Theoretical prediction of the vibrational spectrum of fluorene and

G. F. Musso, R. Narizzano, P. Piaggio, and G. Dellepiane , A. Borghesi. The Journal of Physical Chemistry 1996 100 (40), 16222-16231. Abstract | Full ...
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12223

J. Phys. Chem. 1994, 98, 12223-12231

Theoretical Prediction of the Vibrational Spectrum of Fluorene and Planarized Poly@-phenylene) Lilee Cuff and Miklos Kertesz* Department of Chemistry, Georgetown University, Washington, D. C. 20057 Received: March 18, 1994; In Final Form: June 28, I994@

The a priori predicted vibrational spectra of fluorene and newly synthesized methylene bridged planarized poly@-phenylene)(PPP) are presented. The calculated vibrational frequencies of fluorene are compared to those obtained experimentally to resolve differences between earlier experiments. As a result, some reassignments are made. The vibrational spectra of planarized PPP are extrapolated using oligomers as a starting point within the scaled quantum mechanical oligomer force field (SQMOFF)method. The basis set used is split valence double-5 quality 3-21G. The scaling factors are transferred from benzene and cyclopentadiene as fixed parameters in the polymer calculations. Planarized PPP is predicted to have an inter-ring stretching frequency of 1338 cm-', an upward shift as compared to that of PPP (about 1280 cm-l, experimental value). This shift is largely attributed to the increase in the rigidity of the polymer backbone due to the presence of the bridging group. This frequency shift is also indicative of a higher degree of conjugation due to the planar conformation of methylene bridged PPP. The predicted Raman intensity ratio of the A, modes is compared to that predicted by the effective conjugation coordinate (ECC) theory. Because of the presence of the bridging methylene group, the predictive power of the ECC theory is limited. The predicted IR spectrum shows a strong peak at 844 cm-', a characteristic C-H out-of-plane bending frequency of a 1,2,4,5-tetrasubstitutedphenyl ring. Besides the three new bands originating from the CH2 bridge, we predict two more strong skeletal bands, at 1440 and 1351 cm-l, in the IR spectrum of planarized PPP.

Introduction We recently showed that vibrational spectra, Raman spectra in particular, could provide structural information on pristine' and doped poly(p-phenylene)2(PPP) when used in conjunction with theoretical calculations. The calculation method employed was the ab initio based scaled quantum mechanical oligomer force field (SQMOFF) method. This method enabled us to study quantitatively the structure-spectrum relationship of PPP and the structural evolution of PPP upon doping. We concluded that pristine PPP is nonplanar, having an inter-ring torsional angle of less than 20";' doped PPP has about 30% quinonoid character and an estimated inter-ring C-C bond length of 1.45(2) A.* At that time, the high molecular weight (long chain) PPP had just been synthe~ized,~ but vibrational spectroscopic analyses had not yet been reported. The IR spectrum of long chain PPP published recently4 shows a mediudweak peak at 1603 cm-' which can be assigned to the A, ring deformation mode if the polymer is indeed planar. Its appearance in the IR spectrum is indicative of the lack of planarity. Furthermore, a strong peak appears at 808 cm-', not at a lower frequency expected of a planar PPP, also consistent with the nonplanarity of the polymer. As more spectroscopic data become available, in particular the Raman spectrum, the inter-ring torsional angle could be determined from the approach we presented in our earlier paper. Because nonplanarity in a conductive polymer backbone lessens c~njugation,~ it is desirable to devise a way to improve conjugation and delocalization along the chain, as well as lower the energy band gap between the HOMO and the LUMO. To achieve this goal, Scherf and M ~ l l e n ~synthesized -~ methylene @

Abstract published in Advance ACS Abstracts, November 1, 1994.

0022-365419412098-12223$04.50/0

_I x/2 Figure 1. The unit cell of planarized PPP. Using the SZ screw axis, calculation of vibrational frequencies and intensities is carried out using half the translational unit cell.

bridged PPP (Figure 1). By incorporating the methylene bridge between phenyl rings, a planar backbone is achieved. Some characterizations of this polymer have been done, but no vibrational spectroscopic measurement has been made. Determination of molecular structure is an integral part of chemical research because it provides insight into molecular properties. In the case of conductive organic polymers, structural data are necessary for developing an understanding of their conduction mechanism. Unfortunately, analytical techniques applicable to polymer structural determination could be limited if the polymer is insoluble, as in the case of most conductive organic polymers. Furthermore, the lack of crystallinity of these polymers also renders the X-ray crystallographic technique unsuitable. Where the X-ray crystallographic is not applicable, the use of vibrational spectra and theoretical calculations appears to be a promising approach to date in extracting structural information. In a continuing effort to investigate the spectrum-structure relationship of conductive polymers, we will apply in this study the above-mentioned SQMOFF method to predict the vibrational spectra of newly synthesized planarized PPP. The results will be compared to those of pristine and doped PPP. 0 1994 American Chemical Society

12224 J. Phys. Chem., Vol. 98, No. 47, 1994

Cuff and Kertesz TABLE 1: SCF Optimized Geometry of Cyclopentadiene As Compared to Experimental Results

Computational Methods The SQMOFF method solves the WilsonianloGF determinant in Cartesian coordinates to obtain vibrational frequencies, intensities, and normal mode displacement vectors of a polymer. A detailed description of this method and its applications has been published elsewhere. l1 Further applications since the development of this method have also been published.12-14 This method uses G and F matrices built from an oligomer whose geometries are calculated from ab initio Hartree-Fock theory. The oligomer's dipole moment and polarizability derivatives are used for calculating the vibrational intensities of the polymer. In the present work oligomer calculations are carried out using the Gaussian 9215 program. For a polymer having rings in the backbone, we have usually used trimers. The choice of the size of the oligomer depends primarily on (1) the size of the repeat unit and (2) the extent of delocalization. When the size of the repeat unit is large, the number of repeat units may be limited by computational resources. For a system with extensive delocalization, it is desirable to use a larger oligomer. Since the repeat unit in this case is large, and we are limited by our computational resources, we compromise and use a trimer for building an infinite polymer chain. On the basis of earlier experience, the accuracy of the calculation is more influenced by the limitations of the basis set and the scaling process than by the limited number of neighbors included in the oligomers. The formulation of the G matrix is straightforward because it contains geometrical data and the reciprocal atomic masses of atoms that make up the unit cell. Using periodic boundary condition, the k-dependent force matrix F(k) of the polymer is constructed as follow^:^^^'^

