Ab Initio Study of Geometries and Force Fields of Diphenylacetylene in

J. Phys. Chem. 1993,97, 9103-9112

9103

Ab Initio Study of Geometries and Force Fields of Diphenylacetylene in the Ground State, Radical Cation, Radical Anion, and Lowest Excited Triplet State Atsuhiko Shimojima and Hiroaki Takahashi’ Department of Chemistry, School of Science and Engineering, Waseda University, Tokyo 169, Japan Received: April 21, 1993’

Ab initio calculations of geometries and force fields using the 4-31Gbasis set were carried out a t the RHF and R O H F versions of the SCF level on the ground state SO,radical cation R.+,radical anion R*-, and lowest excited triplet state T1 of diphenylacetylene. It was shown that the molecular geometry approaches a quinoidal structure in the following sequence: SO,R.+,R’-,and TI. Force constants were obtained in terms of local symmetry coordinates and were adjusted with the scale factors transferred from the ones determined in benzene and methylacethylene. Good agreement between observed and calculated normal frequencies was obtained for SO, Re+,and R’- but not for T I . For the TI state, the scale factors for the C-Ph stretch and phenyl skeletal stretches were found to be not transferable. In addition, off-diagonal force constant matrix elements representing the interactions between these coordinates of the different phenyl groups were overestimated, which may be correlated with the instability of the restricted Hartree-Fock solutions.1

Introduction In a preceding paper2we have reported time-resolved resonance and Raman spectra of the radical cation R*+,radical anion P-, triplet state T I of diphenylacetylene (DPA) along with those of isotopically (13C and deuterium) substituted analogues. It was found that the frequencies of the -C stretch and phenyl skeletal vibrations decrease systematically in the order, SO,R’+,P-,and TI, which was interpreted in terms of the bonding nature of the HOMO (highest occupied molecular orbital) and the antibonding nature of the LUMO (lowest unoccupied molecular orbital) with respect to the *-bonding of the -C triple bond and the phenyl ring. However, it was difficult to explain the frequency decrease of the C z C stretch on going from P+to P-,because the HOMO-LUMO considerations suggest that the degree of weakening of the CEC bond is approximately the same for these two radical ions. Also, it was shown that the Raman bands assignable to the C-Ph symmetric stretch exhibited a frequency decrease in the same sequence as the -C stretch. However, since the HOMO has antibonding nature and the LUMO has bonding nature with respect to the 7r-bonding of the C-Ph single bond, a frequency increase in this sequence is expected contrary to the observation. It seems plausible that the deviation from the simple HOMOLUMO considerations can be ascribed to vibrational coupling: the Raman band assigned to the C e stretch has a substantial contribution from the C-Ph symmetric stretch, the degree of which is expected to vary from species to species, SO,P+, R*-, and TI. The vibrational coupling is much more pronounced in the Raman bands assigned to the C-Ph symmetric stretch: in this case the real vibrational mode is considered to involve large contributions of the phenyl vibrational modes, mainly modes 1 and 12 (Wilson vibration number3). Therefore, in order to examine the validity of the HOMO-LUMO considerations it is necessary to carry out normal coordinate calculations to obtain optimized geometries and force constants of each of these species for comparison. As a first step to the normal coordinate calculations of DPA the present investigation was undertaken to obtain optimized geometries and force fields of the Sostate, R’+,R’-,and T1 state by ab initio calculations at the HF/SCF (Hartree-Fock/selfconsistent field) level. The primary concern of this investigation is the examination of whether or not the calculated geometries *Abstract published in Advance ACS Abstracts, August 15, 1993.

and force fields of the transients having open-shell electronic structures, viz., P+, P-,and TI,are consistent with experimental results.

Computational Procedure All calculations were carried out using the GAUSSIAN 86 and 90 packages of programs? Optimized geometries and force constants werecalculated at theRHF/SCF (restricted HF/SCF) level for SOand ROHF/SCF (restricted open-shell HF/SCF) level for R’+,P-,andTlusingthe4-3lGbasisset. Theinfluence of electron correlation on the optimized geometries was not taken into account in this calculation. Ab initio force constants were calculated in terms of Cartesian displacement coordinates at the optimized geometry. Since the ab initio calculations in the SCF level systematicallyoverestimate the force constants, adjustments with empirical scale factors are needed to bring the calculated frequencies into better agreement with the observed values. Usually the scaling is applied to the force constants in internal coordinates using, for instance, the relation F$j = (crc,)1/2Fi,,(where ct and cl are the scale factors associated with the internal coordinates Ri and RI, and F$, and F,, are scaled and unscaled force constant matrix elements, re~pectively),~ so that the diagonal elements of the force constant matrix associated with the same type of internal coordinates share a common scale factor. In order to transform the force constant matrix in Cartesian displacement coordinates, F,, into the force constant matrix in internal coordinates, F, using the relation F = {(BB’)-l)’. BF,B’(BB’)-l (where B is the transformation matrix between the Cartesian displacement coordinate vector X and the internal coordinate vector R with the relation R = BX and ’ denotes the matrix transpose), it is necessary to make the number of internal coordinates equal to the number of normal coordinates of the molecule by removing all redundant coordinates from the internal coordinatevector. In the present calculations we have introduced local symmetry coordinates instead of internal coordinates to perform the scaling and at the same time to remove redundant coordinates.

Results and Discussion

Local SymmetryCoordinates. The local symmetry coordinates adopted for a phenyl group and an ethynyl group are given in Table I, and the internal coordinates are shown in Figure 1. All

0022-3654/93/2097-9103$04.00/00 1993 American Chemical Society

9104

The Journal of Physical Chemistry, Vol. 97, No. 36, 1993

Shimojima and Takahashi

TABLE I: Local Symmetry Coordinates of DPA. The Atomic Numbering and the Notations of Internal Coordinates Are Given in Figure 1 local symmetry coordinate Phenyl Group (In-Plane)

SI= rl S2 = r2 + r3 + r5 + r6 S3 = r2 - r3 + rs - r6 S4 = r2 - r3 + 2r4 - r5 + r6 Ss = r2 - r3 - 2r4 - r5 + r6

s6 = r2 + r3 - rs - r6 Si Rl 4- R2 + R3 + R4 + R5 + R6 Sa = R1- 2R2 + R3 + &-2R5 + R6 S ~ = R I - R ~ + R ~ - R ~ S10' R1 R2 + R3- R4 + R5- R6 S11 3b(R1- R3-& + R6) ~ ( 2 A 1 +A1 - A3 - 2A4 - A5.~ + A6) Si2 = d(RI +-2R2 R3 - R4 2Rs - R6) - 3C(A2 + A3 - A S - A s ) SI3 = 81

