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Ab initio study of the electronic structure and conduction properties of oxy-derivatives of polythiophene
Solid State Communications.
Pergamon
I I. pp.943-946, 1995 Elsevier Science Ltd Printed in Cjreat Britain 0038%1098/93 $9.50 i .OO
Vol. 94, No.
0038-1098(95)00096-8
AllZNZTZO STUDY OF THE ELECTRONIC STRUCTURE AND CONDUCTION OXY-DERIVATIVES OF POLYTHIOPHENE
PROPERTIES
OF
A.K. Bakhshi Department
of Chemistry, Panjab University, Chandigarh-160
014, India
(Received 3 November 1994 b!l A. Zawadobcski)
The electronic structure and conduction properties of two oxyderivatives of polythiophene (PTP), polythiophene monoxide (PTMO) and polythiophenedioxide (PTDO) have been investigated on the basis of the ab initio Hartree Fock crystal orbital method using double-zeta basis set. The addition of oxygen atoms at sulphur in PTP is found to considerably influence the electronic properties of PTP. Both PTMO and PTDO are predicted to have much smaller band gap than PTP. The nature of quasi-one dimensional superlattices of PTP with both PTMO and PTDO and their electronic properties are also briefly discussed. Keywords: structure.
A. polymers,
A. semiconductors.
1. INTRODUCTION IN THE SEARCH for novel electrically conducting polymers, an exciting possibility is provided by the derivatives of polythiophene (PTP) [I]. PTP has a band gap of 2.1 eV and because of its non-degenerate ground state can support polarons and bipolarons as the charge carriers on doping. Theoretical calculations [2] on polymers with non-degenerate ground state have shown that in them band gap (Es,,,) decreases as a function of increasing quinoid character of the polymer back&one. Further from an analysis [3] of the Bloch wavefunctions of the highest occupied and the lowest unoccupied bands of the (Y- o’ linked PTP, it has been found that the substitution on backbone (/?-carbon atoms) would influence both ionization potential (IP) and electron affinity (EA) values while the choice of the heteroatom affects EA more than the IP. Using above results as guidelines, there have been studies of the various derivatives of PTP, notable among these are polyisothianaphthene (PITN) [4, 51, poly (5,6-dioxymethyleneisothianaphthene) (PDOMITN) [6], poly dithieno [3,4b-3’,4’,d] dithiophene (PDTT’) [7] (all with a band gap of the order of 1.1 eV) and a class of novel tunable narrow band gap hetero-aromatic conjugated polymers in which a
D. electronic
band
band gap of as low as 0.75 eV [8] has been achieved. In this paper we investigate the electroni structure and conduction properties of two derivativ s of PTP, polythiophene monoxide (PTMO) and pol thiophene dioxide (PTDO) obtained by adding on and two oxygen atoms at the sulphur atom of each ;: nit cell of PTP respectively. The structures of these/ polymers along with those of PTP are shown in Fig. . None of these polymers has been synthesized yet bu : in view of the current interest in the search for novel conducting polymers with very small band gap va/lues, it is worthwhile to investigate their electronic properties theoretically prior to their synthesis. Tana a et al. 191 have studied these systems using the CND 6 /2 crystal orbital method and have made certain redictions regarding their electronic structure and ! onduction properties, This paper also tests these conclusions using a more reliable ab initio Hartree-Fbck crystal orbital method employing double-zeta basis set. 2. METHODOLOGY The band structure calculations of the (Y- (Y’ linked PTMO and PTDO were performed using their energetically optimised geometry [9] in the framework of the ab initio Hartree-Fock crystal orbital method [lo, 111. In this method, one solves the pseudoeigen-
943
944
PROPERTIES
OF OXY-DERIVATIVES
OF POLYTHIOPHENE
Vol. 94, No. 11
-cII’,:,I
(7)
respectively with PTOO
PTMO
PTP
p$ = c M
Fig. 1. Structures of the unit cells of (a) polythiophene (PTP), (b) polythiophenemonoxide (PTMO), (c) polythiophenedioxide (PTDO).