F(k) = F(0)

calcd this work

ref 22"

exptl ref 23

Cl-C2 C2-C3 c3-c4

Bond Lengths (A) 1.519 1.516 1.329 1.329 1.485 1.480

1.506 1.352 1.474

basis set C2-Cl-C5 Cl-C2-C3 c2-c3-c4

Bond Angles (deg) 3-21G 4-21G 102.1 102.1 109.7 109.7 109.3 109.3

103.2 109.3 109.1

--

a SCF gradient ab initio computational method with (7,3) (4,2) basis set of Roos and Siegbahn on carbon atoms and (4) (2) basis set of Huzinaga on hydrogen atoms.

appropriate, we deviate from the above scheme for the CC/CC coupling constants by replacing the scaling factor (SiSj)'" with an additional off-diagonal scaling factor. The scaling factors used in polymer calculations are transferred from smaller molecules similar to the repeat unit of the polymer. It should be emphasized that no fitting is done to the polymer spectrum; a priori prediction of the vibrational spectrum of the polymer is carried out. In this case, benzene and cyclopentadiene are used to obtain scaling factors for planarized PPP. In the following sections, we will show the suitability of the 3-21G basis set and scaling factors from benzene and cyclopentadiene. To test the suitability of the 3-21G basis set, we carried out geometry optimization and vibrational frequency calculations on benzene and cyclopentadiene using the Gaussian 90z1 program. The vibrational frequencies are then least-squares fitted to experimental frequencies in order to obtain a limited number of scaling factors. As we shall see below, the root mean square error for each molecule is sufficiently small at the 3-21G basis set level. Further, we confirm the transferability of these scaling factors using fluorene. By applying the scaling factors of benzene and cyclopentadiene to fluorene, whose experimental vibrational spectra are known, we are able to check the suitability of these scaling factors.

+ ZFG) exp(ikja) j

where F(0) is the force matrix of the central unit of the oligomer, FG) is thejth neighbor coupling force matrix, and k is the wave vector of the f i s t Brillouin zone. Since a trimer is used in this study, only the first neighbor interactions are included in the above summation. The geometry optimization, force constants, dipole moment, and polarizability derivatives of the trimer are calculated ab initio at the 3-21G basis set level using Gaussian 92. Because the force constants are overestimated at the HF SCF level,'* it is necessary to introduce a set of scaling factors to correct for these systematic errors (due to basis set truncation, anharmonicity, and electron correlation). We adopt the scaling scheme proposed by and the final force matrix elements are F.! 'J = Sill2 Fij Sj1I2,where Si are the scaling factors. When

Results and Discussion Benzene and Cyclopentadiene. The geometries of benzene and cyclopentadiene are optimized with D2h and CZ,symmetries imposed, respectively. The results are listed in Table 1, and they compare favorably with earlier calculated resultsz2 and experimental data.23 The definitions of the internal coordinates used in the process are listed in Table 2 according to the

TABLE 2: Definitions of the Internal Coordinates of Cyclopentadiene no. SI-3 s4.5 s6.7

sa-I1

SlZ-I5 s16-19 s20

sz1 s22 s24 s25 s26 s27

definition

description

R(1.21, R(1,5), R(3,4) R(2,3), W4,5) r(1,6), r(L7) r(2,8), d5,11), r(3,9), 44,101 ~(8,2,1,3),~(11.5,1,4),~(9,3,2,4),~(10,4,3,5) 8(8,2,1)-8(82,3), 8 ( 1 1 S J ) - 8(11,5,4),8(9,3,2) - 8(9,3,4), 8(10,4,5) - 8(10,4,3) 8(6,1,7) 8(6,1.2) - 8(7,1,2) + P(6.13 - 8(7,1,5) 8(6,1,2) + 8(7,1,2) - 8(6,1,5) - 8(7,1,5) a(2,1,5) a[a(1,2,3) + a(1,5,4)1 + b[a(2,3,4) a(3,4,5)1 (a - b)[-a(1,5,4) a(1,2,3)1 (1 - a)[a(2,3,4) - a(3,4,5)1 b[t(5,1,2,3) t(4,5,1,2)] a[s(1,2,3,4) + t(3,4,5,1)] t(2,3,4,5) (a - b)[2(1,2,3,4) - t(3,4,5,1)1 + (1 - a)[t(4,5,1,2) - t(5,1,2,3)1

C-C stretch C=C stretch CHZstretch C-H stretch C-H wag C-H bend CH2 scissor CH2 rock CHI twist ring deformation ring deformation ring torsion ring torsion

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A general scheme is found in ref 20. Normalization factors are chosen such that (&?)-I" = 1, where n; are the coefficients for each coordinate. a = cos 144" = -0.8090 and b = cos 72" = 0.3090. The coordinates are R ( i j ) = Ci-Cj bond length, r ( i j ) = Ci-Hj bond length, a(ij,k) = Ci-C,-Ck angle, P ( i j , k ) = Ci-Cj-Hk angle, y ( i j , k , l ) = Hi-C, out of C,-C~-CI plane, t ( i j , k , ! ) = Ci-Cj-Ck-Cl torsion.

J. Phys. Chem., Vol. 98, No. 47, 1994 12225

Theoretical Prediction of Vibrational Spectra

TABLE 3: Scaled SCF Vibrational Frequencies and Intensities of Cyclopentadiene IR Raman exptl frequency intensity activity frequencyb (cm-1) species (cm-') (km/mol) (A4/amu) in-plane X

Cyclopentadiene

Ai

t B2

3081 3064 2888 1506 1374 1364 1105 996 911 798 3093 3056 1574 1291 1239 1089 96 1 810

23.6 6.52 8.49 1.60 0.54 18.5 0.3 1 0.01 9.17 0.04 4.07 1.53 1.51 0.57 5.90 0.73 14.8 6.68

0.77 56.3 136 44.5 22.2 8.61 24.8 10.9 6.07 3.06 211 93.7 3.71 0.15 0.54 15.4 1.90 1.13

3091 3075 2886 1500 1378 1365 1106 994 915 802 3105 3043 1580 1292 1239 1090 959 805

0.00 0.00 0.00 0.00 10.4 1.50 30.1 112 10.3

12.8 3.55 9.68 0.10 110 3.00 3.26 0.14 3.68

1100 94 1 700 515 2900 925 89 1 664 350

out-of-plane A2

Fluorene Figure 2. The numbering of atoms in cyclopentadiene (top) and fluorene (bottom).