-

+

approximate descriptionb C-Ph str CH str ( 2 ) CH str (7b) CH str (13) CH str (20a) CH str (2Ob) ring breath (1 ring str (8a) ring str (8b) Kekule ( 14) ring str + def 19a) ring str + def ( 19b)

C-Ph i.p. bend CH i.p. bend (3) CH i.p. bend (9a) SI^ 82 - 83 + 85 - 8 6 si6 82-83 2 8 4 - 8 5 & CH i.p. bend (15) CH i.p. bend (18a) SI7 = 8 2 + 83-85 - 8 6 CH i.p. bend (18b) Si8 8 2 - 83 - 2 8 4 - 85 + 8 6 Si9 = 2A1- A2- A3 + 2A4- A s - A6 ring i.p. def (6a) S20 A2- A3 + A s - A6 ring i.p. def (6b) trigonal (12 ) S21 A1 - A2+ A3- Ad+ A s - A6 Phenyl Group (Out-of-Plane) C-Ph O.D. bend CH o.p.*bend ( 5 ) CH 0.p. bend (loa) CH 0.p. bend (lob) CH 0.p. bend (1 1) CH 0.p. bend (17b) chair (4) boat (16a) ring twist (16b) si4

= 8 2 + 8 3 + 8s + 8 6

OH! str m - C i.p. bend OH!+ 0.p. bend C-Ph torsion

Normalizing factorsof the local symmetry coordinatesare neglected. The coefficients, u, b, c, and d, are determined numerically. Internal coordinates represent the displacements of bond lengths and angles. b Vibrational number of the phenyl group is from Wilson.3 the local symmetry coordinates were constructed so as to be orthogonal to the redundant condition given in this table. The coefficients, a, b, c, and d, appearing in the redundancy conditions and in the local symmetry coordinates, S11 and S12, were determined numerically (for benzene having D6h symmetry, these can easily be obtained analytically). Although the local symmetry of the phenyl groups of DPA is CZ, a t most, the 12 local symmetry coordinates related to the , S Z 8 s 3 0 , were phenyl ring skeleton, namely, S 7 S 1 2 , S 1 9 s 2 ~and chosen to be the same as the symmetry coordinates of benzene

/

\

Figure 1. Internal coordinates of diphenylacetylene. wr represents the

displacement of the out-of-plane angle at carbon Ci. tu represents the displacement of the ring CCCC dihedral angle around the C& bond.

TABLE II: Scale Factors Determined in Benzene and Methylacetylene local symmetry

approximate description scale factor Phenyl Group SI C-Ph str 0.8916O sd6 CH str 0.8306 s7 ring breath (1) 0.8255 S8, s 9 ring str (8a,b) 0.8044 SlO Kekuld (14) 0.9581 s11, SI2 ring str + def (19a,b) 0.8268 s13 C-Ph i.p. bend O.770Sb SI4418 CH i.p. bend 0.7708 SI93 s 2 0 ring def (6a,b) 0.7591 s21 trigonal ( 12) 0.7751 s 2 2 C-Ph 0.p. bend 0.7085' s23427 CH 0.p. bend 0.7085 S28 chair (4) 0.7477 s29, s 3 0 boat (16a,b) 0.7406 Ethynyl Group 0.7654 S31 C=C str (=--c-C bend 0.6583d s 3 2 3 S33 C-Ph torsion 0.8W s 3 4 a Common value with C-CH3 stretch. b Common value with CH i.p. bend. Common value with CH 0.p. bend. Considered to be the same as the scale factor of m - C H 3 . Assumed value. coordinate

itself having D~J,symmetry. Other local symmetry coordinates related to the bonds and angles involving hydrogen, S&, Sl4SI8 and S 2 3 S 2 7 , were constructed to be as close as possible to the symmetry coordinates of benzene. With this choice of local symmetry coordinates the vibrational modes of PA and DPA having phenyl groups can easily be understood on the basis of the normal modes of benzene. Also the direct comparison of the diagonal elements of the force constant matrix of these molecules may become feasible. For phenyl ring torsional vibrations, S 2 ~ S p 0we , have chosen the local symmetry coordinates which consist of the displacements of only the CCCC dihedral angles. Although the sum of the displacements of the CCCC, CCCH, and HCCH dihedral angles, (Ci-iCIci+iCi+2 + Ci-iWi+iHi+i + HICICi+iCi+2+ HICiCi+iHi+1)/4, may give a more diagonal representation of the torsional force field, the use of our symmetry coordinates leads to much simpler redundant conditions and also is compatible with a possible extension to polysubstituted phenyl groups. Scale Factor Determination. Scale factors of the phenyl and ethynyl groups were determined by a least squares fitting using the observed normal frequencies of benzene (Bz) and its isotopically substituted analogues, Bz-da, Bz-W6,6 and Bz- 1,3,5d3,7 and methylacetylene (MA) and its isotopically substituted analogues, MA-dl, M A - d 3 , and MA-dd: respectively, in terms of the local symmetry coordinates (Table I). They are listed in Table 11. In order to obtain a good fit between observed and calculated normal frequencies, different scale factors are necessary for each of the ring skeletal vibrations of benzene, namely, S7 (ring breath), SS(ring stretch), SIO (Kekul6 vibration), S11 (ring deformation), Si9 (ring in-plane deformation), Szl stretch (trigonal vibration), S28 (chair deformation), and S Z (boat ~ deformation); the scale factors of vibrations S9, S l z , S20, and s30

