an ab initio study of the vibrational spectra of li-doped thiophene, bithiophene, benzene and...

THEO CHEM

Journal of Molecular Structure (Theochem) 364 (1996) 15-31

An ab initio study of the vibrational spectra of Li-doped thiophene, bithiophene, benzene and biphenyl as model systems for

(bi)polaronic defects

Stephan Irle, Hans Lischka*

Institut fir Theoretische Chemie und Strahlenchemie der Universitiit Wien, Wiihringerstrasse 17, A-1090 Wien, Austria

Received 9 October 1995; accepted 7 December 1995

Abstract

Ab initio SCF investigations of the IR and Raman spectra of the charge-transfer complexes of Li atoms with thiophene, bithiophene, benzene and biphenyl are reported. Computed geometries show an aromatic -+ quinoid transition during the formation of the complexes. The force constants reflect this behavior. As a consequence, the vibrational frequencies are considerably rearranged. IR and Raman intensities are strongly enhanced in the complexes as compared to the undoped compounds. The inter-ring vibrational modes occur at frequencies close to 1600 cm-’ both for di-Li-BT and di-Li-BP. This suggests a reconsideration of the assignment of that mode in the experimental Raman spectrum of the p-oligophenyl dianions.

Keywords: Ab initio calculation; Bipolaron; Charge transfer complex; Polaron; Scaled force field; Vibrational spectra

1. Introduction

Polythiophene, poly(p-phenylene), polypyrrole and many other related n-conjugated organic

polymers display metallic conductivity upon doping with oxidizing, e.g. AsFS or Br2, or reducing, e.g. electropositive metals, agents [l-5]. Charged defect structures like polarons (radical ions) and bipolarons (dications or dianions) are believed to play a major role in the conduction

mechanism of these compounds [6-81. The structural changes are governed by quinoidic distortions of the originally aromatic rings. However, due to the amor-

phous nature of these doped polymers the experimental characterization of their structures and of

* Corresponding author.

their spectroscopic properties is still not satisfactorily solved. This situation has led to studies of smaller oligomers showing metallic conduction properties

that are similar to those of the polymers (see, for example, Refs. [9-131). Of particular relevance to our work is the recent Raman study on sodium- doped poly-p-phenylene and the radical anions and dianions ofp-oligophenyls [14]. The advantage of the study of oligomers is that one can investigate a series of compounds having well-defined degrees of poly- merization under more controllable conditions allowing a better understanding of the polymer properties. Several ab initio SCF [ 15- 191 and semiempirical calculations [:!O-231 on the charged oligomers with or without inclusion of counterions show evidence for the importance of such defect

states.

0166-1280/96/%15.00 0 1996 Elsevier Science B.V. All rights reserved SSDI Ol66-1280(95)04465-S

16 S. Irle, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31

Counterions significantly polarize the electron density of the doped oligomers and influence the localization of charge on the chain, especially in the case of n-doping because of the large polarizability of negative charge created in the conjugated T-system. In a recent study on the structures, the electron densities and energetic stabilities of mono- and di-alkali-doped oligophenyls and oligothiophenes [18], we were able to show that the charge transfer is localized mainly within the monomer unit above which the alkali atom is located. The localization of the defect is much more pronounced in systems with explicit inclusion of counterions than in comparable doubly-charged systems without screening by counterions [17].

Vibrational spectroscopy is, of course, one of the most important ways to study doped and undoped oligomers and polymers [24,25]. Various ab initio [26-301 and semiempirical [31,32] calculations on the vibrational spectra of the undoped oligomers have been reported. Recently, the vibrational spectra of positively charged closed-shell bipolaronic defects in a series of oligothiophenes have been studied by Ehrendorfer and Karpfen [33-351 by means of ab initio SCF and semiempirical PM3 calculations. Cuff et al. [19] presented calculations on the vibrational spectra of doped poly( p-phenylene) by means of their scaled quantum mechanical oligomer force field method.

with the TURBOMOLE program [36]. For the remaining CdCUhtiOUS, the GAUSSIAN 92 Suite of programs [37] was used. Closed-shell molecules were treated on the spin-restricted Hartree-Fock (RHF) level of theory, whereas for open-shell systems the spin- unrestricted Hartree-Fock formalism of Pople and Nesbet [38] was employed. Equilibrium structures were obtained by full geometry optimizations, applying a convergency criterion of 1 x 10d3 atomic units for the root mean square gradient value. The double-zeta basis set of Ahl- richs and coworkers [39] polarized with one d- shell for S and C (o(S) = 0.55, a(C) = 0.80) was chosen for all calculations. The Li DZ basis set was augmented by two p-functions with exponents of o, = 0.55 and o2 = 0.06 which where obtained by exponent optimization for di-Li-bithiophene [18]. These polarization functions play an important role in the charge transfer process from Li to the acceptor molecule [40]. An extended version of the program SCALES developed by Pongor and coworkers [41] was used for the fitting procedure of scaling factors for force constants according to Pulay et al. [42].

3. Equilibrium structures

Our present investigation on the vibrational spectra of polarons and bipolarons is a continuation of our previous study on the electronic structure and energetics of such systems [18], explicitly taking counterions into account. In these investigations we not only treated closed-shell bipolaronic but also open-shell polaronic defects. Because of what has been said in the preceding paragraph about the localized structure of the alkali-doped compounds, we believe we are justified in investigating the vibrational modes of the smallest possible doped oligomers (Li-benzene, Li-thiophene, di-Li-biphenyl and di-Li-bithiophene) as basic model cases for negative polarons and bipolarons.

The molecular structures of undoped and Li- doped thiophene, bithiophene, benzene and biphenyl are depicted in Figs. 1 and 2. The equilibrium geometries of these compounds have been discussed in detail in Ref. [ 181. The main structural change due to the charge transfer is the introduction of a quinoid character which can be described in general terms by the following valence-bond-type formulae:

2. Methodology

The geometry optimizations were performed Formula 1.

S. Irle, H. LischkajJournal of Molecular Structure (Theochem) 364 (1996) 15-31 17

LC*ClC1'C*'= 456 Lc2c1cI'ce = -134.4

Fig. 1. Atomic numbering schemes, bond lengths in A and

torsional angles in degrees for thiophene, bithiophene, benzene

and biphenyl.

For Li-thiophene (see Figs. 1 and 2) the C-S bonds become stretched by 0.080 to 1.805 A. the C2-C3 bond is stretched by 0.070 to 1.417 A and the C3-C4 bond is shortened by 0.051 to 1.383 A. However, 7r-conjugation is not completely destroyed since these bonds do not reach the standard lengths for C-S (1.82 A), C-C (1.54 A) and C=C (1.35 A). Compared to these large differences, the remaining geometrical parameters experience only minor changes.

Upon doping bithiophene with two Li atoms, a double bond of length 1.332 A is formed between

Sl

Fig. 2. Atomic numbering schemes, bond lengths in A,, and

torsional angles in degrees for Li-thiophene, di-Li-bithiophene,

Likbenzene and di-Li-biphenyl.

the rings. Also, the SlC2C2’Sl’ dihedral angle is almost planar at 178”. The quinoid bond length pattern is not fully established within the thiophene rings for the syn-facial arrangement of the two lithium atoms above the two thiophene rings. A change to the anti-facial arrangement also fully introduces these quinoid bond length alternations [18].