Bi

1110 929 714 521 2918 936 887 649 340 8.0' 6.4d

numbering shown in Figure 2. The optimized vibrational frequencies and scaling factors of benzene have been published elsewhere.' The root mean square error of 6.0 cm-I (including rms error errors in C-H stretching frequencies) is small. It must be pointed out that a deviation from the Pulay scaling scheme, as a The xz plane is the molecular plane; therefore, the A:! modes are mentioned in the Computational methods section has to be only Raman active. From ref 25. Theoretical calculation reported applied to benzene due to significant correlation effects. This in ref 25 has a rms error of 15.4 cm-'. dError if C-H stretching phenomenon was first reported by Pulay et al.24 The optimized frequencies are not included. The corresponding error in earlier vibrational frequencies of cyclopentadiene are listed in Table theoretical work46 based on uniformly scaled 6-31G* frequencies is 25.5 cm-l. 3, alongside the corresponding experimental data.25 Unlike benzene, the use of a separate scaling factor for CC/CC coupling TABLE 4: Force Constants and Scaling Factors of force constants on cyclopentadiene only improves the fitting Cyclopentadiene slightly. We also note that the underestimation of the CC/CC force constanta coupling force constants at the SCF level found for b ~ t a d i e n e * ~ - ~ ~ scaling no. int coord description factor this work ref 25 is not observed for cyclopentadiene. The small errors encountered with the use of the 3-21G basis set affirm the suitability 1, 2 C-C (methylenic)stretch 0.9756 4.388 4.761 3 C-C stretch 0.9756 4.818 4.373 of this basis set. The resultant scaling factors and force 4, 5 C=C stretch 0.7718 8.119 8.073 constants of benzene and cyclopentadiene are listed in Table 4. 6, 7 CH2 stretch 0.8139 4.600 (asym) 4.571 Fluorene. The geometry and vibrational frequencies of 4.715 (sym) fluorene are first calculated at the 3-21G basis set level using 8- 11 C-H stretch 0.8139 5.168b 5.150 the Gaussian 92 program. Based on the results of X-ray 12-15 C-Hwag 0.6967 0.377b crystallographic studies on f l ~ o r e n e ,we ~ ~fixed . ~ ~ the symmetry 16-19 C-H in-plane deformation 0.7772 0.427b 20-23 CH2 scissor 0.7433 0.620 of this molecule to be CzVfor ease of computation. Within the rock 0.7433 0.369 SCF framework, the optimized geometry compares favorably wag 0.7678 0.580 with experimental data (see Table 5 ) . The SCF vibrational twist 0.7433 0.551 frequencies are then scaled using the scaling factors of benzene 24,25 ring deformation 0.7785 1.576 and cyclopentadiene, as listed in Table 6. The definition of 1.454 26, 27 ring torsion 0.8017 0.428 the internal coordinates is listed in Table 7 according to the 0.325 numbering shown in Figure 2 . The a priori determined vibrational frequencies of fluorene are compared to those a The units for stretching and bending force constants are mdyn/A and (mdyn-,&)/rad2, respectively. Average values. The complete scaled calculated using a dynamical force method and experimental quadratic force matrix is available as supplementary material. values in Table 8. A comprehensive vibrational analysis of fluorene has been spectroscopy. Except for a small number of weak bands, their carried out by Witt32 based on IR spectra of the gas phase, assignments agree well with those made by Witt. When the solution, pellet, and crystalline layer of fluorene, in addition to large number of normal modes and the complexity of the published Raman and phosphorescence spectra of fluorene. vibrational spectra are considered, a small number of disagreeShortly after that, Bree and Z ~ a r i c hreported ~ ~ their vibrational ments is almost inevitable. Because the theoretical calculation analysis of a fluorene crystal using polarized infrared and Raman

12226 J. Phys. Chem., Vol. 98, No. 47, 1994

Cuff and Kertesz

TABLE 5: Selected Geometrical Data of Fluorene exptl calcd Cl-C2 C2-C3 c3-c4 c4-c5 C5-C6 C6-C7 C1-C8 C2-C7 C6-Cl-C2 Cl-C2-C3 c2-c3 -c4 c 3 -c4-c5 C4-C5-C6 C5-C6-C1 C2-Cl-C8 Cl-C2-C7 c2-c7-c9

ref 30

ref 31

Bond Lengths (A) 1.396 1.397 1.377 1.386 1.389 1.385 1.386 1.385 1.387 1.390 1.381 1.387 1.476 1.472 1.524 1.504 Bond Angles (deg) 120.6 120.7 120.5 120.5 119.0 118.7 120.5 120.9 120.6 120.7 118.8 118.5 108.7 108.3 110.3 110.4 102.1 102.7

1.398 1.397 1.388 1.388 1.391 1.394 1.491 1.504 122.0 120.3 117.4 122.0 121.3 117.0 107.9 110.8 102.7

'See Figure 2 for numbering of atoms; CzVsymmetry is assumed in calculations.

TABLE 6: Force Constants and Scaling Factors of Fluorene scaling factof

force constantsb

48-53

C-C stretch C-C (inter-ring) stretch C-C (methylenic) stretch CH2 stretch C-H stretch C-Hwag C-H in-plane deformation inter-ring torsion CH2 scissor rock wag twist phenyl ring deformation

0.8725 0.8725 0.9756* 0.8139* 0.8279 0.7134 0.7666 0.8000 0.7433* 0.7433* 0.7678' 0.7433* 0.7438

54-59

phenyl ring torsion

0.7367

60,61

5-membered ring deformation

0.7785*

62,63

5-membered ring torsion

0.8017*

6.647' 4.738 4.559 4.769 5.137' 0.424' 0.497' 0.347 0.634 0.443 0.617 0.594 1.271 1.271 1.279 0.260 0.260 0.284 1.706 1.713 0.226 0.153

no. 1-12 13 14, 15 16, 17 18-25 26-33 34-41 42-43 44-47

int coord description

Scaling factors transferred from benzene and cyclopentadiene; those from cyclopentadiene are marked with an asterisk. bThe units for stretching and bending force constants are mdyn/A and (mdyn*A)/rad2, respectively. Average value. The complete scaled quadratic force matrix is available as supplementary material.