+

Geometries and Force Fields of Diphenylacetylene should be equal to those of their degenerate counterparts, SS, S11, and S29, respectively. For the ring skeletal stretches, SrS12, a common scale factor couldbeusedexcept forSlowhichis theso-calledKekulCvibration. The force constant for this vibration is calculated to be much lower as compared with other ring stretches. Therefore, its scale factor should be larger than those for the rest, which makes it impossible to share a common scale factor. This effect has been recognized by Pulay et al.9 as being due to the appearance of the Hartree-Fock lattice instability,lJO and they had to introduce extra scale factors for the off-diagonalelementsof the interactions between the CC stretches and also between the CC stretch and the ring deformation, in addition to the usual scale factor for the CC stretch. When the local symmetry coordinates which we have adopted in the present calculations are used, introduction of such extra off-diagonal scale factors are not necessary. By simply applying a different scale factor to the force constant of the Kekul6 coordinate Slo, the same effect as the introduction of the extra scale factors for the off-diagonal elements of the CC stretch interactions is automatically attained. This is one advantage of the use of local symmetry coordinates for both the scaling and the elimination of redundant coordinates. Only one scale factor is required for each of the groups of local symmetry coordinates involving hydrogen: all C H stretches can share a common scale factor and so can all C H in-plane bends and all C H out-of-plane bends. We have also calculated the force fields of benzene and methylacetylene using the 4-31G* basis set and found that the inclusion of polarization functions (d-orbitals) as the orbitals of carbon atoms gives much better force constants for the out-ofplanevibrations (CH out-of-plane bend for benzene and C 4 - H in-plane and out-of-plane bends for methylacetylene) than the simple 4-31G basis set. However, the use of the 4-31G* basis set for force field calculations of such large molecules like PA and DPA is not practical because of too much computation. Therefore, the 4-3 1G basis set was used throughout, disregarding the possibility of poor agreement between observed and calculated frequencies of out-of-plane vibrations. The scale factors for the C-Ph in-plane bend and C-Ph outof-plane bend are not determined in benzene and methylacetylene. Their values are set equal to those of the C H in-plane bend and C H out-of-plane bend, respectively. The scale factor for the force constant of the C-Ph torsion, the torsion around the molecular axis, is not determined either. Its value is assumed to be 0.8. Scale factors for the C-Ph stretch and C e - P h bend are considered to be not much different from those of the C-CH3 stretch and CEC-CH~ bend, respectively. In order to examine the frequency adjustability of the scale factors given in Table 11, the observed and calculated frequencies of benzene and its isotopically substituted analogues are compared in Table 111, those of methylacetylene and its isotopically substituted analogues in Table IV. It is seen that the agreement between the observed and calculated frequencies is, in general, excellent for these molecules, assuring a good adjustability of the scale factors. Also, in order to examine the transferability of the scale factors toother ground-state molecules, ab initio calculations of the force constants of phenylacetylene (PA) were carried out. The observed and calculated normal frequencies of PA are given in Table V. The very good agreement between them except for the C-Ph in-plane bend and C-Ph out-of-plane bend, for which the assumed values of the scale factors were used, strongly assures a good transferability of the scale factors listed in Table I1 to in-plane vibrations. The agreement between observed and calculated frequencies of C H stretches is not particularly good for all the molecules calculated. This is attributable to the fact that the anharmonicity S19,

The Journal of Physical Chemistry, Vol. 97, No. 36, I993 9105 of C-H stretches is much larger than that of C-D stretches, and therefore, the complete adjustment of both frequencies with a common scale factor may not be accomplished. It is also probable that overtone and combination bands often lie in the 3000-cm-1 region and observed C H stretches may be shifted from their original position due to Fermi resonance with them. With regard to the vibrational assignment of a phenyl group, one point should perhaps be mentioned. Usually modes 19a and 19b (1479 cm-1 in benzene) are considered to be characterized as the mixed modes of ring stretch in-plane deformation with a minor contribution of the C H in-plane bend, and modes 18a and 18b (1036 cm-l in benzene) as the C H in-plane bend with a minor contribution of the ring stretch in-planedeformation.11 The PED (potential energy distribution) in Table I11 (S11,63%; S17, 30% for 18a, whereas S17, 70%; S11, 37% for 19a) tells us that the characterizations of 19a (19b) and 18a (18b) may better be reversed. However, in the deuterated species, benzene-&, the PED is consistent with the usual characterizations: S17, 61%; S11, 32% for 18a (812 cm-l); SI^, 65%; Sl7, 40% for 19a (1330 cm-1). This means that in the normal species the intrinsic frequency of the C H in-plane bend is slightly higher than that of the ring stretch in-plane deformation at around 1300 cm-1 and, by coupling one component having a larger contribution of the C H in-plane bend, goes up to 1479 cm-1 while the other, with a larger contribution of the ring stretch deformation, comes down to 1036 cm-I. In contrast, since the intrinsic frequency of the CD in-plane bend is much lower than that of the ring stretch deformation, the component with a larger contribution of the ring stretch deformation is upshifted slightly to 1330 cm-1 while the component with a larger contribution of the C H inplane bend is slightly downshifted to 812 cm-1 in the deuterated species. Optimized Geometries. Optimized geometries of SO, Re+,P-, and TI determined by using the 4-31G basis set at the R H F and ROHF versions of the SCF level are given in Table VI. All the molecular species are in planar and linear structures. The optimized geometry of Soagreesvery well with theX-ray results.12 This may be considered to provide an assurance to the accuracy of the calculation at the HF/SCF level using the 4-31G basis set as far as the optimized geometry is concerned. It is seen in this table that the C e bond lengthens in the sequence SO,R*+= Pand T1, which corresponds very well with the prediction from HOMO-LUMO considerations but not exactly with the observed Raman frequencies of the C = C stretch: 2217 cm-1 (SO),2142 cm-I (P+), 2091 cm-l (Re-), and 1974 cm-1 TI).^ Also, the C-Ph bond is seen to shorten in the same sequence, suggesting that the C-Ph bond strengthens and, hence, the force constant of the C-Ph stretch increases in this sequence,again in good accord with the prediction from HOMOLUMO considerations but in almost opposite trend with the observed frequencies of the C-Ph stretch: 1141 cm-l (SO), 1144 cm-1 (Re+), 1134 cm-l (P-), and 1120 cm-1 (TI). This problem will be discussed later. It is also readily recognized from this table that the geometries of the transients approach a quinoidal structure in the above sequence with the structure of P-approximately the same as that of R*+,indicating thevalidity of the simple HOMO-LUMO considerations. The geometry of TImay be regarded as an almost complete quinoid. Normal Coordinate Calculations. Observed and calculated normal frequencies of the SOstates of DPA and its isotopically substituted analogues,SO-l3C,So-ds, and SO&, are given in Table VII. The PEDS of isotopically substituted analogues may differ substantially from that of the normal species given in the table. The vibrational mode description corresponds to the PED of the normal species. The agreement between observed and calculated frequencies is very good. The agreement of the Cstretch at 2217 cm-1 is slightly worse as compared with other vibrations.

+

+

+

+

+

+

9106 The Journal of Physical Chemistry, Vol. 97, No. 36, 1993


TABLE III: Observed' and Calculated Normal Frequencies of Benzene (Bz) and Its Isotopically Substituted Analogues, Bz-& Bz-13Cs, and Bz-1,3,5-dk and the PED for Bz approximate Bz BPd6 Bz-W6 BZ-1,3,5-d3 Vib no! 1 2 3 4

obs 992 3059 1346 703 989

calc 992 3083 1357 709 1003

obs 945 2293 1055 599 830

calc 945 2289 1056 584 862

obs 957 3034 1333 680 981

calc 957 3071 1346 689 991

ring def

606

607

579

579

589

586

CH str

3046

3050

2266

2253

3024

ring str

1596

1598

1553

1555

CH i.p. bend

1178

1169

869

1Oa b 11

CH o.p.bend

849

839

CH o.p.bend

670

12 13 14 15 16a b 17a

trigonal CH str Kekul6 CH i.p. bend boat CH 0.p. bend

5 6a

descriotion ring breath CH str CH i.p. bend Chair CH o.p.bend

obs 955 2282 1322 697 918

955 2265 1310 699 936

592

593

3041

2274

2264

1542

1543

1575

1575

853

1171

1163

1101

1093

664

653

842

833

E"

