to those for benzene and coronene because of their planar D6h structures. Calculated electronic states for kekulene by a semiempirical SCF-MO CI methodl49l5are shown in Table 4. The ground electronic state (SO) of kekulene is lAlg. The lowest excited singlet state (SI) is ~ B Zas~in, the case of benzene and coronene. Although the electronic transition between lB2,(S1) and 'Al,(So) is symmetry forbidden in a D6h symmetry, vibronic intensity borrowing via eZg perturbing vibrations induces an allowed electronic transition character of the lElu-lAlg transition. The lowest excited triplet state (TI) is 3Blu,as in benzene and coronene. The electronic transition between T1 and SO is also symmetry forbidden with active perturbing vibrations of the e2, species. B. Application of the M0/8ST Model to Planar Vibrations. Planar frequencies for kekulene calculated by the MO/ 8ST model are listed in Table 5. For comparison calculated frequencies by Cyvin et a1.40 and observed f r e q u e n c i e ~are ~~,~~ also listed in Table 5. Calculated relative vibronic activities for e2g modes for the 1B2u-1Algtransition are shown in Figure la. Calculated 0- 1 components of Franck-Condon factors for the 1B2u-1Alg and 3B1u-1Alg transitions are shown in Figure 1, parts b and c, respectively. C. Vibrational Analyses of Observed Spectra. Spectroscopic properties of kekulene were studied by Staab, Diederich, and their c o - ~ o r k e r s .Although ~~ the fluorescence and phosphorescence spectra of kekulene in 1,2,4,5-tetrachlorobenzene at 1.3 K were reported by Schweitzer et al.,39 vibrational analyses have not been made. Figure 2 shows the observed fluorescence spectrum of kekulene. Observed spectral lines are classified into two subspectra originating from two sites in the host crystal, as indicated in the earlier work.39 Observed bands labeled by frequencies in cm-' without parentheses are ascribed to site I, and bands with parenthesized frequencies are assigned to site II. The 0-0 transition bands are labeled by the transition frequencies. Vibrational assignments are shown by frequencies for fundamental and combination bands. Frequency errors involved in the analyses are estimated to be &5 cm-'. The observed phosphorescence spectrum of kekulene and the vibrational assignments in terms of two-site subspectra are shown similarly in Figure 3. Most of prominent bands in the fluorescence (Figure 1) are assigned to e2g fundamentals, as shown in Table 5. The modes of 442,657,748, 965, and 1235 cm-l are ascribed to the false origin bands induced by vibronic intensity borrowing. Observation of similar intensities between couples of these false origin bands for sites I and I1 indicates that populations for the two sites are nearly the same. The band of 748 cm-' for site I1 may be assumed to be overlapping with the band of 848 cm-l for site I. Together with the 848 cm-l mode, frequencies of 135, 353, 1118, 1161, 1295, 1381, 1469, 1569, and 1575 cm-'
J. Phys. Chem., Vol. 98,No. 40,I994 10067
Planar Vibrations of Benzenoid Hydrocarbons TABLE 5: In-Plane Frequencies of Kekulene (cm-1) obsd calcd fluorescenceb phosphorescenceb aig
ezg
this work
Cyvin"
3057 3055 3055 1606 1451 1425 1284 1207 1140 730 638 237 3057 3056 3055 3054 1585 1576
3035 3034 303 1 1626 1522 1393 1166 1152 1040 668 603 196 3038 3034 3034 3032 1683 1598
(I)
(11)
1435 1276
1431
(1)
(11)
1621 1452 1427 1277
1619 1445 1425 1282
246
1575
1577
253
1577
1571
obsd fluorescenceb phosphorescenceb
calcd this work
Cyvina
(I)
(11)
(1)
(In
1549 1472 1414 1384 1326 1267 1237 1224 1149 1114 978 837 725 67 1 596 438 366 123
1569 1537 1465 1431 1324 1274 1195 1152 1077 1052 868 842 67 1 591 530 390 310 105
1569 1469
1564 1469
1469
1471
1381 1295
1385 1299
1295
1235
1240
1294 1254 1239 1231
1161 1118 965 848 748 657
1163 1123 972 849 748 662
442 353 135
446 352 139
calcd el,
azg
calcd
this work
Cyvina
3057 3055 3055 3054 1614 1598 1520 1442 1423 1401 1355 1282
3038 3055 3034 303 1 1665 1595 1564 1524 1475 1441 1349 1282
obsd IRC 3020 3007 1595 1522 1468 1411 1404
calcd
calcd
calcd
this work Cyvin"
this work Cyvin"
3037 1637 1541 1480 1432 1265
bl,
3056 3056 3054 1562 1492 1360
3038 3034 3034 1604 1494 1341
Cvvin"
1269 1214 1169 1133 976 832 719 660 587 524 266
1174 1161 1106 1048 884 788 670 596 524 476 223
obsd IRC 1230 1174 1127 959 850
1285
this work Cyvin" 3055 1626 1492 1396 1375 1279
this work
bzu
3057 1566 1552 1417 1324 1228
3032 1687 1589 1502 1411 1236
calcd this work Cyvin" 1168 992 836 586 524
1125 915 758 554 451
calcd
calcd
this work Cyvin" 1253 1022 831 676 470 320
1209 951 835 669 394 275
this work Cyvin" 1214 1110 1093 747 530 245
1148 1077 996 610 474 214