is made on an isolated molecule, we compare the predicted frequencies with the experimental values obtained with the gas phase sample. For the out-of-plane modes, our results compare favorably with those observed experimentally, with errors falling in the range 1-7 cm-'. Similar good agreement is also obtained with the in-plane BZ modes, with errors of 3-15 cm-'. With the exception of 2 modes, the calculated in-plane A1 mode frequencies deviate from experimental values by a small margin of 1-13 cm-'. We are uncertain of the quality of the calculated value of 835 cm-' because, as pointed out by Witt in his report, the assignment of the 870 cm-l band to be an AI is not without uncertainties. The corresponding frequency of the crystal is determined to be 960 and 857 cm-' by Witt and Bree and Zwarich, respectively. The other large deviation (33 cm-') is

between the calculated 1446 cm-' and the observed 1413 cm-l modes (in the gas phase). This mode also displays the largest difference between the crystal and gas phases. It is interesting to note that the calculated value is closer to the frequency of the crystal. A few disagreements between experimental results and between experimental and our theoretical results require some elaborations. First, the crystal frequency of 1324 and 1319 cm-' (Raman) tentatively assigned to be an A1 mode by Witt and Bree and Zwarich, respectively, is not predicted by our calculation. Neither is it predicted by the calculation of Matsunuma et al.34 On the other hand, the Raman peak at 1156 cm-' observed and tentatively assigned as an A1 fundamental by Bree and Zwarich is predicted by both theoretical calculations. Thus, we conclude that the 1156 cm-l peak, not the 1324 cm-' peak, is in fact a fundamental peak. Second, the two lowest A1 modes are assigned to significantly different frequencies by Witt and Bree and Zwarich. Our calculation supports the assignments by Bree and Zwarich. Similarly, our calculation also supports the assignments of Bree and Zwarich on the two lowest B2 frequencies. The assignment of the 472 and 414 cm-l peaks by Witt to be A1 and BZ modes, respectively, could be switched the other way around for a better agreement. On the basis that only one of the calculated frequencies shows a significant deviation from the experimental frequencies of gaseous fluorene, we conclude that the transferability of scaling factors from benzene and cyclopentadiene to fluorene is excellent. Thus, the use of this set of scaling factors on planarized PPP which consists of fluorene as part of its unit cell is justifiable. Planarized PPP. The unit cell of planarized PPP consists of two phenyl rings with two methylene groups at all-trans positions (see Figure 1). Taking advantage of the Sz screw axis, we use one phenyl ring with one methylene group attached as repeat unit. Because of the large number of atoms in a repeat unit and limited computational resources, we include only the first neighbor interactions. The oligomer used has three phenylene rings bridged with methylene groups. The geometry of the central phenyl ring and the methylene group of this oligomer used in the polymer calculations is shown in Table 9. This 3-21G basis set optimized geometry agrees well with that obtained using a MOSOL35,36calculation for infinite chain and PM337parameterization. Compared to planar and helical PPP, the inter-ring bond length of planarized PPP is significantly shorter. To examine the effect of planarizing the phenyl ring backbone, we will compare the results of planarized PPP to those obtained for 20" helical PPP1*2(a model which has the best agreement with experimental data). To facilitate this comparison, we will assume that both polymers have a factor group which, to the first approximation, is isomorphous to the &h point group. This assumption works well with PPP where the exclusivity between IR and Raman is observed experimentally. However, we must be aware of the possible appearance of IR active modes in the Raman spectrum as weak peaks and vice versa. The irreducible representation is worked out to be 11Ag 5B1, 11B2, 5B3, 5Au 10B1, 5B2, 10B3,, where the gerade modes are Raman active and the ungerade modes are IR active. There are 42 in-plane modes at k = 0 and n/h, Le., 11A, llB2, 10B1, f 10B3,. The remaining 20 are out-of-plane modes, of which the A, modes are spectroscopically inactive. Table 10 lists the scaling factors and force constants of planarized PPP as compared to those of 20" helical PPP. The scaling factors used for the phenyl ring are the same for both

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J. Phys. Chem., Vol. 98, No. 47, 1994 12227

Theoretical Prediction of Vibrational Spectra

TABLE 7: Definitions of the Internal Coordinates of Fluorene no. definition description C-C stretch (phenyl ring) R(1,2),R(2.31,R(3,4),R(4,5),R(5,6),R(6,1),R W ) ,R(9,10),R(10,11),Wl,W, R(12,13),R(13,8) s1-I2 C-C stretch (inter-ring) R(1,8) s13 C-C stretch (methylenic) R(2,7),R(7,9) s14.15 CHZstretch r(7J4).r(7,W s16.17 C-H stretch 43,161,r(6,19),r(5,18),4417,r(10,20),413,23),r(12.221,r(1121) SlS-25 C-H wag s26-33 ~(16,3,2,4), ~(19,6,1,5), ~(18,5,4,6), ~(17,4,3,5), ~(20,10,9,1 l),~(23,13,8,12), ~(22,12,11,13), ~(21,11,10,12) C-H bend (in-plane) s34-41 8(1,6,19) - p(5,6,19), 8(6,5,18)- /%4,5,18),/%5,4,17)- 8(3,4,17), 8(4,3,16)- 8(2,3,16),8(8,13,23)/3( 12,13,23), p( 13,12,22)- /3( 1 1,12,22),B( 12,11,21)- B( 10,11,21), B( 1 1,10,20)- 8(9,10,20) inter-ring torsion t(10,9,8,1) - r(7,9,8,10), t(3,2,1,8) - t(7,2,16) s42,43 CH2 scissor S44 p(14,7,15) CHI rock s45 8(2,7,14)- P(2,7,15)+ 8(9,7,14)- 8(9,7,15) CH2 wag 8(2.7,14)+ 8(2,7,W- 8(9,7,14)- 8(9,7,15) s46 CH2 twist 8(2,7,14)- p(2,7,15)- ,49,7,14)+ 8(9,7,15) s47 Phenyl Rings ring deformation a(6,1,2)- a(1,2,3)+ a(2,3,4)- a(3,4,5) a(4,5,6)- a(5,6,1) S48 a(13,8,9)- a(8,9,10)+ a(9,10,11)- a(10,11,12)+ a(11,12,13)- a(12,13,8) ring deformation s49 a(1,2,3)- a(2,3,4)+ a(4,5,6)- a(5,6,1) ring deformation s50 a(8,9,10)- a(9,10,11)+ a(11,12,13)- a(12,13,8) ring deformation s5 I ring deformation 2a(6,1,2)- a(1,2,3)- a(2,3,4) 2a(3,4,5)- a(4,5,6)- a(5,6,1) s5z ring deformation 2a(13,8,9)- a(8,9,10)- a(9,10,11) 2a(10,11,12)- a(11,12,13)- a(12,13,8) s53 ring torsion t(6,1,2,3) - t(2,3,4,5) + t(3,4,5,6)- t(5,6,1,2) s54 ring torsion - t(3,4,5,1)+ t(4,5,1,2) - t(5,1,2,3) t(1,2,3,4) s55 ring torsion - t(1,2,3,4) + t(2,3,4,5)- t(3,4,5,6) t(4,5,6,1)- t(5,6,1,2) t(6,1,2,3) s56 ring torsion t(13,8,9,10) - t(8,9,10,11) + t(9,10,11,12)- t(10,11,12,13) t(11,12,13,8)- t(12,13,8,9) s57 -t(6,1,2,3)+ 2t(1,2,3,4) - t(2,3,4,5) - t(3,4,5,6) 2t(4,5,6,1) - t(5,6,1,2) ring torsion S58 -t(13,8,9,10) 2t(8,9,10,11) - t(9,10,11,12) - t(10,11,12,13) + 2t(11,12,13,8) - t(12,13,8,9) ring torsion s59 Five-Membered Ring ring deformation a(2,7,9)+ a[a(1,2,7) a(7,9,8)] b[a(2,1,8)+ a(l,8,9)] S60 ring deformation s 61 (a - b)la(1,2,7)- a(7,9,8)1+ (1 - a)[a(2,1,8)- a(1,8,9)1 ring torsion b[t(9,7,2,1) + t(8,9,7,2)]+ a[t(7,2,1,8)+ t(1,8,9,7)] t(2,1,8,9) s62 ring torsion (a - b)lt(1,8,9,7) - W,2,1,8)1+ (1 - a)[t(8,9,7,2) - @,7,2,1)1 s63 ~~~