71 1

705

662

496

486

669

660

Az''

533

519

1008 3068 1309 1149 404

1010 3040 1300 1158 405

963 2282 1282 823

981 3053 1273 1139 392

974 3031 1253 1154 393

Ai'

351

970 2242 1294 823 349

1003 3054 1252 911 375

1004 3063 1276 909 375

966

968

789

793

958

957

926

924

CH i.p. bend and ring str + def

1036

1037

812

808

1017

1017

833

827

ring str + def and CH i.p. bend

1479

1481

1330

1332

1450

1450

1412

1418

Ai' Ai' A2" E'

calc

PED for B i

b 7a

b 8a

b 9a

b

b 18a b 19a

&' E"

E'

b 2276 3073 3068 2274 3054 3058 3060 CH str 3054 b 0 Observed frequencics from ref 6 for Bz,Bz-d6, and Bz-I3C and ref 7 for Bz-1,3,5-d3. Wilson vibration n ~ m b e r . Only ~ the PED for Bz is given. Values less than 10% are neglected. 20a

TABLE IV Observed' and Calculated Normal Frequencies of Methylacetylene (MA) and Its Deuterated Analogues, MA-& MA-&, and MA-& and the PED for MA approximate MA MA-di description obs calc obs calc 2616 2624 3335 3365 AI CH str 2910 2929 2910 2928 CH3 sym str 2008 1999 2142 2145 C=C str 1391 1395 1391 1395 CH3 sym def C-C str 930 929 b 915 2980 2991 E CH3 deg str 2981 2991 1451 1440 CH3 deg def 1451 1440 CH3 deg rock 1036 1047 1035 1047 m - H bend 639 630 503 513 329 335 318 309 C=C-C bend a Observed frequencies from ref 8. Denotes not observed. This may indicate that the scale factor of t h e m stretch force constant determined in aliphatic methylacetylene is not appropriate for the aromatic DPA: much better agreement can be obtained with the scale factor determined by using the observed stretch frequencies of PA and DPA. The vibrational assignment based on PED is in good agreement with the results of normal coordinate calculations by BaranoviC and Colombo'3 except for the assignment of the C-Ph in-plane

MA-d3 obs calc 3335 3365 2142 2150 2110 2098 1111 1110 840 843 2235 2213 1049 1037 835 842 636 628 306 311

MA-dd obs calc 2624 2616 2107 2110 2008 1995 1107 1110 833 b 2235 2213 1049 1037 842 835 507 500 293 288

PED for MA CH str (95) CH3 sym str (100) C=C(83), C-C( 13) CH3 sym def (106) C-C(85), m ( 1 3 ) CH3 deg str (101) CHI deg def (94) CH3 deg rock (85) m - H bend (103) m - C bend (97)

bend belonging to the Bjg species. Although they assigned the band at 759 cm-i to this mode, our calculated frequency is 587 cm-1. PalmW assigned the band at 535 cm-* to this mode based on normal coordinate calculations, however, since he assigned this band also to the CMC-C out-of-plane bend of t h e l y s p i e s , an ambiguity still remains. The PED in Table VI1 shows that the band at 2217 cm-i which is empirically assigned to t h e m stretch involves a considerable

The Journal of Physical Chemistry, Vol. 97, NO. 36, 1993 9107

Geometries and Force Fields of Diphenylacetylene

TABLE V Observed. and Calculated Normal Frequencies of Phenylacetylene (PA) and Its Deuterated A ~ l o g u e PA-4, ~, PA-& and PA-d, and the PED for PA ~~

AI

BI

A2 B2

approximate description e - H str 2 20a 13 G=C 8a 19a C-Ph str 9a 18a 12 1 6a 20b 7b 8b 19b 3 14 15 18b =--H i.p. bend 6b C-Ph i.p. bend m - C i.p. bend 17b 10b 16b 5 1Oa 11

obs 3332 3078 3067 3047 2120 1601 1488 1192 1175 1028 998 760 465 3096 3058 1573 1447 1330 1282 1157 1070 649 613 518 152 968 842 418 985 915 756

calc 3336 3085 3070 3050 2140 1609 1495 1202 1174 1028

4 C=C-H 0.p. bend C-Ph 0.p. bend

689 613 530

689 630 5 29

691 482 531

689 478 564

639 612 470

642 617 461

637 415 491

634 442 516

16a =-C

349 140

355 135

340

335 129

330

333 129

322

318 123

a Observed

0.p. bend

PA

lo00

759 463 3078 3059 1577 1445 1327 1286 1163 1077 649 619 509 156 97 1 836 404 996 921 759

PA-dl obs calc 2609 2604 3086 3078 3070 3066 3046 3050 1996 1984 1609 1600 1494 1488 1195 1193 1174 1175 1025 1028 998 lo00 755 758 458 459 3096 3078 3058 3059 1573 1577 1441 1445 1329 1327 1278 1286 1157 1163 1070 1077 450 482 625 623 563 531 154 146 968 971 841 836 419 404 985 996 916 921 759 757

b

C-Ph CrC2

crc3

crc4

b

PA-ds obs calc 2610 2604 2300 2290 2292 2272 2284 2250 1980 1996 1571 1574 1378 1379 1136 1131 867 862 834 838 952 957 107 709 449 448 2287 228 1 2279 2259 1553 1538 1323 1325 1034 1036 1275 1283 841 839 821 819 477 444 601 602 513 555 146 141 765 794 704 650 349 348 825 859 767 774 553 552

b

PED for PA

frequencies by King and s0.1~ Denotes not observed.