Li-benzene exhibits the same electronic and geometrical features as the benzene radical anion where ab initio SCF and CI calculations have already been reported by Hinde et al. [43]. Two structures of C6H6-, close in energy, are found corresponding to the occupation of either of the two degenerate benzene LUMOs of e2u type. The molecular point group reduces to D2h. One of the two states (2Biu) shows a quinoid bond length alternation pattern and the other (2Au) an anti-quinoid pattern. This situation can be analyzed in terms of the Jahn-Teller theorem [44,45] and on the basis of the nodal properties of the singly occupied lezu orbitals (see Ref. [43] and references cited therein). Analogous to Hinde et al. [43], we restrict ourselves to calculations within the framework of the Born-Oppenheimer approximation, neglecting coupling between different electronic states. This procedure can certainly be regarded as only a first approximation, especially when calculating the vibrational frequencies reported later on. For the Li-benzene complex, one obtains two geometries with the same character- istics as for C6H6- (see Ref. [ 181). The point group is further reduced to Ch due to the asymmetric polar- izing effect of the Li+ counterion. The two structures correspond to the 2A1 and 2A2 states, respectively. Vibrational analysis shows that the 2Ai state is a local minimum, whereas the other structure is a saddle point (one imaginary frequency of 2451’ cm-‘) for the interconversion of one local minimum structure to an equivalent one obtained by cyclic permutation of carbon-carbon single- and double-bonds. The 2A, state is the one with the quinoid geometry. Its bond length alternation pattern is more pronounced by M 0.02A than in the Li-thiophene case, and the molecule is found to be boat-shaped by z 15” with the atoms Cl and C4 oriented towards Li. In the following, we only consider the ‘Ai minimum structure further.

For di-Li-biphenyl, the bond length alternation pattern within the rings is comparable to the

18 S. Irle. H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31

Li-benzene case, the intra-ring double bonds even being slightly shorter. The rings in di-Li-BP pos- sess chair-conformation with a torsional angle of 14”, in contrast to Li-benzene. The molecule possesses CzV symmetry, and the torsional angle for C2ClCl’C2’ is 0”. Shortening the ortho-hydrogen bond lengths by 0.02 A relaxes the strain only a little,’ the distance between them still being smaller than their sum of van der Waals radii. This steric hindrance leads to stretching of the inter- ring double bond by 0.037 A relative to di-Li- bithiophene.

Our previous SCF calculations on the open-shell systems have been performed with the ROHF method [18]. Since for an analytical calculation of force constants only the UHF method was avail- able, all geometries were reoptimized using UHF. Only a relatively small spin contamination was found ((S2) = 0.82 and 0.79 for Li-thiophene and Li-benzene, respectively). Therefore, the ROHF and UHF geometries are very similar and are not explicitly tabulated here.

Electron correlation is very important for the energetic stability of the charge transfer systems [18]. At the SCF level (even with very large basis sets), these complexes are not bound with respect to Li atoms and the neutral molecule. Electron correlation calculations at the MP2 and MP3 levels show the charge-transfer systems to be stable [18] (Li-benzene is probably metastable in the gas phase). However, all structures investigated here are local minima even at the SCF level. A comparison of SCF and MP2 geometries (see Ref. [18]) for the monomer and dimer subsystems shows only relatively small effects due to electron correlation. Since we are mainly interested in the vibrational frequency shifts of the intramolecular modes within the monomers and dimers and not in the intermolecular vibrations of lithium, we consider it justified to use the much more economical SCF method for the calculation of force constants.

4. Vibrational spectra

4.1. Scaling procedures

Scaling of the force constants according to Pulay

Table I SCF/DZP force constant scaling factors for thiophene and

bithiophene (BT), benzene and biphenyl (BP), all-trans-hexa-

and all-trans-octatetraene

Type of coordinate Thiophene/BT Benzene/BP Oligoenes

CS 0.927

c-c 0.902 0.841 0.867

c=c 0.729 0.707

CC aromatic 0.836

CH 0.832 0.834

Ring bends 0.806 0.829

CCH bends 0.826 0.832

CH out-of-plane 0.736 0.756

Ring torsions 0.815 0.777

CC/CC ortho 0.791

CC/CC meta 0.455

CC/CC para 0.643

c=c/c=c 1.754

CC/C-C 1.178

c=c/c-c 1.158

et al. [42] is a very useful way to account for systematic errors such as the neglect of anharmo- nicity effects, basis set defects and electron correlation. In many cases, “conventional scaling” is sufficient, and typical values for the scaling factors range between 0.7 and 0.9. This kind of scaling was used for the thiophene systems. However, for special cases like acyclic conjugated compounds (1,3-butadiene, 1,3,5_hexatriene and higher homo- logues of this series), it has been demonstrated that separate scaling factors larger than unity have to be chosen for the coupling constants between CC single and double bonds [46,47]. Moreover, the so-called “Kekule constraint” of Scherer and Overend [48], i.e. the equality of ortho-, meta- and para-coupling constants, has been proven to be unjustified [29]. Therefore, individual scaling factors for the CC/CC coupling force constants have been employed for benzene, biphenyl and the oligoenes. The scaling factors for the undoped compounds were obtained from fits to the experimental frequencies of thiophene [49], bithiophene (BT) [50], benzene [29] and biphenyl (BP) [51]. They are given in Table 1 together with the carbon- carbon scaling factors derived from all-trans- 1,3,5hexatriene and all-trans-1,3,5,7_octatetraene

S. Irle, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31

Table 2 Vibrational frequencies, IR intensities and Raman activities of thiophene and Li-thiophene and approximate assignments’

19

Calc. IR Raman int. act.

Exptb Approx. assignment

Thiophene Al

B2

A2

BI

RMSD errorC

Li-thiophene A’

AN

3121 3.2 233.9 3126 C-H str. 3092 4.2 92.3 3098 C-H str. 1424 19.4 57.0 1409 c=c 1358 0.1 4.2 1360 C=C str., CCH bend 1075 4.6 12.1 1083 CCH bend 1025 1.0 6.0 1036 C-C str., CCH bend 835 33.7 9.7 839 C-S str. 603 1.5 8.3 608 Ring def.

3118 0.7 1.9 3125 C-H str. 3080 5.1 90.0 3086 C-H str. 1502 0.2 0.8 1504 C=C str. 1270 8.5 0.1 1256 CCH bend 1075 3.4 8.7 1085 CCH bend 867 1.6 0.4 872 C-S str. 755 0.0 4.9 763 Ring def. 897 0.0 2.4 898 C-H oop 693 0.0 1.7 683 CH oop 564 0.0 0.4 565 Ring def. 878 1.4 0.4 867 C-H oop 696 132.8 0.3 712 C-H oop 442 1.9 1.9 452 Ring def.

7.9

3095 3077 1415 1291 1063 1009 762 721 638 534 502 353 209

3091 3062 1369 1206 1000 852 829 686 546 509 249

3.5 246.7 C-H str. 4.5 96.9 C-H str. 4.6 97.8 C=C str. 1.4 11.8 CCH bend, C-C str. 1.4 45.7 CCH bend 8.6 66.5 C-C str.