c exP (-jk(&
(8)
- R,)C~,,&&,
k
and the two electron integral is given by
value equation for different k values in the Brillouin zone. F(k) and are the Fock and Overlap matrices in the k representation. The index n denotes the band while N is the number of neighboring cells explicitly taken into account. The Fock and Overlap matrix elements are given by S(k)
Fob(k) = 5
exp -(ikRi)
-fz,
(2)
j=-N
s,,(k)
= 2
exp(-ikRj)Sjljb,
(3)
j=-N
where s$ = (&)]x’b(r))
(4)
f SJ’b= ho’ + go’ ab
(5)
ab’
In equation (5), the one electron term (h$,) and the two electron term g$ are given by h$ = -1/2(xjl]A]x’b(r)) +
~~(-&‘+a//‘. h
_xi is the bth atomic basis function in the unit cell denoted by the upper index j; Z, and R, are the charge and position of the oth nucleus and Cd,,,(k) are the components of the mth eigenvector of equation (1). The first summation in equation (8) runs over all doubly filled bands and the second runs over the Brillouin zone. The eigenvalues e,(k) give the band structure of the polymer. All the computations were performed using Clementi’s double-zeta basis set [12] (75 basis functions for PTMO and 85 basis functions for PTDO). All the multicentre two electron integrals larger than the threshold value of lo-‘a.u. were calculated and the interactions up to second neighbors were taken into account.
Rh
- R&(r))
(6)
0
and
3. RESULTS AND DISCUSSION The most important electronic properties such as the IP (corresponding to the top of the valence band), EA (corresponding to the bottom of the conduction band), the band gap and the total energy per unit cell of PTMO and PTDO are given in Table 1. Also given in this table are the corresponding results of PTP [ 161 obtained using the same method and the same basis set. Both the highest occupied and the lowest unoccupied bands in each system are found to be r bands. PTMO and PTDO are found to have
Table 1. Calculated electronic properties (in electron volts) of polythiophenemonoxide (PTMO), polythiophenedioxide (PTDO) and polythiophene (PTP)
PTMO Ionisation potential Electron affinity Valence bandwidth Conduction bandwidth Band gap Scaled value of band gap Total energy per unit cell (a.u.)
8.093 3.951 4.04 1 5.088 4.142 1.14 -1317.107634
PTDO 11.156 5.611 3.953 4.358 5.545 1.53 - 1644.65602 1
PTP 7.749 0.145 3.413 2.937 7.604 2.1 -1174.301889
Vol. 94, No. 11
PROPERTIES
OF OXY-DERIVATIVES
much smaller band gap than PTP and are therefore expected to be less insulating than PTP. The calculated order of band gap is PTMO < PTDO < PTP. This order is not in agreement with the order PTDO < PTMO < PTP obtained by Tanaka et al. [93 using the CNDOj2 crystal orbital method. The calculated values of band gap for all the systems are found to be very large. This is the well known overestimation of the band gap in the Hartree-Fock method. Using better basis sets and taking into account electron correlation effects the calculated band gap values will come closer to the experimental ones as has been observed earlier in the case of trans-PA [14]. If we divide our DZ band gap values for the systems by 3.62 (the factor between theoretical and experimental gap in the case of PTP), we obtain values of 1.14 and 1.53 for PTMO and PTDO respectively. The smaller band gap of oxy-derivatives of PTP as compared to that of PTP is the result of increase in both EA and IP values. The calculated trend for both electron affinity and ionization potential values is PTDO > PTMO > PTP. It. therefore, means that PTDO is expected to have the largest capacity to form highly conducting materials on doping with electron donors (n-doping) while PTP is expected to be the best candidate for formingp-doped conducting materials (i.e. with electron acceptors). The CND0/2 calculations, on the other hand, predict PTDO to be the most promising candidate for both p- and n-doping. The Bloch wavefunctions corresponding to the top of the valence band and the bottom of the conduction band for PTP, PTMO and PTDO are depicted schematically in Fig. 2. An analysis of these wavefunctions shows that in both PTP and PTMO, the contributions to the top of the valence band come only from the p_ orbitals of the backbone carbon atoms and not at all from the pz orbitals of the heteroatoms whereas in PTDO the p._ orbitals of the