TABLE VI: Optimized Geometries of So, R'+, R.-, and TI of DPA. Values in Parentheses Are Observed Valued2 so R'+ R'TI

c=c

PA-ds obs calc 3332 3336 2290 2300 2272 229 1 2250 2282 2122 2140 1572 1575 1382 1379 1136 1137 868 862 839 834 956 957 716 712 454 454 2287 228 1 2279 2259 1538 1557 1325 1323 1034 1036 1274 1283 842 839 822 819 648 646 602 596 502 497 151 b 766 794 704 650 348 349 825 859 768 774 553 540

Bond Length (A) 1.194 (1.198) 1.224 1.431 (1.438) 1.384 1.392 (1.386) 1.413 1.381 (1.376) 1.370 1.384 (1.368) 1.392 Bond Angle (deg) 119.0(119.1) 119.6 120.4 (120.3) 119.9 120.2 (120.0) 119.7 119.8 (120.1) 121.2

1.224 1.387 1.424 1.372 1.394 116.1 121.4 121.6 117.9

1.257 1.341 1.443 1.359 1.402 116.9 120.8 121.0 119.5

contribution (20-30%) of the C-Ph stretch. The band at 1141 cm-1 which is assigned to the C-Ph stretch is actually a heavily mixed mode of C-Ph stretch, phenyl mode 12, and phenyl mode 1 with the contribution of the three being approximately equal. The band at 999 cm-1 which is assigned to the trigonal vibration is a mixed mode of the trigonal vibration and the ring breath with their contributions being both approximately 50%. Although the band at 104 cm-I is assigned to the ring breath, thevibrational mode of this band is heavily mixed, and besides, the contribution of the ring breath is small (only 8%); it should be noted that the ring breathing vibration is not concentrated on one mode but is distributed over several ring modes. The agreement of out-ofplane vibrations is not very good as anticipated. In the case of Sods analogues, the one-to-one correspondence of the frequencies

to the normal speciesmay not be possible because of the difference in molecular symmetry. Observed and calculated normal frequencies of the radical cation R'+ of DPA and its isotopically substituted analogues, R'+-W, R'+-dlo, and R'+-ds, are given in Table VIII. Although observed frequencies are available only for the A, species (Al species for R'+-ds) due to time-resolved resonance Raman spectroscopy,2 all the calculated frequencies are given in this table in order to show that the calculated frequencies of other symmetry species are also reasonable values. The very good agreement between the observed and calculated frequencies of the A, species (and AI species) and the fact that all thecalculated values of the normal frequencies belonging to other symmetry species are those which are expected for the normal modes of R'+ strongly suggest that the scale factors listed in Table I1 have good transferability to the radical cations as well. Observed and calculated normal fequencies of the radical anion R'-of DPA and its isotopically substituted analogues, RLJ3C, R'--dlo, and R'--ds, are given in Table IX. Here too, all the calculated frequencies are shown despite the lack of observed frequencies except for those belonging to the A, species. The good agreement between observed and calculated normal frequencies indicates that the scale factors determined for molecules having a closed-shell electronic structure are transferrable to radical anions having an open-shell electronic structure. Observed and calculated normal frequencies of the lowest excited triplet state T I of DPA and its isotopically substituted analogues, T l - W , TI&, and TI-&,, are given in Table X. It is



TABLE MI: Observed' and Calculated Normal Frequencies of the So State of DPA and I b Isotopically Substituted Analogues, and the PED for

SO-'%, S&O, S&

approximate description CH str (2) CH str (20a) CH str (13) c=--C str ring str (8a) ring def (19a) CH i.p. bend (9a) C-Ph str CH i.p. bend (18a) trigonal (12) ring breath( 1) ring def (6a) 2 2Oa 13 8a 19a C-Ph str 9a 18a 12 1 6a CH str (20b) CH str (7b) ring str (8b) ring def (19b) CH i.p. bend (3) Kekuld (14) CH i.p. bend (15) CH i.p. bend (18b) ring def (6b) C-Ph i.p. bend m C - C i.p. bend 20b 7b 8b 19b 3 14 15 18b 6b m - C i.p. bend C-Ph i.p. bend CHo.p.bend ( 5 ) CH 0.p. bend (loa) CH 0.p. bend (1 1) chair m - C o.p.bend boat C-Ph 0.p. bend

so obs 308 1 3054 3042 2217 1596 1482 1178 1141 1026 999 704 256 3062 3052 3040 1600 1499 1310 1176 1028 1001 845 539 3062

SO-W

calc obs b 3086 b 3070 b 3050 2256 2183 1606 1596 1490 1482 1174 1178 1145 1140 1027 b 999 999 704 699 b 255 b 3086 b 3070 3050 b b 1616 b 1510 1316 b b 1174 b 1029 b 999 b 841 b 538 b 3079 b 3059 b b 1565 1577 b 1443 1444 b 1326 1326 b 1277 1287 1160 1163 b 1090 1077 b 626 b 633 587 535 b b b 161 b 3082 3079 3022 3059 b b 1574 1577 b 1444 1445 b 1328 1327 b 1280 1287 1158 1163 b 1070 1077 b 620 b 621 b 473 458 43 b b 986 994 b 919 b 920 759 b 770 692 b 688 614 b b 416 380 b 139 151 b 5 983 994 b 1Oa b 914 918 11 b 756 756 chair b 688 690 C-Ph 0.p. bend b 511 510 b 279 boat 289 b 47 b C=C-C o.p,bend CH 0.p. bend (17b) 965 b 969 CH 0.p. bend (lob) 840 b 834 ring twist 399 b 405 17b b 965 969 10b b 845 834 ring twist b 40 1 403 C-Ph torsion b 11 b a Observed frequencies of SOand Sodlo are from ref

So-dio

SO-ds

calc obs calc obs obs PED for SO 3086 2278 2291 AI b 3056 3070 2278 2272 b 3070 3060 2278 2250 b 3050 2214 2217 2255 2217 2255 1565 1576 1606 1562 1570 1394 1404 1490 1359 1367 1178 1174 1174 867 860 1112 1111 1145 1086 1086 1027 826 827 b 796 999 999 959 955 999 678 68 1 699 655 662 255 b 245 b 250 3086 2275 2291 b 229 1 3070 2275 2272 b 227 1 3050 2258 2250 b 2250 1615 1569 1584 1600 1612 1509 1412 1430 1492 1501 1269 1310 b 1225 b 1174 b 872 852 868 1029 763 768 b 1028 999 960 957 956 959 836 849 846 845 b b 535 523 524 531 3079 2289 2281 Bi b 2281 b 2260 3059 2275 2260 1577 1538 1538 b 1538 1444 1320 1325 b 1327 b 1036 1326 b 1036 1287 1273 1284 b 1284 b 1163 b 839 839 1076 b 819 b 819 630 b 614 b 605 b 570 580 b 577 161 b 151 b 156 3078 2289 2281 b 228 1 b 2260 3058 2275 2259 1577 1538 1538 b 1577 1445 1445 1321 1326 b 1327 1034 1036 b 1327 1287 1275 1284 b 1287 b 1163 1163 843 839 b 1077 1077 819 819 621 599 596 b 628 452 449 442 b 450 b 40 42 b 43 994 b 860 Bz b 994 920 b 783 b 919 768 b 656 760 b 688 688 b 570 b 607 b 514 b 587 414 b 376 b 391 139 b 130 b 134 994 b 857 b 858 918 766 770 b 779 756 639 626 647 b 688 550 537 b 533 509 452 444 474 b 217 b 263 b 27 1 47 b 45 b 46 969 b 793 Az b 969 834 b 649 b 834 405 b 350 b 404 969 782 793 b 793 b 834 665 649 649 403 b 349 b 349 11 b 10 b 10 13, and those of S0-I3Cand So-ds are from ref 2. Denotes not observed.