27.0 10.6 C-S str. 70.4 24.9 C-H oop

157.7 33.4 C-H oop 27.5 7.7 Ring bend 50.4 32.0 Li-Ring str.

1.1 20.3 Li tors. 17.8 19.8 Ring def. 1.7 42.7 C-H str. 0.3 82.8 C-H str. 4.7 6.9 CCH bend

17.9 5.6 CCH bend 43.3 1.2 C-C str.

0.5 1.5 Ring def. 0.4 4.1 C-H oop 0.3 7.8 C-S str.

80.6 0.6 Ring tors. 84.3 5.8 C-H oop 39.7 38.2 Li tors.

a Frequencies in cm’, IR intensities in km mol-’ , Raman activities in A4 amu-‘. b Ref. [49]. ’ Defined as [Ciwi(v~’ - r~~“)~/C~w~]“~ where veXp and zlcB” are the experimental and calculated frequencies, and Wi = l/vf”” x 1000.

20 S. Irle, H. Lischka/Journal of Molecular Structure (Theochem) 364 (1996) 15-31

[52,53]. The accuracy of the fits is quite satisfactory for our purposes. In all cases the 1 /v-weighted root mean squares deviation (RMSD) error is about 8 cm-’

The transfer of scaling constants from the undoped, aromatic compounds to the doped, quinoid species is not straightforward. The doped thiophene and bithiophene cases are probably not so problematic because the aromaticity of thiophene is much lower in comparison to benzene (see, for example, Refs. [54] and [55] and references cited therein). No extra scaling of coupling force constants was considered necessary here, in line with the calculations by Ehrendorfer and Karpfen [33-351 on the vibrational spectra of positive bipolaron defects in oligothiophenes. Thus, the scaling factors from thiophene/bithiophene were used for Li-thiophene and di-Li-BT, taking the

IR intensity [km mol-‘1

inverted bond length alternation into account. Scaling factors for the C3-C4 and C4-C5 bonds which are intermediate between single and double bonds were computed as the geometric mean of the single and double bond scaling factors.

The scaling factors chosen for benzene/biphenyl are very specific for the aromatic case. Since in the doped compounds there is a strong quinoid character, the “aromatic” scaling factors are certainly not well suited in the latter case. There- fore, we decided to apply the scaling factors determined for polyenes (Table 1) for the carbon backbone and to take those involving hydrogen atoms and ring bending/torsional modes from the aromatic systems. Scaling of coupling force constants was done in two ways: in scheme I the standard scaling procedures were used without any special modifications of CC coupling force

Raman activity [A4amd]

60 -

50

40 Thiophene

30

20 .

160

140

120

100

80

60

40

20

0

Li-thiophene

I I

120

100

80

I Li-thiophene

I ! I I

2000 1800 ,600 1400 ,*0* 1000 800 600 400 200 0 2000 ,800 1600 1400 1200 1000 BOO 600 400 200 0

Wavenumber [cm11 Wavenumber [cm-l]

Fig. 3. Theoretical infrared and Raman line spectra of thiophene and Li-thiophene excluding CH stretches.

S. Me, H. Lischka/Journal of Molecular Structure (Theochem) 364 (1996) 15-31 21

constants; in scheme II the coupling force constants determined from the polyenes were applied. Because of lack of experimental spectra, it is difficult to decide which of these schemes is to be preferred. For most modes, results are very similar. Scheme I involves less assumptions and we therefore will always refer to these frequencies in the subsequent discussion and indicate differences to scheme II as necessary. All force constants belonging to internal coordinates of Li were left unscaled.

4.2. Thiophene and Li-thiophene

For thiophene, the strongest IR band is by far the one corresponding to the C-H out-of-plane mode at 696 cm-’ (see Table 2 and Fig. 3). Next in intensity comes the symmetric C-S stretching mode at 835 cm-‘. The CC stretching vibrations in the region of 1025 to 1502 cm-’ show only intensities up to 20 km mol-‘. The highest of these bands correspond to a stretching of the C=C double bonds. In the Raman spectrum, the symmetric C=C stretching mode gives rise to the strongest band (excluding CH stretches) with an activity of 57 A4/amu. All other Raman-active modes not corresponding to C-H stretching modes show activities of only up to 12 A4/amu. Due to the nonplanar structure of Li-thiophene, new bands appear both in the IR and Raman spectra. IR and Raman intensities are found to be generally enhanced due to uptake of charge in the ring system (see Table 2 and Fig. 3). The C-H out-of- plane mode (originally at 696 cm-‘) is still by far the most IR-intensive vibration, but it is red-shifted to 638 cm-‘. The red shift of this band might be caused by the high negative extra charge on the a-carbon atoms (-0.20 e-) weakening the C-H bond. Probably for the same reason, the C-H out-of-plane band at 721 cm-’ has moved from 878 cm-’ and rises sharply in intensity from 1 to 70 km mol-‘. C-H stretching modes are shifted uniformly by z 20 cm-’ towards lower frequencies. The C-S band is down-shifted to 762 cm-‘, thereby indicating the weakening of the C-S bonds. CC stretching bands are found to be generally lower than those of neutral thiophene, located within a region of 1000 to 1415 cm-‘. The lowest of

these bands shows a remarkably high IR intensity of 43 km mol-’ . The highest one corresponds to a stretching of the C3-C4 bond for which the largest force constant is obtained (see below). In the Raman spectra, the most noticeable effects can be found in modes corresponding to symmetric C-C single bond stretching that increase in activity by a factor of 10 (in the region of 1000 to 1080 cm-‘). Also, vibrations appearing at smaller wavenumbers, e.g. the strong IR-active C-H out-of- plane band, and some ring-bending modes, show large variations in activity. Since their absolute scattering activity is small, these changes are not spectacular. Vibrations involving lithium appear at rather low frequencies (249, 353 and 502 cm-‘), typical for ionic interactions. These fre.quencies might be even lower since lithium modes were left unscaled. The most intensive of these modes is the Li-ring stretch motion.

Force constants of stretching coordinates undergo drastic changes when thiophene becomes charged. Those of the C-S bonds decrease by 1.0 mdyn A-’ with a value of 3.2 mdyn A-’ for Li- thiophene, and the former double bonds C2=C3 and C4=C5, with force constants of 7.0 mdyn A-‘, show values of 5.3 mdyn A-’ which is even below that of the former single bond C3-C4 (5.7 mdyn A-‘). Instead, the force constant of this bond js the only one to rise slightly by 0.2 mdyn A-‘. Therefore, the force constants of Li-thiophene are in line with the small bond length alternations which form, nevertheless, a quinoidic pattern.

4.3. Bithiophene and di-Li-bithiophene

As for thiophene, the most intensive IR-active band corresponds to a symmetric C-H out-of- plane motion at 691 cm-’ (see Table 3 and Fig. 4). Again, CC stretching modes are located in the range of 1041 to 1562 cm-’ and are comparatively low in IR intensity (at most 36 km mol-‘). The most IR-intensive symmetric C-S stretching mode appears at 833 cm-‘, similar to thiophene. The Raman spectrum is dominated by two totally symmetric vibrations (excluding CH stretches) of the double bond skeleton. The most intensive vibration of B symmetry appearing in the Raman

22

Table 3

S. Me, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) IS-31

Vibrational frequencies, IR intensities and Raman activities of bithiophene and approximate assignmentsa

Calc. IR Raman int. act.