Reference 40; calculated frequencies of the five-parameter model. Reference 39; (I) and (11) refer to site I and II,respectively (see the text and Figures 2 and 3). Reference 42. may also be assigned to e~ vibrations because of the twin structures in the observed spectrum. The calculated activities of the ezg modes in Figure l a are in good agreement with the experiment. An exceptional disparity for the 1237 cm-' mode may be due to mode mixing among similar frequency modes of the same symmetry species. Some combination bands in the fluorescence spectrum revealed that alg fundamentals of 1284 and 1428 cm-' are the most active accepting modes, having relatively large FranckCondon factors. This is confirmed by the calculated FranckCondon factors in Figure lb; calculated Franck-Condon factors of 1284 and 1425 cm-' are the largest two. Appearance of the 0-0 band for the symmetry forbidden 1B2u-1Algtransition can be ascribed to the perturbation effect due to the skeletal deformation of the molecular structure in the host crystal or the low-symmetry crystal field. The larger intensity of the 0-0 band for site TI in contrast to the equally appearing false origin bands indicates that a large distortion in the ground state raising its energy results in the lower transition
energy for site II. An asymmetric intensity distribution between couples of fundamental bands in the fluorescence, as observed for ca. 1280 and 1435 cm-', may be ascribed to the alg fundamentals associated with the induced intensities of the 0-0 bands. For the phosphorescence, the intensity distribution of fundamental bands between the two subspectra is similar to the relative magnitude of the 0-0 bands, as can be seen in Figure 3. On the basis of this trend, the most prominent fundamental bands of 1277, 1427, and 1621 cm-' can be assigned to the alg modes. The calculated largest three Franck-Condon factors for the 3B1U-1Algtransition in Figure IC are in good agreement with the observed three prominent bands. Some weak bands in the phosphorescence spectrum include fundamental frequencies of eZg modes, such as 1469 and 1577 cm-'. This indicates that crystal field effects on the symmetry forbidden transition from T1 are important for the phosphorescence of kekulene in the trichlorobenzene host. In the case of phosphorescence, relative intensities between the two sites are affected by triplet
10068 J. Phys. Chem., Vol. 98, No. 40, 1994
Ohno and Shinohara
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Figure 1. Calculated relative vibronic activities for kekulene. Vibrational frequencies are in cm-I. (a) Vibronic intensities for ezg modes for the transition. (c) 0- 1 components of Franck-Condon 1B2u-IAlg transition. (b) 0- 1 components of Franck-Condon factors for the factors for the 3Blu-LAlgtransition.
state dynamics. In view of the difference in the site splitting for the fluorescence (104.4 cm-') and phosphorescence (87.4 cm-'), crystal field effects must also be important in the excited states.
D. Comparison of the M0/8 Model with the Cyvin Model. The rms frequency error of the present calculation for observed planar vibrations of kekulene is 16 cm-', whereas the rms error for the Cyvin model is 51 cm-'. These values indicate the lower bound of average frequency errors, since a simple comparison between calculated and observed frequencies generally yields smaller deviations than those for correct assignments. In the case of the Cyvin model, the observed alg fundamental of 1278 cm-' (1276 cm-' for the site I fluorescence, 1277 and 1282 cm-' for the site I and site I1 phosphorescence, respectively) shows no calculated frequencies within 100 cm-', and the active perturbing vibration of 969 cm-' found in the fluorescence (965 cm-' for site I and 972 cm-' for site 11) has no calculated frequencies within 80 cm-l. In addition to these, more than 10 of the 35 compared frequencies show deviations
larger than 50 cm-'. Large disparities in the Cyvin model are mainly due to the lack of interaction force constants for CC bond stretchings, as mentioned in the previous work.'O Although the Cyvin model has only five parameters for planar vibrations and is denoted as the five-parameter m0de1,4~%~ its application to large aromatics should be made carefully. By the Cyvin model, the rms error for benzene amounts to 106 cm-', with a maximum error of +242 cm-' for Y14(b2~).~ Even with Keating's internal coordinates for bendings4*rather than commonly used Decius's bendings,' the Cyvin model yielded a rms error of 79 cm-' for benzene, with a maximum error of +216 cm-' for ~ 1 4 . The extraordinally higher frequencies for the bzu mode are due to the absence of the CC interaction force constants in the five-parameter model. E. Infrared Intensities. Figure 4 shows the observed infrared spectrum4*and calculated intensities. Dipole moment derivatives were calculated numerically by ab initio calculations with the 6-31G basis sets for Cartesian displacements obtained from the M0/8 model. In contrast to the case of benzene in Table 3, calculated IR intensities are rather similar between
J. Phys. Chem., Vol. 98, No. 40, 1994 10069
Planar Vibrations of Benzenoid Hydrocarbons