seen that the calculated fequencies of the stretch, phenyl 8a mode, and C-Ph stretch of the A, species do not agree with the observed frequencies, and those of 8a mode and C-Ph stretch

of the Bi, species are abnormal in spite of the fact that other vibrational modes exhibit reasonably good agreement. Although the calculated normal frequencies of the symmetry species Bl,,


The Journal of Physical Chemistry, Vol. 97, No. 36, I993 9109

TABLE VIII: Observed’ and Calculated Normal Frequencies of Re+of DPA and Its Isotopically Substituted Analogues, R’+-W, R’+-Aa and R’+-& and the PED for R’+ R’+ p+-13C R’+-dlo R’+-ds amroximate descrbtion obs calc obs calc obs calc obs calc PED for R’+ b 3107 b 3107 CH str (2) b 2307 A1 b 3107 S2(76). Sd23) CH str (2Oa) b 3088 b 3088 b 2285 b 3088 CH str (13) b 3079 b 3079 b b 3078 2274 2142 2167 2103 2128 2142 2166 c=--C str 2142 2166 8a 19a 9a

C-Ph str 18a 12 1

6a 20a 13 8a 19a

C-Ph str 9a 18a 12 1 6a

CH str (20b) CH str (7b) 8b 19b 14 3 15 18b 6b

C-Ph i.p. bend m - C i.p. bend 20b 7b 8b 19b 14 3 15 18b 6b

C=C-C i.p. bend C-Ph i.p. bend CH 0.p. bend ( 5 ) CH 0.p. bend (loa) CH 0.p. bend (11) chair

c----C-C 0.p. bend boat

C-Ph 0.p. bend 5 1Oa

11 chair

C-Ph 0.p. bend boat

(=--c-C o.p.bend CH 0.p. bend (17b) CH 0.p. bend (lob)

1590 1464 1188 1144 b

988 703 b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

1581 1466 1185 1131 1011 992 696 259 3106 3088 3079 1550 1473 1356 1164 1011 990 828 528 3101 3085 1537 1429 1346 1310 1167 1085 621 566 154 3101 3085 1538 1431 1346 1313 1167 1086 608 461 45 1016 951 774 655 597 396 124 1016 951 765 653 476 259 45 985 825 380

1590 1464 1188 1140 b


1581 1466 1185 1130 1011 992 696 259 3106 3088 3079 1549 1471 1348 1163 1011 990 824 525 3101 3085 1537 1429 1346 1310 1167 1085 618 560 154 3101 3085 1538 1431 1346 1313 1167 1086 608 455 44 1016 951 773 654 590 394 124 1016 951 765 653 475 257 44 985 825 380 986 825 391 53

ring twist 17b 985 825 10b 391 ring twist C-Ph torsion 53 a Observed frequencies from ref 2. Denotes not observed. Bzg, Bse, Au, Bz,, and B3, are not shown in this table due to the lack of observed values; all of them are of reasonable values. Of particular interest is that the calculated frequencies of the 8a mode (1458 cm-I) and C-Ph stretch (1068 cm-l) of the A,

1551 1327 867 1101 b


1539 1327 859 1089 823 950 660 249 2306 2285 2274 1501 1408 1241 847

1586 1404 1180 1123

858

b

950 759 515 2299 2278 1478 1349 1298 1038 843 825 603

988

b

948 680 b b b b

1534 b

1284 863

B1

550

145 2299 2278 1479 1350 1301 1038 843 826 585

445 42 870 794 663

B2

555

503 357 116 869 789 637 505

425 244 42 805

641 329 807 643 337 48

A2

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

1571 1391 1172 1108 1011 950 675 254 2307 2285 2274 1516 1467 1280 855

848 990 786 521 3101 3085 1537 1430 1346 1312 1167 1085 616 557 150 2299 2278 1479 1349 1300 1038 843 826 593 453 43 1016 951 769 649 575 372 120 870 791 657 504 453 252 44 986 825 333 806 642 386 51

species are much lower than their observed frequencies (1565 and 1120 cm-1, respectively) while those of the B1, species (2930 and 1557 cm-1, respectively) are much higher than their expected values. This is attributable to the calculated force field in which



TABLE M: Observed' and Calculated Normal Frequencies of R'- of DPA and Its Isotopically Substituted Analogues, R'--W, R'--dab and R'--dk and PED for R'approximate R'R*--l3C description obs calc obs calc b CH str (2) b 3056 3056 b b 3040 3040 CH str (20a) b 2999 CH str (13) 2999 b CMC str 2091 2129 2053 2091 8a 1582 1598 1582 1598 1453 1461 1453 1461 19a 1173 1170 1173 1170 9a C-Ph str 1134 1146 1134 1145 1003 1003 b b 18a 98 1 975 981 975 12 1 689 684 689 684 6a 257 257 b b b 2 b 3054 3054 b 3040 3040 b 20a b 2998 2998 b 13 b 1519 1517 b 8a 1467 b 19a 1468 b b C-Ph str 1368 b 1362 1137 b b 1136 9a b 1003 1003 b 18a b 12 b 938 936 b 783 1 785 b b b 524 521 6a CH str (20b) b 3045 b 3045 b 3003 CH str (7b) 3003 b b 8b 1503 b 1503 19b 1427 b b 1427 14 1329 b b 1329 1279 3 1280 b b 15 1139 b b 1139 18b 1062 1062 b b 6b b b 623 621 b C-Ph i.p. bend 573 b 566 155 b b 155 C=C-C i.p. bend b 3046 b 3046 20b b b 3003 3003 7b b 1503 1503 b 8b 1428 1428 b b 19b 1329 b 1329 14 b 1281 b 1282 3 b 1139 1139 b 15 b 1063 1063 18b b b 6b b b 616 616 b b 463 CMC-C i.p. bend 457 43 43 b b C-Ph i.p. bend CH 0.p. bend (5) b 943 b 943 b b CHo.p.bend(11) 806 806 chair 706 705 b b CH 0.p. bend (loa) 665 664 b b C-Ph 0.p. bend 526 521 b b 361 b b boat 364 b C e - C o.p.bend 134 134 b b 943 5 b 943 805 b b 11 805 700 b chair 700 b b b 665 1Oa 665 466 C-Ph 0.p. bend 467 b b b b 225 227 boat b 45 b 45 CMC-C 0.p. bend CHo.p.bend (17b) b 937 b 937 b b CH 0.p. bend (lob) 782 782 ring twist 415 b b 415 17b b 937 b 937 10b 785 785 b b b b ring twist 416 416 C-Ph torsion b b 60 60 a Observed frequencies from ref 2. Denotes not observed.