Exptb Approx. assignment

A 3114 0.2 364.2 3089 0.5 179.9 3075 0.0 144.6 1562 0.2 362.0 1454 2.1 829.0 1383 0.0 21.2 1258 0.2 12.0 1219 5.7 3.4 1074 0.0 25.5 1041 0.1 28.3 894 0.8 1.2 854 14.3 1.9 824 5.7 11.0 754 7.0 8.8 691 132.4 0.5 674 1.1 27.1 567 0.1 1.5 471 3.2 2.3 359 0.1 2.6 284 0.0 2.5 118 2.3 1.4 37 0.3 5.6

3114 2.7 5.4 3088 4.9 26.6 3076 19.8 13.4 1498 9.1 1.6 1432 36.1 2.9 1326 0.4 1.4 1205 17.0 2.0 1075 4.0 2.8 1043 4.8 1.0 898 0.2 9.8 893 0.0 2.0 843 2.1 2.9 833 58.6 0.6 752 10.0 1.2 691 0.1 1.1 608 2.3 1.3 587 3.1 5.6 523 2.2 1.9 280 0.1 4.5 108 0.3 2.1

RMSD errorC 8.1

3107 3080 3074 1557 1446

1250 1227 1083 1056 894 863 815 740 703 675

_

458 _ _

_

3104 3076 3064 1498 1413 1325 1205 1078 1047 894

_

826 _ _

_ _

C-H str. C-H str. C-H str. C=C str. C=C str. C-C str., CCH bend CCH bend Interring str. CCH bend CC str., CCH bend C-H oop C-S str. C-H oop Ring def. CH oop Ring def. Ring tars. Ring tors. Ring def. Ring def. Ring tom. Torsion

CH str. C-H str. C-H str. C=C str. C-C str. C=C str., CCH bend C=C str., CCH bend CCH bend C-C str. C-S str., Ring def. C-H oop C-H oop C-S str. Ring def. C-H oop Ring def.

Ring tors. Ring tors. Ring tors. Ring def.

a Frequencies in cm-‘, IR intensities in km mol-‘, Raman activities in A4 amu-’ b Ref. [50]. ’ As defined in Table 2.

S. Me, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31 23

spectrum below 1600 cm-’ corresponds to C-S stretching and is located at 898 cm-‘.

Turning to the spectra of di-Li-BT (Table 4 and Fig. 4) one immediately recognizes new intensive bands covering the whole range of wavenumbers and reaching up to 795 km mall’ in IR intensity and 4385 A4/amu in Raman activities. The prominent C-H out-of-plane mode at 668 cm-’ no longer gives rise to the strongest band in the IR spectrum. The most intensive peak is located at 1449 cm-‘, corresponding to an asymmetric stretching of C3-C4, while the symmetric mode located 13 cm-’ above shows an intensity of only 16 km mol-’ . Apart from hydrogen stretching vibrations, the highest band at 1590 cm-’ can clearly be assigned to the inter-ring stretching which is extremely blue-shifted by 371 cm-’ due to the formation of the central double bond. It is

IR intensity [km moV]

140 1 BT 120

the dominant feature of the Raman spectrum, being one order of magnitude more Raman-active than all other vibrations. Modes corresponding to lithium motions are found in the region of 145 to 571 cm-t, where the peak at 470 cm-’ possesses the highest IR intensity with 231 km mol-‘. C-H stretching frequencies are red-shifted as in the case of thiophene, the lowest two being even more strongly affected, with shifts of nearly 30 cm--‘.

We note that the theoretical spectra of doubly positive charged BT without counterions reported by Ehrendorfer and Karpfen [33] are rather similar in shape to those of di-Li-BT, with differences of about +30 cm-’ on average. In particular, we also note that in their calculations, the highest Raman- active mode (excluding CH stretches) at around 1600 cm-’ is related to inter-ring stretching. These authors also report a remarkably fast

Raman activity [A4amu-l]

BT

di-Li-BT 3500 di-Li-BT

1. ,! !, ! :, \ , ?1..,1.1!.. . ! ,

2000 1800 1600 1400 ,200 1000 BOO 600 400 200 0 2000 1s00 1600 1400 1200 1000 800 600 400 200 0

Wavenumber [cm-l] Wavenumber [cm-l]

Fig. 4. Theoretical infrared and Raman line spectra of BT and di-Li-BT excluding CH stretches.

24 S. Irle. H. LischkajJoumal of Mdecular Structure (Theochem] 364 (1996) 15-31

Table 4

Vibrational frequencies, IR intensities and Raman activities of

di-Li-bithiophene and their approximate assignmentsa

Calc. IR

int.

Raman

act.

Approx. assignment

A 3106 0.2 482.6 C-H str.

3080 3.1 127.7 C-H str.

3046 4.9 224.2 C-H str.

1590 8.5 4385.4 Interring str.

1462 16.1 201.8 C=C, C-C str.

1346 18.3 210.7 C-C str., CCH 1247 2.5 15.2 C-C str., CCH 1145 11.4 321.9 C-C str., CCH

1059 1.6 21.5 CCH

1036 1.3 59.1 C-C str.

908 3.7 70.6 C-H oop

812 43.1 9.3 Ring def.

693 169.9 94.2 C-S str.

668 44.1 124.2 C-H oop

628 7.7 46.9 Ring def, C-C str. 571 19.0 139.9 Ring tom., Li tars.

516 14.1 140.1 Li-Ring str.

491 50.8 307.1 Ring tars. 409 0.4 12.8 Ring def.

335 1.2 5.0 Li-Ring str.

293 0.4 53.3 Ring tars.

273 0.4 21.5 Ring tow

145 2.5 143.1 Li tars.

97 0.6 2.4 Torsion

63 5.6 6.0 Ring def.

B 3106 10.1 114.6 C-H str.

3079 3.2 32.6 C-H str.

3048 18.0 49.4 C-H str. 1449 794.7 149.4 C=C str.

1386 277.8 20.7 C-C str., CCH 1267 81.2 7.4 CCH 1100 37.5 1.8 C=C str., CCH

1060 8.2 0.3 C-C str., CCH 1018 22.3 0.4 c-c SW. 908 13.5 9.6 C-H oop 865 10.0 0.7 Ring def. 768 16.8 7.6 C-S str. 694 15.3 1.1 C-S str. 661 21.2 0.1 C-H oop 629 11.1 5.1 Ring tars. 550 170.2 20.4 Ring def. 519 194.6 24.5 Ring def.

506 17.3 12.9 Ring tors. 470 231.0 70.8 Li-Ring str., C-H oop 318 59.5 25.9 Li-Ring str. 150 144.2 13.7 Li tom. 131 5.0 13.7 Ring tars. 117 14.9 5.6 Ring def.

a Frequencies in cm-‘, IR intensities in km mol-‘, Raman activities in A4 amu-’

convergence of the Raman spectra with chain length. The similarity between the computed vibrational spectra for di-Li-BT and those of the BT dication is certainly related to the fact that both systems show quinoidic distortions.