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A general scheme is found in ref 20. Normalization factors are chosen such that (&z?)-'" = 1, where ni are the coefficients for each coordinate. 144" = -0.8090,and b = cos 72" = 0.3090. The coordinates are R(ij) = Ci-Cj bond length, r(ij) = Ci-Hj bond length, a(ij,k)= Ci-Cj-Ck angle, P ( i j , k ) = Ci-C,-Hr angle, y ( i j , k , l ) = Hi-C, out of Cj-Ct-C, plane, t(ij,k,Z) = Ci-Cj-Ck-Ci torsion. a

a = cos

polymers. Scaling factors from cyclopentadiene used in parts of planarized PPP are not required for 20" helical PPP. The two sets of scaled force constants are very similar except for the inter-ring stretching force constant. (Listed under Jivemembered ring as C-C (para) in Table 10.) There is an increase in the inter-ring stretching force constant consistent with the geometry of the planarized PPP unit cell which has a shorter inter-ring C-C bond length. We now examine the predicted IR and Raman spectra of planarized PPP with comparison to 20" helical PPP. The simulated IR spectrum of planarized PPP, in the 800-1600 cm-' region, is shown in Figure 3 (top). A complete set of calculated IR frequencies and intensities is given in Table 11. Compared to PPP, a number of new peaks appear. The ones due to CH2 scissoring, wagging, and rocking motions are indicated on the spectrum. Besides these peaks, two new peaks appear in the 1350-1450 cm-' region. In the lower frequency region, a strong peak appears at 844 cm-'. This value falls in the frequency range consistent with the characteristic C-H out-ofplane bending frequency of 1,2,4,5-tetrasubstitd benzene. The corresponding frequency of PPP is calculated and experimentally determined to be 809 and 804 cm-', respectively. The calculated Raman frequencies and activites of planarized PPP are listed in Table 12. As in 20" helical PPP, the strongest peak (1636 cm-') is mainly a ring stretching mode. However, the 1582 cm-I peak has no counterpart in 20" helical PPP. The inter-ring stretching frequency is located at 1338 cm-l, an upward shift of 68 cm-' from that of 20" helical PPP. Smaller upward shifts, from 1222 to 1250 cm-', are also observed for the next A, mode. The very weak peak at 770 cm-' corresponds to the 785 cm-' peak of 20" helical PPP. A simulated Raman

spectrum of planarized PPP is shown in Figure 3 (bottom). The Raman spectrum of 20" helical PPP is overlaid on top for comparison. The vector displacements of major IR and Raman peaks are depicted in Figure 4. We note that the general appearance of the two Raman spectra is similar except for the intensity ratio (I,&) of peaks A and B. In accordance with experimental we calculated the intensity of peak B to be higher than that of peak A in the case of 20" helical PPP. The reverse is predicted for planarized PPP. This reversal is not surprising since peak B is of C-H in-plane bending in nature. There are four C-H groups in PPP as compared to half that number in planarized PPP. Therefore, the intensity of peak B is expected to decrease going from PPP to planarized PPP. The reason for the growth in the peak A (inter-ring stretching mode) intensity is not immediately apparent. In order to better understand the Raman intensity pattem of planarized PPP, we tum to the effective conjugation coordinate (ECC) t h e ~ r y ~put l - ~forward ~ by Zerbi et al. The ECC theory states that there exists a totally symmetric linear combination of intemal coordinates which describes the change in equilibrium geometry of the ground state to excited state. This mode is termed as the 5? mode. (For this reason the ECC theory is also known as 5? mode theory.) Except for a perfect onedimensional polymer, this .G? mode is not a normal mode. By this definition, the 5e mode is the mode that most strongly couples the geometry to the electronic structure. Hence, according to the ECC theory, if the .G? mode is coupled to a totally symmetric normal mode (A, mode), it lends intensity to this normal mode. In other words, a normal mode would have the highest intensity if it has the most 9 2mode character. It