R'--dlo obs calc b 2266 b 2247 b 2210 209 1 2129 1545 1563 1314 1327 858 848 1092 1096 815 b 939 942 648 649 247 b b 2266 b 2246 b 2208 b 1471 1410 b 1237 b

the diagonal force constant matrix elements for the coordinates SI(C-Ph stretch) and& (8a) and the off-diagonal forceconstant matrix elements for the interactions between these coordinates

b b b b b b b b b b

b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b

Ai

808

847 927 728 511 2253 2216 1442 1372 1248 1026 822 814 602 558 146 2254 2216 1442 1372 1250 1027 823 814 591 446 40 803 699 595 518 468 333 125 802 690 592 506 404 214 43 759 608 368 760 613 363 55

Bi

Bz

A2

R'--dS obs calc b 3055 b 3040 2998 b 209 1 2129 1574 1584 1445 b 1164 1152 1110 1117 b 1003 976 962 668 663 252 b b 2266 b 2247 2209 b 1531 1501 1421 1409 1264 1279 849 840 b 825 928 942 753 b 517 b b 3046 3003 b 1503 b 1428 b 1329 b 1281 b b 1139 1063 b 620 b 565 b 151 b b 2254 2216 b 1442 b b 1372 1249 b 1027 b b 822 b 814 597 b 454 b b 41 b 943 b 806 704 b 665 b 52 1 b b 346 b 130 b 802 693 b 593 b b 497 b 429 22 1 b b 44 b 937 b 783 b 416 b 759 b 610 b 363 b 58

PED for R'-

of the different phenyl groups, (SI,SI'),(SI, SS'), and (S8,SS'), are abnormally large as shown in Tables XI and XII. Also, the force constants associated with the coordinates S, ( r i m breath)

The Journal of Physical Chemistry, Vol, 97, No. 36, 1993 9111


TABLE X Observed’ and Calculated Normal Frequencies of the TI State of DPA and Its Isotopically Substituted AM~O~WS, and PED for Tlb Tl-W. T1-dlO,and T 1 - L approximate description CHstr (2) CH str (20a) CH str (13) C=C str 8a 19a

Ti

TI-IT obs calc C A, C 3088 C C 3075 3051 C C 1974 1942 2077 1458 1565 1565 1426 1436 1440 1174 1174 9a 1180 1120 C-Ph str 1067 1120 12 975 975 979 18a 888 887 C C 1 664d 671 67od 67 1 255 255 6a C C BI, CH str C 3100 C 3100 CH str 3078 3078 C C CH str 3057 C c 3057 2924 8a C 2930 C 1551 C-Ph str 1557 C c 1409 1411 19a C C 1194 1194 9a C c 1008 1008 18a C C 12 C 981 C 981 1 832 c C 836 6a C C 523 521 Observed freuuencies from ref 2. Only the freuuencies of the A. species. Denotesnot observed. Mean value of tde Fermi double:. obs

calc 3088 3075 3051 2113 1458 1426 1180 1068 979

Ti-dio obs calc

TI-& calc PED for TI C 3094 2292 AI C C 2270 C 3077 C 2250 C 3055 1964 2113 1974 21 13 1384 1544 1517 1430 1281 1273 1419 1409 846 810 1149 1180 1087 1049 1109 1060 945 922 975 980 c 791 C 8 54 629 639 644 653 C 245 c 250 C 2291 C 2292 C 2267 C 2269 C 2248 2245 C C 2943 2957 1523 C 1547 1533 C C 1256 1232 1256 C 879 820 816 C 846 c 984 917 C 959 953 C 774 746 C C 509 C 516 and BI,species are given due to the lack of observed frequencies of other symmetry

TABLE XI: Comparison of the Scaled Force Constants (Dia OMI Elements of the Force Constant Matrix) of the Stretch, C-Ph Stretch, and Phenyl Skeletal In-Plane P-,and TI Modes 1,6a, 8% 12,14, and 19a of SO,P+,

d

approximate description

so

force constants” R’+ R’-

TI 14.889 12.522 12.508 10.308 C=C str F(Sai, S ~ I ) 5.839 6.732 6.896 10.817* C-Ph str FWI,Si) 7.518 7.236 6.913 7.8836 ring breath (1) F(S7, S7) 6.729 6.368 5.953 1O.38Ob ring str (8a) Ss) 6.626 5.941 5.679 4.808 (8b) W 9 , Sg) Kekuld vib (14) F(S10, Slo) 4.109 4.367 4.415 3.819 4.134 3.781 3.702 3.444 ring str + def (19a) F ( S I ISI’) , ( 19b) F(Siz, Sd 4.149 4.261 4.097 4.255 ring def (6a) F(Sm Si91 0.827 0.815 0.810 0.798 (6b) F(Szo, Szo) 0.806 0.780 0.789 0.766 trigonal vib (12) F(Szl, S21) 0.836 0.837 0.831 0.835 0 md/A for stretches and md A for deformations. 6 Abnormal value due to probable appearanceof the instabilities of Hartree-Focksolutions.

TABLE XII: Comparison of the Scaled Off-Diagonal Force Constant Matrix Elements Between the C-Ph Stretch ( S ) and Phenyl Modes 1 and 8a (&), of Different Phenyl and TI. Denotes the Coordinates of Groups of &, P+,P-, the Other Phenyl Group So R’+ R‘TI F(S1, SI’) -0.026 0.225 4.009 -2.747

(e)

WI,S7‘)

F(S7, S7’) F(S7, Ss’)

0.017 0.021 -0.002 -0.006

F(S8, S i )

-0.005

W i , Ss‘)

-0.117 -0.235 0.059 0.114 0.224

-0.145 -0.229 0.266 0.391 0.584

1.690 3.801 -1.057 -2.407 -5.465

appear to be somewhat large. Since the structure of the phenyl groups of TIis almost quinoid-like, it is naturally anticipated that the scale factors of the C-Ph stretch and the phenyl 8a mode determined in benzene in the SO state may not exhibit good transferability. However, the calculated frequencies of these vibrational modes deviate too much from the observed or expected values to be adjustable by scale factors. One may correlate these abnormally large force constants of the T1 state associated with the skeletal coordinates along the molecular axis, viz., Si, S7, and SSwith the instability of the