Force constants of neutral BT are very close to the corresponding values of thiophene. The inter- ring force constant is typical for a single bond with 5.4 mdyn A-‘. The largest one in di-Li-BT belongs to the inter-ring double bond (7.5 mdyn A-‘), followed by those of C4-C5 (6.5 mdyn A-‘) and C3-C4 (5.8 mdyn A-‘). Thus, the incompleteness of the quinoid distortion on the edges of doped BT is, therefore, also reflected by the force constants. Unexpectedly, the C2-C3 force constant is higher by 0.2 mdyn A-’ than in the thiophene case, although its bond length is larger by 0.051 A.

Table 5

Vibrational frequencies, IR intensities and Raman activities of

benzene and their approximate assignmentsa

Calc. IR Raman Expt.b Approx. assignment

int. act.

AIs

A,, hu

B2u

Q3

E I”

A 2u

%

%

E2u

3080 0.0 370.6

999 0.0 56.4

1366 0.0 0.0

3043 0.0 0.0

1010 0.0 0.0

1314 0.0 0.0

1135 0.0 0.0

3054 0.0 132.4

1603 0.0 11.9

1162 0.0 5.7

606 0.0 4.8

3069 46.1 0.0

1490 11.4 0.0

1027 3.3 0.0

663 110.4 0.0

988 0.0 0.0

691 0.0 0.0

838 0.0 1.4

964 0.0 0.0

402 0.0 0.0

RMSD

errorC 8.2

3056

1599

1178

606

3064

1482

1037

673

990

707

846

967

398

C-H str.

Ring breath

CCH bend

C-H str.

CC str., CCH bend

C-C str. (Kekule)

C-C str.

CH str.

C-C str.

CCH bend

Ring def.

CH str.

C-C str.

CCH bend

C-H oop

C-H oop

Ring tars.

CH oop

CH oop

Ring tors.

a Frequencies in cn~‘, IR intensities in km mol-‘, Raman

activities in A4 amu-‘.

b Ref. [29].

’ As defined in Table 2.

S. Irle. H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31 25

4.4. Benzene and Li-benzene

The IR and Raman spectra of benzene (see, for example, Refs. [29,56,57] are well known. The results of our calculations are given in Table 5 and Fig. 5. Only four fundamentals appear in the IR spectrum belonging to Et, and AZu symmetries, the most intensive one being the AZu C-H out-of- plane mode at 663 cm-‘. The Raman spectrum shows 7 peaks; the totally symmetric ring breath mode at 999 cm-’ is clearly apparent beside the hydrogen stretching modes, with an activity of 56 A4/amu. Although the diagonal CC force constant of benzene is only 6.6 mdyn A-’ (vs. 7.0 mdyn A-’ for the C=C double bond in thiophene), the largest stretching frequency for benzene at 1603 cm-’ exceeds the highest one of thiophene by 103 cm-‘, thus indicating the strong coupling effects in benzene.

The IR and Raman spectra of Li-benzene (Table 6 and Fig. 5) are rich in visible bands due to the reduced molecular symmetry. IR intensities are somewhat enhanced, whereas Raman activities increase by one order of magnitude. Below 1600 cm-‘, the highest two frequencies at 1551 and 1434 cm-i can be clearly assigned to stretching of C2=C3 and C5=C6. Both are IR and Raman allowed. The ring breath and the Kekule modes are red-shifted with respect to benzene by 100 and 80 cm-‘. C-C single bond stretching modes occur at low frequencies of 775 and 999 cm-‘. The IR- intensive CH out-of-plane mode of benzene is red-shifted by z 30 cm-‘, which is only half of the corresponding shift in thiophene. It still gives rise to the highest peak of the IR spectrum. C-H stretching modes are red-shifted in general, but some of them are affected only to a small extent (Ar,,Bi,). The Raman spectrum is dominated by

IR intensity [km mol-7 Raman activity [A4amu-I]

60 -

“’ i Benzene 50 Benzene 1cJo 40 80

30 . 60

20 40

2000 1800 1600 1400 1200 1000 800 600 ‘loo 200 0 2000 1800 1600 1400 1200 1000 BOO 600 400 200 0

Li-benzene

2000 1800 1600 1400 1200 1000 800 600 400 200 0 2000 1800 1600 1400 1200 1000 800 600 400 200 0

Wavenumber [cm’] Wavenumber [cm-l]

Fig. 5. Theoretical infrared and Raman line spectra of benzene and Li-benzene excluding CH stretches.

26 S. Irle. H. Lischka/Journal of Molecular Structure (Theochem) 364 (1996) 15-31

Table 6

Vibrational frequencies, IR intensities and Raman activities of LiPbenzene and their approximate assignments”

Caleb IR

int.

Raman

act.

Approx. assignment

Al

B2

A2

Bl

3075 3.1 283.6 C-H str.

3053 0.8 180.4 C-H str.

1551 (1567) 1.8 502.0 C=C str.

1141 0.1 160.5 C-C str., CCH bend

900 (953) 1.8 437.7 Ring breath

738 4.4 367.0 C-H oop

636 147.4 172.9 C-H oop

532 18.6 10.5 Ring def.

479 68.7 166.9 Ring tars, LiPring str.

286 7.9 200.2 LiPring str.

3070 16.2 45.7 C-H str.

3038 4.2 0.6 C-H str.

1419 0.6 0.2 C-C str., CCH bend

999 1.5 0.6 C-C str.

934 (918) 3.4 15.0 C-H oop

918 (895) 65.2 1.4 Ring def.

621 45.2 0.2 C-H oop

542 133.6 15.7 Ring tars.

278 40.0 117.9 Li tars.

3038 0.0 155.3 C-H str.

1327 0.0 0.2 CCH bend, C-C str.

1286 0.0 1.6 CCH bend

944 0.0 0.0 C-H oop

775 (719) 0.0 23.2 C-C str., Ring def.

597 0.0 8.1 Ring def.

433 0.0 0.9 Ring tors.

3058 52.1 15.5 C-H str.

1434 3.7 56.2 C=C str.

1234 (1208) 59.1 58.7 CCH bend, C-C str. (Kekulk)

1115 (1105) 3.5 3.0 CCH bend

989 0.9 2.4 CCH bend

759 (775) 0.1 6.1 C-H oop

213 22.8 0.2 Li-Ring str.

a Frequencies in cm-‘, IR intensities in km mol-‘, Raman activities in A4 /amu-’

b Scheme I (scheme II in parentheses where differences exceed 10.0 cm-‘).

the C=C A, symmetric stretching mode at 1551 cm-’ and by the ring breath mode, both showing scattering activities of more than 400 A4/amu.

For the Li-benzene complex, the larger of the two CC stretching force constants is that for the C2=C3 and C5=C6 double bonds with 6.2 mdyn A-‘. However, this value is even smaller compared to the value of 6.6 mdyn A-’ in benzene. The lower one is the absolute lowest of all the CC bonds discussed here, with only 4.4 mdyn A-‘, although the corresponding bond length is not the largest. These relatively small force constants are certainly an

indication of the loss of aromaticity by charge transfer.