945
OF POLYTHIOPHENE
heteroatoms also contribute to the top of the valence band. The picture is however different in the case of contributions to the bottom of the conducti4n band. Here there are contributions from the p_ odbitals of all the atoms including heteroatoms in case of PTP and PTMO but no contribution from the pi orbitals of the heteroatoms in case of PTDCj. These differences in the Bloch wavefunctions khall be manifested in the nature of K electrons in \iolved in the doping processes, i.e. p-doped PTP and PTMO and n-doped PTDO shall have no involvement of 7~ electrons of the heteroatoms whereas n-doped PTP and PTMO and p-doped PTDO shall have1 involvements of the electrons of all the atoms including heteroatoms. That this is so has already beeh verified through ESR measurements on both p- an n-doped PTP [15] and can be verified in the case of P4 MO and PTDO whenever they are synthesized. 4. POLYMERIC
SUPERLATTICES
An interesting possibility of designing lectronic properties intermediate between those of ewo components is through growing quasi-one di ensional superlattices (or copolymers) which have ta for made properties depending upon the nature o f the two semiconducting components, their relative amounts and their arrangement in the polymer chai d [16]. The band alignments of the pairs PTP-PTMO and PTPPTDO for the superlattices are shown in ig. 3. In both these pairs the top of the valence ba f d of one component lies within the band gap of the ther and the bottom of the conduction band of the s cond lies in the band gap of the first and therefore 1 0th these pairs of superlattices are expected to beldng to the class of Type II-staggered. The calculated1 values of the ratio of the conduction band disconti uity AE, n (which is equal to the difference in the electron affinities of the two components) and the valence band discontinuity AE,, (which is equal to the difference in the ionization potentials of the two
5.611 PTP
PTMO
PTDO
Fig. 2. Orbital patterns of (a) the top of the valence band and (b) the bottom of the conduction band of PTP, PTMO and PTDO. White (black) circles indicate negative (positive) LCAO coefficients. Lined circles indicate oxygen atoms.
8,093
I Fig. 3. Band alignments of the (a) PTP-PTMO (b) PTP-PTDO superlattices.
-11,156 EV
and
946
PROPERTIES
OF OXY-DERIVATIVES
components) are for the pairs PTP-PTMO and PTP-PTDO are 11.07 and 1.60 respectively. One therefore expects, as has been earlier observed in the case of the Type-11 staggered superlattices of polythiophene and polypyrrole too [17], that in both PTP-PTMO and PTP-PTDO superlattices, a higher percentage of either component shall improve the intrinsic conductivity of the copolymer chain. An increase in the percentage of smaller band gap component (PTMO or PTDO) shall make the chain more p-dopantphilic while the n-dopantphilicity of the copolymer chain shall increase with increase in the proportion of larger gap component PTP. 5. CONCLUSIONS In this paper we have investigated the electronic structure and conduction properties of PTMO and PTDO - the two oxy-derivatives of PTP on the basis of ab initio Hartree-Fock crystal orbital method using double-zeta basis set. Our results show that the bonding of oxygen atoms to sulphur atoms through the coordinate bonds in PTMO and PTDO makes them less insulating than PTP. PTMO is predicted to be the most conducting polymer in the intrinsic state with a band gap of the order of 1.1 eV. On the basis of their band alignments, the quasi-one-dimensional superlattices of PTP with both PTMO and PTDO are predicted to belong to the class of Type-II staggered superlattices. The detailed investigations of their electronic structure and conduction properties based on negative factor counting method is in progress and shall be reported later.