obs

restricted HartreeFock solution.’ As the optimized geometry of the TIstate is such that the two phenyl groups are almost quinoid-like and the bond order of the C = C bond is decreased quite a bit while that of the two C-Ph bonds is increased considerably (Table VI), the molecule may be regarded as an extended conjugated system. It has been shown that for sufficiently long conjugated systems the HartreeFock solution is unstable (in this case “triplet” instability) and there exists a symmetry-breaking HartreeFock solution which is lower in energy than the usual symmetry-adapted Hartree-Fock solutionl.9 and is characterized by charge-density waves’s exhibiting bondorder alterations or spin-density waves.16.17 We found that the ROHF method gives a symmetry-breaking structure which is lower in energy than the symmetry-adapted structure: an asymmetric structure in which one phenyl group takes a quinoid structure while the other phenyl group is in a normal phenyl structure is lower in energy than the symmetric structure having D2h symmetry with the two phenyl groups taking the same quinoid-like structure. This asymmetric structure, however, cannot explain the observed resonance Raman spectra of the TIstate2 and, therefore, does not correspond to the actual TI state structure. The existence of the symmetry-breaking structure which is lower in energy than the symmetry-adapted structure should be ascribed to the incompleteness of the ROHF version of the HartreeFock method, and the abnormal values of the force constants of the C-Ph stretch and phenyl 8a mode are considered to arise from the instability of the symmetryadapted structure. The occurrence of the instability of the restricted HartreeFock solutions is not very surprising since one can expect energy lowering due to spin polarizations if the restriction of the double occupancy of the orbitals is lifted. Indeed, we found that the use of the U H F (unrestricted HartreeFock) method gives good force constants for the T1 state also. We shall present the results of the U H F calculations of the optimized geometries and force constants of P+, P-,and T1 of DPA in detail in a forthcoming paper.18 Comparison of Force Constants. The scaled force constants (diagonal elements of the force constant matrix) of the stretch, C-Ph stretch, and phenyl in-plane skeletal modes 1, 6a

9112 The Journal of Physical Chemistry, Vol. 97, No. 36, 1993 (6b), 7, 8a (8b), 12, 14, and 18a (18b) of SO,Re+,and Re- are compared in Table XI. It is seen that the force constant of the C=C stretch reduces on going from SOto Re+and R*-, with the values of Re+and R'being approximately equal, in good accord with the HOMOLUMO prediction. This means that the bond order of the C=C bond of P-is not much different from that of R'+ and the difference in the observed C=C stretch frequencies between P+ and Re- (2142 cm-1 for R*+ and 2091 cm-' for R*-) should be attributed to vibrational coupling; comparisons of the PED in Tables VII-X reveal that the contribution of SI(C-Ph stretch) increases in the sequence, SO,P+, R*-, and TI, which accounts for the reduction of the C=C stretch frequency on going from P+to Re- despite the almost equal values of their C=C stretch force constants. The force constant of the C-Ph stretch is seen to increase in the order SO,R*+,and P-,with the values of R'+ and Pbeing not much different, again in accord with the HOMO-LUMO prediction. This trend, however, is not in good accord with the observed C-Ph stretch frequencies (1 141 cm-' for SO,1144 cm-' for P+, and 1134 cm-1 for P-). This discrepancy is also attributable to the vibrational coupling as is seen in the PED given in Tables VII-IX; the contribution of S1 reduces while that I increases in the above sequence, leading of S ~(trigonalvibration) to the gradual reduction of the C-Ph stretch frequency in the above sequence. The comparison of the force constants of phenyl vibrations is more involved. The force constants of 8a (8b) and 19a (19b) decrease in the order SO,P+, and R*-, while that of the Kekul6 vibration increases in the same sequence. On the other hand, the force constants of in-plane skeletal deformations 6a (6b) and 12 do not exhibit appreciable changes on going from SOto P-.Both the HOMO and LUMO have *-bonding character with respect to some of the C-C bonds of the phenyl ring, but they also have wantibonding or r-nonbonding character with respect to the rest of the C-C bonds. Therefore, while some of the C-C bonds are weakened, other C - C bonds of phenyl groups are strengthened in R*+, P-,and T I , with different degrees of weakening and strengthening among them. This may be the reason why some forceconstantsincrease whileothers decrease or remain practically unchanged on going from SOto TI.

Shimojima and Takahashi The off-diagonal force constant matrix elements representing the interactions between the C-Ph stretch (SI) and phenyl skeletal modes 1 (ST)and 8a (SS)of different phenyl groups are given in Table XII. It is interesting to note that although their values are negligibly small in SO as are usually the case, they are substantial in Re+and P-. This indicates that the correlation between the vibrationsalong the molecular axis of different phenyl groups becomes larger on going from SOto Re+, R*-, and T I , which parallels the larger electron delocalization of the radical ions and triplet state as compared with So.

Acknowledgment. The authors are grateful to the Computer Center, Institute for Molecular Science, Okazaki National Research Institutes, for the use of the HITAC M-680H and Library Program. References and Notes (1) Cizek, J.; Paldus, J. J . Chem. Phys. 1967, 47, 3976; 1970,52, 2919. (2) Hiura, H.; Takahashi, H. J. Phys. Chem. 1992, 96, 8909. (3) Wilson, E. B., Jr. Phys. Rev. 1934, 45, 706. (4) Frisch,M. J.;Binkley, J. S.;Schlegel, H. B.;Raghavochari,K.;Melius, C. F.; Martin, R. L.; Stewart, J. J. P.; Babrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; Defrees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. GAUSSIAN 86; Carnegie-Mellon Quantum Chemistry Publishing Unit: Pittsburgh, PA, 1984. (5) Fogarasi, G.; Pulay, P. J . Mol. Struct. 1977, 39, 275. (6) Painter, P. C.; Koenig, J. L. Spectrochim. Acta 1977, A33, 1019. (7) LaLau, C.; Snyder, R. G. Spectrochim. Acta 1971, A27, 2073. (8) Duncan, J. L.; Mckean, D. C.; Nivellini, G. D. J. Mol. Struct. 1976, 32, 255. (9) Pulay, P.; Fogarasi, G.; Boggs, J. E. J. Chem. Phys. 1981,74,3999. (10) Toyota, A.; Tanaka, T.; Nakajima, T. Int. J . Quantum Chem. 1976, 10, 917. (1 1 ) Dollish, F. R.; Fateley, W. G.; Bentley, F. F. Characteristic Roman Frequencies of Organic Compounds;John Wiley & Sons: New York, 1974. (12) Mavridis, A.; Moustakali-Mavridis,I. Acta Crystallogr. 1977,833. 3612. (13) BaranoviC, G.; Colombo, L. J . Mol. Srruct. 1986, 147, 276. (14) Palm& K. Spectrochim. Acta 1988, MA, 341. (15) Fenton, E. W. Phys. Rev. Lett. 1968, 21, 1427. (16) Fukutome, H. h o g . Theor. Phys. 1968,40, 1227. (17) Harris, R. A.; Falikov, L. M. J . Chem. Phys. 1969,50,4590; 1969, 51, 5034. (18) Shimojima, A.; Takahashi, H. To be published. (19) King, G. W.; So, S. P. J . Mol. Spectrosc. 1970, 36, 468.

Ab Initio Study of Geometries and Force Fields of Diphenylacetylene in

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