Li modes are found in the same region as for thiophene systems. The Li-ring stretching mode is located a little lower (479 cm-‘) indicating a weaker interaction, in agreement with our previous calculations [ 181.

The two different sets of coupling force constants (scheme I and scheme II) mostly affect the CC stretch and ring deformation modes of Li-benzene. The ring breath and Kekule modes are calculated at 900 and 1234 cm-’ with scheme I and at 953 and

S. Me, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31 21

1208 cm-’ with scheme II. Even more affected is the A2 ring deformation located at 775 cm-’ (scheme I) as compared to 719 cm-’ with scheme II. In total, there are eight modes that differ by more than 10 cm-’ in both scaling schemes. The RMSD between the frequencies calculated with the two scaling schemes is only 9.7 cm-‘.

IR-intensive bands (excluding CH stretches) of biphenyl belong to two C-H out-of-plane motions (see Table 7 and Fig. 6). CC stretch modes appear in the region between 1450 and 1620 cm-‘. The most important Raman active modes are located at 1619 cm-’ (intra-ring CC stretching), 1287 cm-’ (inter-ring stretching), and 967 cm-’ (symmetric intra-ring breath).

4.5. Biphenyl and di-Li-biphenyl

Similar to the spectrum of benzene, the most

Table 7

The IR and Raman spectra of di-Li-BP (Table 8 and Fig. 6) show extraordinarily enhanced intensities and scattering activities compared to BP. IR

Vibrational frequencies, IR intensities and Raman activities of biphenyl and their approximate assignments”

Calc. IR Raman Expt.’ Approx. assignment Calc. IR Raman Expt.h Approx. assignment

int. act. int. act.

A 3080 0.0

3067 0.0

3049 0.0

1619 0.0

I523 0.0

1287 0.0

1173 0.0

1030 0.0

1000 0.0 967 0.0

837 0.0

736 0.0

408 0.0

303 0.0

56 0.0

RI 3071 30.0

3064 40.7

3057 6.4

1603 14.4

1498 41.6

1169 0.4

1041 0.8

1012 0.1

998 5.7

967 0.5

837 0.1

609 1.6

403 0.3

R? 3078 45.2

3074 9.4

1573 5.4

1443 11.5

547.1

122.8

51.5

279.7

10.3

103.3

4.9

20.5

0.1

80.4

1.3

11.9

2.1

4.8

11.2

63.6

28.4

7.0

2.3

0.0

1.1

0.0

0.0

1.4

7.2

1.0

0.9

0.1

0.2

40.2

0.9

0.6

_ 1613

1505

1282

1190

1029

1003

964

838

740

403

315

_

_

_

1595

1481

1174

1042

1007

990

964

838

609

403

_

_

1567

1439

C-H str.

C-H str.

C-H str.

C-C str.

C-C str.

4-4 str.

CCH bend

C-C str., CCH bend

Ring def., C-C str.

CH oop

CH oop

Ring def.

Ring tors.

Ring def.

Torsion

C-H str.

C-H str.

CH str.

C-C str.

C-C str.

CCH bend

CC str., ring def.

CC str., ring def.

Ring def.

C-H oop

C-H oop

Ring tors.

Ring tors.

C-H str.

C-H str.

C-C str.

C-C str.

1344 2.5

1270 0.0

1146 0.0

1076 4.5

980 0.1

921 1.2

774 8.1

687 12.4

624 0.0

541 3.9

266 0.0

93 0.2

B3 3054 11.4

3048 0.3

1587 0.3

1469 2.3

1340 0.0

1311 0.0

1146 0.1

1072 0.3

980 0.1

904 2.6

733 81.7

689 45.3

612 0.0

496 8.6

352 0.3

119 1.0

RMSD

errorC 8.1

1.0 1337 CCH bend, C-C str.

0.7 I266 CCH bend

3.1 1155 CCH bend

0.0 1072 CCH bend

0.7 979 C-H oop

1.1 917 C-H oop

0.1 778 C-H oop

1.6 670 C-H oop

1.9 628 Ring def.

1.5 543 Ring tors.

4.9 269 Ring tors.

4.5 112 Ring tors.

14.5

195.5

5.7

3.1

1.2

0.0

14.0

0.6

0.1

0.0

0.3

0.1

9.5

0.0

0.0

2.1

_

1595

1455

1376

1317

1158

1090

964

902

735

698

615

486

367

CH str.

C-H str.

C-C str.

C-C str.

CCH bend, C-C str.

CCH bend

CCH bend

CCH bend, ring def.

C-H oop

Ring tars., C-H oop

Ring tars., C-H oop

C-H oop

Ring def.

Ring tors.

Inter-ring bend

Inter-ring bend

a Frequencies in cm-‘, IR intensities in km mol-‘, Raman activities in A4 /amu-’

b Ref. [51].

’ As defined in Table 2.

28 S. Irle, H. Lischka/Journal of Molecular Structure (Theochem) 364 (1996) lS-31

IR intensity [km mol-l]

I, I_ I II., I I,

2000 Ill00 ,600 1400 1200 1000 800 600 400 200 0

700

600

500

400

300

200

100

0

di=Li-BP

,. I I;,1 ;..,.. 11 2000 la00 1800 1400 1200 1000 500 500 400 200 0 2000 ,500 ,500 1400 1200 1000 500 800 400 200 0

Wavonumbor [cm’] Wavenumbor [cml]

Raman activity [A4amw1]

12000

10000

8000

6000

4000

2000

0 I di-LbBP

u.:. .,I . ...! ..,. :?. !.. ’ ..,... (

Fig. 6. Theoretical infrared and Raman line spectra of BP and di-Li-BP excluding CH stretches.

intensities increase by one, and Raman activities by two orders of magnitude. Inter-ring stretching occurs as the highest (scaling scheme I) and most prominent peak in the Raman spectrum at 1578 cm-‘. However, this wavenumber is somewhat lower than that of di-Li-BT inter-ring stretching due to steric hindrance caused by the hydrogens, which is absent in di-Li-BT. In addi- tion to its high Raman activity, the corresponding IR intensity is also high, with 160 km mol-’ . This band has been blue-shifted by about 300 cm-’ relative to BP and is fortuitously located close to the position of the most prominent Raman peak of the undoped molecule. This drastic blue-shift stems from the change of the inter- ring single bond in BP to a double bond in doped BP. An intra-ring C=C stretching mode of B2 symmetry is also located rather close to the

inter-ring frequency. It has, however, a much lower Raman activity.

The originally dominant Raman peak at 1619 cm-’ is significantly red-shifted in the doped complex. C-H stretches do not show the clear trend towards red-shifting as for the complexes discussed above. The highest symmetric mode involves mainly stretching of ortho-hydrogens and is blue-shifted by 16 cm-’ due to the planarization of the two phenyl rings upon doping.