12228 J. Phys. Chem., Vol. 98, No. 47, 1994 TABLE 8:

FluorenP

Cuff and Kertesz

Calculated and Experimental Vibrational Frequencies, Theoretical IR Intensities, and Raman Activities of calcd this work

species in-plane Ai

B2

out-of-plane A2

Bi

exptl

freq

IR int

Raman act

ref 34 freq

ref 33 (crystal) freq

1625 1595 1474 1446 1388 1347

0.01 1.09 0.01 20.8 3.48 0.02

290 17.7 49.9 4.52 22.5 21.4

1615 1588 1489 1437 1382 1333

1287 1231 1185 1165 1088 1022 835 734 629 413 209 1624 1600 1474 1448 1318 1304 1200 1185 1164 1107 1028 998

0.05 0.82 4.00 0.00 1.74 0.54 0.02 0.04 0.68 11.1 0.21 1.36 0.59 13.2 28.4 9.68 2.35 4.06 0.09 1.75 0.29 3.50 1.36

58.3 101 0.20 8.05 9.63 42.7 27.7 19.8 0.27 0.00 0.40

1263 1226 1152 1091 1018 943 845 731 642 399 144

1612* 1570 1480 1400 (?), 1450* 1397 1349 1319’ (?) 1291 1231 1186 1156*’ 1089 1016 857 (?), 846* 743* 628 421* 217

800

1.16

0.01

620 543 480

7.92 0.01 0.44

0.29 10.1 0.01

1146 99 1 949 875 787 726 564 429 272 132 992 963 913 852 732 697 467 413 238 95

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.21 7.68 0.13 2.52 159 12.90 2.26 11.1 10.8 0.96

11.4 1.59 2.95 1.02 0.06 2.49 0.44 2.60 14.0 0.01 0.10 0.92 0.46 0.27 0.05 0.57 0.41 0.01 2.00 0.33

8.04 0.01 8.71 0.64 6.18 0.81 20.9 0.00 9.97 0.5 1 0.52 0.54

1521 (?) 1471 1440 1336 1303 1215 1188 1146* 1103 1023 994 904’ 722’ 618 542 487

ref 32 (crystal) freq

ref 32 (gas) freq

1610* 1576

1612 1583

1448 1400 1343 1324 (?)

1413 (?)

1234 1190

1334 1230 1186

(?)

1092 1022 960 (?) 738* 633 472 (Bz?) 262 (?)

1092

1478 1451 1311 1300 1198’ 1160 (AI?) 1156 1109 1025 1000

1482 1455 1313 1297

870 (?)

1170 1150 1033 1007

624 490 414’ (Ai?)

623

954 914 842b 740 698 5456 (?) 411* 212* (?)

956

788

287 1153 (?) 95 1 910 84 1 735 693 413 260

855 738 696 410

a The units for frequency, IR intensity, and Raman activity are cm-’, km/mol, and A4/amu, respectively. Experimental frequencies from IR spectra are listed; data from Raman spectra are marked with an asterisk. Tentative assignment by the original authors. (?) indicates disagreement in assignment.

’

can be written down that the intensity of a kth normal mode is proportional to the square of its eigenvector, Le., I k = ILm12, where L a is the scalar product of the kth normal mode and the G? mode. Accordingly, the intensity ratio of any two A, mode can be written as 4/Ik = ILg,I2/lLg~l2. By defining G? in Cartesian coordinates, we write G? = BX, where B is the

transformation matrix and X is the Cartesian displacement vector. Also, the normal mode matrix Q can be written as Q = Lw-lG? = Lx-lX, where Lg-l and Lx-’ are transformation matrices. Therefore, L;f = BLx. W e set up the G? mode of planarized PPP as shown in Figure 5 . This has the same definition as the one used for PPP. Since

J, Phys. Chem., Vol. 98, No. 47, 1994 12229

Theoretical Prediction of Vibrational Spectra

TABLE 9: Optimized Carbon Skeleton Geometry of the Unit Cell of Planarized PPP and P P P PPP planarized ppp 3-21G PM3'

planar 3-21G

Bond Lengths (A) 1.390 1.435 1.392 1.380 1.386 1.379 1.380 1.388 1.392 1.475 1.467 1.499 1.522 1.502 Bond Angles (deg) 120.9 116.3 119.9 121.9 119.2 121.9 108.7 121.9 110.3

Cl-C2 C2-C3 c3-c4 Cl-C9 C2-C7 C6-C 1-C2 Cl-C2-C3 c2-c3-c4 C9-Cl-C2 c7-c2-c1

helical (20") 3-21G 1.390 1.380 1.390 1.500

TABLE 10: Force Constants and Scaling Factors of Planarized PPP As ComDared to Helical (20") PPP ~

description C-C stretch C-H stretch C-H in-plane deformation C-H wag ring deformation ring torsion