Diagonal force constants of BP are 4.5 mdyn A-’ for the inter-ring and x 6.6 mdyn A-’ for the intra-ring C-C bonds. For the lithium-doped complex, yalues of 6.9 mdyn ApI0 (inter-ring), 4.7 mdyn A-’ (CJ-C2), 7.9 mdyn A-’ (C2-C3) and 5.4 mdyn A-’ (C3-C4) are found. The geometry parameters and force constants are therefore in nearly perfect agreement, indicating the

S. Irle. H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31 29

Table 8

Vibrational frequencies, IR intensities and Raman activities of di-Li-biphenyl and their approximate assignmentsa

Caleb IR Raman

int. act.

Approx. assignment Caleb IR Raman Approx. assignment

int. act.

Al 3096 5.1 292.5 C-H str.

3081 0.0 472.9 C-H str.

3030 8.5 176.6 C-H str.

1578 (1563) 159.6 12620.3 f#-4 str.

1482 (1455) 100.4 683.4 C=C str.

1365 (1354) 9.3 116.2 C-C str., CCH

1174 (1184) 39.8 598.3 CCH

979 (965) 1.2 3.4 C-C str., ring def.

956 3.6 207.4 C-H oop

955 (935) 20.7 795.5 Ring def.

741 361.7 20.0 C-H oop

694 (712) 7.7 158.8 C-H oop

659 7.9 327.3 C-H oop

638 52.5 566.6 Ring tors.

504 21.5 912.3 Li-ring str.

346 0.0 10.1 Ring tors.

318 0.0 254.3 Ring def.

245 4.0 58.3 Li tars.

54 1.4 9.5 4-4 bend

IQ 3082 7.2 43.8 C-H str.

3071 0.0 3.0 C-H str.

3029 31.1 13.9 C-H str.

1523 (1579) 677.1 801.2 C=C str.

1437 (1427) 6.8 15.7 C=C str.

1141 (1156) 126.5 49.3 CCH

1002 (992) 3.9 0.0 Ring. def.

975 149.9 60.1 C-C str., ring def.

938 0.1 35.4 Ring def.

907 72.3 35.2 Ring def.

756 14.0 107.5 C-H oop, ring tors.

692 10.3 9.1 C-H oop

648 183.3 144.4 C-H oop

562 9.1 1.6 Ring def.

522 6.9 85.5 Ring tars.

472 (438) 78.9

292 0.3

89 6.4

A2 3071

3031

1464 (1444)

1384

1249 (1294)

1215 (1239)

1084 (1106)

1047 (1001)

936 (956)

748

606

470

399

265

84

0.0 2.2 C-H str.

0.0 341.8 C-H Str.

0.0 7.1 C=C str.

0.0 1.3 C-C str.

0.0 2.4 CCH

0.0 2.7 CCH

0.0 1.6 CCH

0.0 8.3 C-C str.

0.0 3.3 C-H oop

0.0 0.6 Ring tars.

0.0 3.0 Ring. def.

0.0 1.9 Ring tors.

0.0 0.1 Ring def.

0.0 4.8 Li tars.

0.0 0.9 4-p tors.

BI 3094 29.2 5.6 C-H str.

3032 59.6 24.1 C-H str.

1469 (1430) 10.4 3.8 C=C str.

1371 178.5 0.3 C-C str., CCH

1290 (1277) 210.4 0.1 CCH

1200 8.8 3.2 CCH

1064 63.2 13.1 CCH

1012 1.6 0.1 C-C str.

991 7.9 3.0 C-Hoop

763 18.6 0.2 C-H oop

615 0.8 1.6 Ring def.

483 27.6 19.9 Ring tors., LI tors

256 0.5 54.4 Li tors.

162 2.1 0.3 +r$ bend

39.3 Li-ring str

25.4 Li tors.

62.8 4-4 tors.

a Frequencies in cm-‘, IR intensities in km mol-‘, raman activities in A4 /amu-’

b Scheme I (scheme II in parentheses where differences exceed 10 cm-‘).

quinoid distortion. The diagonal intra-ring CC stretch force constants in di-Li-BP are roughly 1 mdyn A-’ larger than the respective ones in

Li-benzene. Twenty frequencies of di-Li-BP differ by more

Li-ring stretch frequency is also affected by the different scaling schemes. The RMSD between both schemes is only 5.1 cm-’ compared to an RMSD value of 9.7 cm-’ for Li-benzene.

than 10 cm-’ between scaling schemes I and II.

Most of them are located in the CC stretching region between 955 and 1578 cm-‘. The biggest differences amount to about 56 cm-’ and concern C=C stretching modes. Interestingly, the B2

5. Conclusions

Information on the structures and vibrational spectra of lithium-doped aromatic systems serving

30 S. Irle, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31

as models for polaronic and bipolaronic defects has been presented. As a consequence of the formation of quinoidic structures from the conjugated aromatic rings, a significant rearrangement of the vibrational modes takes place. Moreover, because of the charge-transfer from Li to the conjugated r-system, the intensities of the IR and Raman lines are increased substantially (one order of magnitude and more). This effect is much more pronounced in the case of the di-Li complexes. One of the main features for di-Li-BT and di-Li-BP is the formation of an inter-ring CC double bond due to the charge transfer. Concomitantly, the inter-ring vibrational mode is blue-shifted by M 300 cm-‘. It is located a little below 1600 cm-’ and constitu- tes the most prominent peak in the Raman spectrum for both the doped BT and BP cases. This finding agrees well with the theoretical results by Ehrendorfer and Karpfen [35] who also report a remarkably fast convergence of the Raman spectra with respect to chain length. Assuming a similar behavior for the oligophenyl series, we expect the inter-ring vibration for the bipolaron defects in p-oligophenyls to be in the region between 1550 and 1600 cm-‘. Raman spectra of p-oligophenyl dianions in solution have been reported by Furukawa et al. [14]. In this work the inter-ring stretching mode was assigned to bands in the region between 1320 and 1357 cm-‘. This assignment is certainly not in agreement with our calculations. From our results obtained from the two scaling schemes (1578 and 1563 cm-‘), we cannot imagine that our calculated values, which are already corrected empirically by scaling, would be shifted in more accurate calculations by more than 200 cm-’ towards 1320 or 1357 cm-’ as required by the experimental assignment. Also, the aforementioned fast convergence of the Raman spectra with chain length on oligo- thiophene dications [35] does not support any significant reductions of the inter-ring frequency. Of course, calculations on larger p-oligophenyls would be required in order to investigate the actual chain length dependences in more detail. Moreover, great care has to be exercised when comparing our quantum chemical calculations on isolated complexes with measurements in solution.

Acknowledgment

This work was carried out with the support of the Austrian “Fonds zur Fiirderung der wissen- schaftlichen Forschung”, project no. P9569-CHE. The calculations were carried out in part on the DEC Alpha 2100 4/275 cluster of the Vienna University Computer Center.

References

[I] J.E. Frommer and P.R. Chance, Encyclopedia of Polymer

Science and Engineering, John Wiley, New York, 1986.

[2] A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Rev.

Mod. Phys. 60 (1988) 781.

[3] J.-L. Bredas and R.R. Chance (Eds.), Conjugated

Polymeric Materials: Opportunities in Electronics, Opto-

electronics and Molecular Electronics, NATO-AS1 Series

E182, Kluwer, Dordrecht, 1990.

[4] J.-L. Bredas and R. Silbey (Eds.), Conjugated Polymers -

The Novel Science and Technology of Highly Conductive

and Nonlinear Optically Active Materials, Kluwer,

Dordrect, 1991.

[5] R. Roncali, Chem. Rev., 92 (1992) 711.

[6] R.H. Baughman, J.L. Bredas, R.R. Chance, R.L. Elsen-

baumer and W.L. Shacklette, Chem. Rev., 82 (1982) 209.

[7] J.L. Brbdas, R.R. Chance and R. Silbey, Phys. Rev. B, 26

(1982) 5843.

[8] J.L. Bredas and G.B. Street, Act. Chem. Res., 18 (1985)

309.

[9] D. Jones, M. Guerra, L. Favaretto, A. Modelli, M.

Fabrizio, and G. Distefano, J. Phys. Chem., 94(1990) 5761.

[lo] P. Bluerle, Adv. Mater., 4 (1992) 102.

[l l] S. Hotta and K. Waragai, Adv. Mater., 5 (1993) 896.

[12] H. Gregorius, W. Heitz and K. Mullen, Adv. Mater., 5

(1993) 279. [13] M.G. Ramsey, D. Steinmtiller and F.P. Netzer, Synth.

Met., 54 (1993) 209.

[14] Y. Furukawa, H. Ohtsuka and M. Tasumi, Synth. Met., 55

(1993) 516.

[15] J.-L. Brbdas, B. Themans, J.G. Fripiat, J.M. Andre and

R.R. Chance, Phys. Rev., 29 (1984) 6761.

[16] C. Ehrendorfer and A. Karpfen, J. Phys. Chem., 98 (1994)

7492.


10196.

[18] S. Irle and H. Lischka, J. Chem. Phys., 103 (1995) 1508.

[19] L. Cuff, C. Cui and M. Kertesz, J. Am. Chem. Sot., 116

(1994) 9269.

[20] D.S. Boudreaux, R.R. Chance, J.L. BrMas and R. Silbey,

Phys. Rev. B, 28 (1988) 4180. [21] S. Stafstrom and J.-L. Brbdas, Phys. Rev. B, 38(1988) 4180.

[22] R. Lazzaroni, M. Liigdlund, S. Stafstrom, W.R. Salaneck

and J.L. Bredas, J. Chem. Phys., 93 (1990) 4433.

S. Irle, H. LischkalJournal of Molecular Structure (Theochem) 364 (1996) 15-31 31

[23] C. Fredriksson and S. Stafstrtim, J. Chem. Phys., 101 [40] S.M. Bachrach and A. Streitwieser, J. Am. Chem. Sot., 106

(1994) 9137. (1984) 5818.

[24] G. Zerbi, M. Gussoni and C. Castiglioni, in Ref. [4].

[25] C. Castiglioni, M.D. Zoppo and G. Zerbi, J. Raman

Spectrosc., 24 (1993) 485.

1261 C. Kui, M. Kertesz and H. Eckhart, Synth. Met., 41 (1991)

3491.

[27] M. Kofranek, T. Kovar, H. Lischka and A. Karpfen, J.

Mol. Struct. (Theochem), 259 (1992) 181.

[28] F. Negri and M.Z. Zgierski, J. Chem. Phys., 100 (1994)

2571.

[41] P. Pulay, G. Fogarasi, G. Pongar, J.E. Boggs and A.

Vargha, J. Am. Chem. Sot., 105 (1983) 7037.

[42] P. Pulay, G. Fogarasi, F. Pang and J.E. Boggs, J. Am.

Chem. Sot., 101 (1979) 2550.

[43] A.L. Hinde, D. Poppinger and L. Radom. J. Am. Chem.

Sot., 100 (1978) 4681.

[44] H.A. Jahn and E. Teller, Proc. R. Sot. Ser. A, 161 (1937)

220.

[29] P. Pulay, G. Fogarasi and J.E. Boggs, J. Chem. Phys., 74

(1981) 3999.

[45] H.A. Jahn, Proc. R. Sot. Ser. A, 164 (1938) 117.

[46] T.P. Hamilton and P. Pulay, J. Phys. Chem., 93 (1989)

2341.

[30] L. Cuff and M. Kertesz, Macromolecules, 27 (1994) 762.

[31] J.T.L. Navarette and G. Zerbi, Synth. Met., 28 (1989) C18.

[32] J.T.L. Navarette, B. Tian and G. Zerbi, Synth. Met. 38

(1990) 299.

[47] M. Kofranek, A. Karpfen and H. Lischka, Int. J. Quant.

Chem., Quant. Chem. Symp., 24 (1990) 721.

[48] J.R. Scherer and J. Overend, Spectrochim. Acta, 17 (1964)

345.

[33] C. Ehrendorfer and A. Karpfen, Vib. Spectrosc. 8 (1995)

293.

[49] J.M. Orza, M. Rico and J.F. Biarge, J. Mol. Spectrosc., 19

(1966) 188. [34] C. Ehrendorfer and A. Karpfen. J. Mol. Struct., 349 (1995)

417. [50] G. Zerbi, B. Chierichetti and 0. Inganas, J. Chem. Phys., 94

(1991) 4637.


5341. [51] R.M. Barrett and D. Steele, J. Mol. Struct., It (1971)

105. [36] R. Ahlrichs, M. Bar, M. Haser, H. Horn and C. Kolmel,

Chem. Phys. Lett., 162 (1989) 165.

[37] M.J. Frisch, G.W. Trucks, M. Head-Gordon, P.M.W. Gill,

M.W. Wong, J.B. Foresman, B.G. Johnson, H.B. Schlegel,

M.A. Robb, E.S. Replogle, R. Gomperts, J.L. Andres,

K. Raghavachari, J.S. Binkley, C. Gonzales, R.L. Martin,

D.J. Fox, D.J. Defrees, J. Baker, J.J.P. Stewart and J.A.

Pople, Gaussian 92, Rev. B, Gaussian, Inc., Pittsburgh, PA,

1992.

[52] H. Yoshida and M. Tasumi, J. Chem. Phys., 89 (1988)

2803.

1531 M. Kertesz,J. Koller and A. Azman, J. Chem. Sot. Chem.

Commun., (1978) 575.

[38] J.A. Pople and R.K. Nesbet, J. Chem. Phys., 22 (1954) 571.

[39] A. Schafer, H. Horn and R. Ahlrichs, J. Chem. Phys., 97

(1992) 2571.

[54] A.R. Katritsky, P. Barczynski, G. Musumarra, D. Pisano

and M. Szafran, J. Am. Chem. Sot., 111 (1989) 7.

[55] S.E. Galembeck, N.B. da Costa, M.N. Ramos and B.deB.

Neto, J. Mol. Struct. (Theochem), 282 (1993) 97.

[56] H. Spedding and D.H. Whiffen, Proc. R. Sot. London Ser.

A, 238 (1956) 245.

[57] J.M. Fernandez-Sanchez and S. Montero, J. Chem. Phys.,

90 (1989) 2909.

an ab initio study of the vibrational spectra of li-doped thiophene, bithiophene, benzene and...

Documents