C-C stretch C-H stretch CHZscissor rock wag twist ring deformation ring torsion

inter-ring torsion

~~~

~

scaling factor

1400

1200 1000 Wavenumber (cm-1)

800

I

~

force constantG planarized

Phenyl Ring 0.8725 6.744' 0.8279 5.O9lb 0.7666 0.495' 0.7134 0.7438

m

Planarized PPP mlo~

Helical PPP

118.2 120.9 120.9 120.9

a Numbering of the atoms is depicted in Figure 2, taken from the middle part of a trimer. 'Unit cell data of a periodic boundary conditions calculation.

~

m

0.414' 1.364 1.364 1.357 0.7367 0.278 0.320 0.351 Five-Membered Ring 0.8725 4.803 (para) 0.9756 4.622 (methylenic) 0.8139 4.620 (asym) 4.742 (sym) 0.7433 0.636 0.7433 0.447 0.7678 0.620 0.7433 0.598 0.7785 1.725 1.720 0.8017 0.248 0.180 Inter-ring 0.8000 0.684

helical (20') 6.649' 5.163' 0.529' 0.427' 1.251 1.196 1.382 0.228 0.340 0.305 4.499

The units for stretching and bending force constants are mdyn/A and (mdyn*A)/rad2,respectively. Average values.

there is more than one way of defining a linear combination of internal coordinates for the G? mode, we use this definition as an approximation with the effect of the methylene bridge neglected. The justification of this approximation comes from the study on fluorene. Matsunumo et al.34found that the change in geometry from the ground state to the excited state of fluorene only affects the methylene group very slightly. Since the unit cell of planarized PPP has the structure of fluorene in it, we expect similar behavior from methylene groups of planarized PPP. The intensity ratios of selected A, modes predicted by the G? mode model are compared to those determined by the SQMOFF method in Table 13. The 1636 cm-' mode is predicted to be the one having the strongest intensity by both methods. Markedly different intensity ratios are predicted for

I

1600

1400

1200

1000

aoo

Wavenumbedcm-1) Figure 3. Graphical representations of theoretical vibrational spectra of planarized PPP (-) and 20" helical PPP (- - -). (Top) IR spectrum. (Bottom) Raman spectrum. The peaks in the spectra are generated using Gaussian functions: Zj = Zi exp(v,f/2u), where Zi is the calculated intensity of the ith mode, v, is the frequency relative to the ith normal mode frequency, and u = 25 cm-'. the next two peaks. While the SQMOFF method shows the inter-ring stretching mode (1338 cm-') to be the next strongest peak, the 53 mode theory predicts that the 1582 cm-' peak is the next strongest. The discrepancy observed here can be attributed to the assumption that the effect of the methylene bridge is insignificant. The effect of the methylene bridge on the polymer backbone can also be seen from the frequency shifts of peaks A and B, as compared to PPP. The upward shift of 68 cm-I predicted for the inter-ring stretching mode cannot be attributed solely to the increase of the force constant of 0.304 mdyn/A. Doped PPP whose inter-ring stretching frequency is about 1330 cm-' has an inter-ring stretching force constant of 5.475 mdyn/A. It is therefore clear that the bridging methylene group contributes to the rigidity of the polymer backbone. Conclusions We use the SQMOFF method to predict vibrational spectra of planarized PPP and examine the main features of IR and Raman spectra with reference to PPP. We justify the use of the moderate 3-21G basis set in this study on the basis of good agreement between calculated and experimental frequencies of benzene and cyclopentadiene. We also confirm the transferability of the scaling factors from benzene and cyclopentadiene

12230 J. Phys. Chem., Vol. 98, No. 47, 1994 TABLE 11: Calculated Raman Frequencies (cm-l) and Activities (di4/amu)of Planarized PPP. The Four Strongest A, Modes (excluding C-H Stretching) of 20" Helical PPP Are Listed for Comparison planarized PPP helical (20")PPP symmetry frequency activity frequency activity In-Plane Modes 1636 3270 1630 1343 1582 310 1388 62.9 CH2 scissor 1338" 1102 127P 122 1250 232 1222 314 1047 142 44.4 185 11 770 8.10 655 3.22 337 1504 17.2 1422 15.1 1349 2.86 1280 10.3 1210 28.8 CHzwag 1195 1.88 1165 24.2 2.12 807 642 1.74 Out-of-Plane Modes 951 11.6 CH2 rock 0.32 913 1.72 712 0.14 416 0.12 160 1148 21.1 CHZtwist 775 7.76 0.04 515 444 18.8 222 10.6 Inter-ring stretching mode. using fluorene. These results and others1*2J2-14,44,45 validate the soundness of the SQMOFF method in predicting vibrational spectra of polymers. The a priori determined spectra of planarized PPP offer insights into the influence of the methylene bridge. The IR spectrum is predicted to be more complex than that of PPP. Besides the appearance of normal modes due to CH2 scissoring, wagging, and rocking, two medium strong peaks are located in the 1350-1450 cm-l region. The characteristic C-H out-ofplane bending mode of PPP disappears. Instead a peak appears at 844 cm-'. This frequency is consistent with the C-H outof-plane bending frequency of 1,2,4,5-tetrasubstitutedbenzenes. The effect of the bridging methylene group is most visible from the Raman spectrum. The presence of this bridging group significantly increases the rigidity of the polymer backbone, as evident from the large increase in the inter-ring stretching frequency despite only a small increase in the corresponding force constant. The methylene group also influences the predictive power of the ECC theory since its effect cannot be neglected. Further, the reversal of the intensity ratio of peaks A and B (as compared to 20' helical PPP) can be attributed to the presence of the bridging group. We hope that these predictions will stimulate experimental work on various planarized p~lyphenylenes.~~ Three isomers of planarized polyphenylenes (all para, all meta, and para-meta) have been mentioned in the work by Scherf and M ~ l l e n . ~ - ~ Vibrational spectroscopy in conjunction with accurate quantum mechanical modeling is capable of resolving some of the structural issues, central to the understanding of the properties of these potentially important new materials.

Cuff and Kertesz TABLE 12: Calculated Infrared Spectrum of Planarized PPP planarized PPP symmetry frequency (cm-I) intensity (km/mol) In-Plane Modes B ~u 1487 31.4 C-C skeletal 1440 34.9 C-C skeletal 1351 57.1 C-C skeletal 1195 13.5 CH2wag 1146 10.1 1026 0.38 801 0.14 419 0.48 B3u 1660 1.70 1608 1.34 1390 6.64 CHz scissor 1224 0.54 841 1.70 0.18 689 536 0.00 472 0.60 Out-of-Plane Modes Bz~ 958 29.2 CH2 rock 844b 39.8 515 6.40 41 1 19.6 189 9.64 Au 1149 0.00 CHz twist 866 0.72 695 0.78 301 7.04 145 1.74 C-H stretching frequencies are omitted. A comparison between the IR spectrum of planarized PPP and that of the helical (20")PPP is illustrated in Figure 3. 1,2,4,5-tetrasubstittedphenyl ring C-H outof-plane wag.

770

844

1338

1351

1440

16%

1487

Figure 4. Vector displacement representations of major Raman active A, modes (top) and prominent IR active modes (bottom).

Figure 5. Linear combination of the internal coordinates of the GZ mode. SF! = N(46r2 - 6rl - 26r3),where N is the normalization factor. Note that the methylene bridging group is not part of the GZ mode. The arrows given correspond to a unit cell plus the adjacent C atoms in the neighboring cells, which are in phase and correspond to a phonon mode at k = 0. Acknowledgment. This work is supported by grants from the NSF (No. DMR-91-15548) and the NSF Pittsburgh Supercomputer Center (No. DMR-920006P).

Theoretical Prediction of Vibrational Spectra

J. Phys. Chem., Vol. 98, No. 47, 1994 12231

TABLE 13: Comparison between Intensity Ratios of the A, Modes of Planarized PPP As Predicted by the SQMOFF Method and the ECC Theory intensity ratio frequency (cm-I)

SQMOFF

ECC theory

1636 1582 1338 1250 1047 770

1.o 0.095 0.32 0.071 0.043 0.014

1.o 0.18 0.14 0.060 0.03 1 0.017

Supplementary Material Available: Tables listing the complete set of scaled force matrices of cyclopentadiene and fluorene (10 pages). Ordering information is given on any current masthead page. References and Notes (1) Cuff, L.; Kertesz, M. Macromolecules 1994, 27, 762. (2) Cuff, L.; Cui, C.; Kertesz, M. J. Am. Chem. Soc. 1994,116, 9269. (3) Gin, D. L.; Conticello, V. P.; Grubbs, R. H. J. Am. Chem. Soc. 1992, 114, 3167. (4) Gin, D. L.; Avlyanov, J. K.; Min, Y.; MacDiarmid, a. G. Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.) 1994, 35, 287. ( 5 ) Bredas, J. L.; Themans, B.; Fripiat, J. G.; Andre, J. M. Phys. Rev. B 1984,29, 6761. (6) Scherf, U . Synthesis 1992, JanJFeb., 23. (7) Scherf, U.; Mullen, K. Polymer 1992, 33, 2443. (8) Scherf, U.; Bohnen, A,; Mullen, K. Makromol. Chem. 1992, 193, 1127. (9) Scherf, U. Synth. Met. 1993, 55-57, 767. (10) Wilson, E. B., Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; McGraw-Hill: New York, 1955. (11) Cui, C. X.; Kertesz, M. J. Chem. Phys. 1990, 93, 5257. (12) Cui, C. X.; Kertesz, M.; Eckhardt, H. Synth. Met. 1991, 41-43, 3491. (13) Eckhardt, H.; Baughman, R. H.; Buisson, J. P.; Lefrant, S.; Cui, C. X.; Kertesz, M. Synth. Met. 1991, 43, 3413. (14) Cuff, L.; Kertesz, M.; Geisselbrecht, J.; Kurti, J.; Kuzmany, H. Synth. Met. 1993, 55, 564. (15) Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Gill, P. M. W.; Wong, M. W.; Foreman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari,K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. In Gaussian 92; Gaussian Inc.: Pittsburgh, 1992. (16) Painter, P. C.; Coleman, M. M.; Koenig, J. L. The Theory of

Vibrational Spectroscopy and its Applications to Polymeric Materials;

Wiley: New York, 1982. (17) Tadokoro, H. Structure of Crystalline Polymers; Wiley: New York, 1979. (18) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; Defrees, D. J.; Binkley, J. S.; Frisch, M. J.; White, R. A,; Hout, R. F.; Hehre, W. J. In?.J. Quanfum

Chem., Quantum Chem. Symp. 1981, 15, 267. (19) Pulay, P.; Fogarasi, G.; Boggs, J. E.; Vargha, A. J. Am. Chem. Soc. 1983, 105, 7037. (20) Forgarasi, G.; Pulay, P. Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, pp 125. (21) Frisch, M. J.; Head-Gordon. M.; Trucks, G. W.; Foreman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, J. S.; Gonzalez, C.; Defrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seeger, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.; Topiol, S.; Pople, J. A. In Gaussian 9 0 Gaussian Inc.: Pittsburgh, 1990. (22) Saebo, S.; Cordell, F. R.; Boggs, J. E. J. Mol. Struct. 1983, 104,

221. (23) Damiani, D.; Ferretti, L.; Gallinella, E. Chem. Phys. Lett. 1976, 37, 265. (24) Pulay, P.; Fogarasi, G.; Boggs, J. E. J. Chem. Phys. 1981, 74,3999. (25) Castelluci, E.; Manzelli, P.; Fortunato, B.; Gallinella, E.; Mirone, P. Spectrochim. Acta 1975, 3IA, 451. (26) Guo, H.; Karplus, M. J . Chem. Phys. 1991, 94, 3679. (27) Bock, C. W.; Panchenko, Y. N.; Pupyshev, V. I. J. Comput. Chem. 1990, 11, 623. (28) Kofranek, M.; Lischka, H.; Karpfen, A. J. Chem. Phys. 1992, 96, 982. (29) Szalay, P. G.; Karpfen, A.; Lischka, H. J. J . Chem. Phys. 1987, 87, 3530. (30) Belsky, V. K.; Zavodnik, V. E.; Vozzhennikov, V. M. Acta Crystallogr. 1984, C40, 1210. (31) Gerkin, R. E.; Lundstedt, A. P.; Reppart, W. J. Acta Crystallogr. 1984, C40, 1892. (32) Witt, K. Spectrochim. Acta 1968, 24A 1115. (33) Bree, A.; Zwarich, I. J. Chem. Phys. 1969, 51, 912. (34) Matsunuma, S.; Kamisuki, T.; Adachi, Y.; Maeda, S.; Hirose, C. Spectrochim. Acta 1988, 44A, 1403. (35) Stewart, J. J. P. MOSOL Manual; USAF: Colorado Springs, CO, 1984. (36) Stewart, J. J. P. QCPEBull. 1985, 5, 62. (37) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (38) Buisson, J. P.; Krichene, S.; Lefrant, S. Synth. Met. 1987, 21, 229. (39) Furukawa, Y.; Ohta, H.; Sakamoto, A.; Tasumi, M. Spectrochim. Acta 1991, 47A, 1367. (40) Lefrant, S.; Buisson, J. P.; Eckhardt, H. Synth. Met. 1990, 37, 91. (41) Castiglioni, C.; Gussoni, M.; Zerbi, G. Synth. Met. 1989, EZ, 29. The letter G? is used in this joumal for the more customary Russian “ja”. (42) Zerbi, M.; Chierichetti, B. J. Chem. Phys. 1991, 94, 4637. (43) Zerbi, G.; Gussoni, M.; Castiglioni, C. Conjugated Polymers; Bredas, J. L., Silbey, R., Eds.; Kluwer Academic: Netherlands, 1991; pp 435. (44) Kofranek, M.; Kovar, T.; Karpfen, A,; Lishka, H. J. Chem. Phys. 1992, 96, 4464. (45) Kofranek, M.; Kovar, T.; Lishka, H.; Karpfen, A. J. Mol. Strucr. 1992, 259, 181. (46) Karni, M.; Oref, I.; Burcat, A. J . Phys. Chem. Ref. Data 1991, 20, 665. (47) For interpretation of the Raman spectrum, see Cuff, L.; Kertesz, M.; Scherf, V.; Mullen, K. Synth. Met., Proceedings of ICSM 1994, Seoul, Korea, in press.