OF POLYTHIOPHENE
Vol. 94, No. 11
REFERENCES
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A.K. Bakhshi, Annual Reports of Royal Society (Physical Chemistry), Section C, 89, 147 (1992). J.L. Bredas, J. Chem. Phys. 82, 3808 (1985). AK. Bakhshi, J. Ladik & M. Seel, Phys. Rev. B35, 704 (1987). M. Kobayashi, N. Colaneri, M. Boysel, F. Wudl & A.J. Heeger, J. Chem. Phys. 82, 5717 (1985). A.K. Bakhshi & J. Ladik, Solid State Commun. 61, 71 (1987). Y. Ikenoue, F. Wudl & A.J. Heeger, Synth. Met. 40, 1 (1991). C. Taliani, G. Ruani, R. Zamboni, A. Bolognesi, M. Catellani, S. Destri, W. Porzio & P. Ostoja, Synth. Met. 28, C507 (1989). S.A. Jenekhe, Nature 322, 345 (1986). K. Tanaka, S. Wang & T. Yamabe, Synth. Metals 30, 57 (1989). G. Del Re, J. Ladik & G. Biczo’, Phys. Rev. 55, 997 (1967). J.M. Andre, L. Gouverneur & G. Leroy, Znt. J. Quant. Chem. 1,427, 451 (1967). L. Gianolio, R. Pavani & E. Clementi, Gazz. Chim. Ztal. 108, 181 (1992). A.K. Bakhshi, J. Chem. Phys. 96,2339 (1992). S. Suhai, Phys. Rev. B27, 3506 (1983). M. Kobayashi, J. Chen, T.C. Chung, F. Moraes, A.J. Heeger & F. Wudl, Synth. Metals 9, 77 (1984). A.K. Bakhshi, Superlattices and Microstructures 11, 465 (1992). A.K. Bakhshi & J. Ladik, Inr. J. Quant. Chem. 42, 997 (1992).
Pergamon
I I. pp.943-946, 1995 Elsevier Science Ltd Printed in Cjreat Britain 0038%1098/93 $9.50 i .OO
Vol. 94, No.
0038-1098(95)00096-8
AllZNZTZO STUDY OF THE ELECTRONIC STRUCTURE AND CONDUCTION OXY-DERIVATIVES OF POLYTHIOPHENE
PROPERTIES
OF
A.K. Bakhshi Department
of Chemistry, Panjab University, Chandigarh-160
014, India
(Received 3 November 1994 b!l A. Zawadobcski)
The electronic structure and conduction properties of two oxyderivatives of polythiophene (PTP), polythiophene monoxide (PTMO) and polythiophenedioxide (PTDO) have been investigated on the basis of the ab initio Hartree Fock crystal orbital method using double-zeta basis set. The addition of oxygen atoms at sulphur in PTP is found to considerably influence the electronic properties of PTP. Both PTMO and PTDO are predicted to have much smaller band gap than PTP. The nature of quasi-one dimensional superlattices of PTP with both PTMO and PTDO and their electronic properties are also briefly discussed. Keywords: structure.
A. polymers,
A. semiconductors.
1. INTRODUCTION IN THE SEARCH for novel electrically conducting polymers, an exciting possibility is provided by the derivatives of polythiophene (PTP) [I]. PTP has a band gap of 2.1 eV and because of its non-degenerate ground state can support polarons and bipolarons as the charge carriers on doping. Theoretical calculations [2] on polymers with non-degenerate ground state have shown that in them band gap (Es,,,) decreases as a function of increasing quinoid character of the polymer back&one. Further from an analysis [3] of the Bloch wavefunctions of the highest occupied and the lowest unoccupied bands of the (Y- o’ linked PTP, it has been found that the substitution on backbone (/?-carbon atoms) would influence both ionization potential (IP) and electron affinity (EA) values while the choice of the heteroatom affects EA more than the IP. Using above results as guidelines, there have been studies of the various derivatives of PTP, notable among these are polyisothianaphthene (PITN) [4, 51, poly (5,6-dioxymethyleneisothianaphthene) (PDOMITN) [6], poly dithieno [3,4b-3’,4’,d] dithiophene (PDTT’) [7] (all with a band gap of the order of 1.1 eV) and a class of novel tunable narrow band gap hetero-aromatic conjugated polymers in which a
D. electronic
band
band gap of as low as 0.75 eV [8] has been achieved. In this paper we investigate the electroni structure and conduction properties of two derivativ s of PTP, polythiophene monoxide (PTMO) and pol thiophene dioxide (PTDO) obtained by adding on and two oxygen atoms at the sulphur atom of each ;: nit cell of PTP respectively. The structures of these/ polymers along with those of PTP are shown in Fig. . None of these polymers has been synthesized yet bu : in view of the current interest in the search for novel conducting polymers with very small band gap va/lues, it is worthwhile to investigate their electronic properties theoretically prior to their synthesis. Tana a et al. 191 have studied these systems using the CND 6 /2 crystal orbital method and have made certain redictions regarding their electronic structure and ! onduction properties, This paper also tests these conclusions using a more reliable ab initio Hartree-Fbck crystal orbital method employing double-zeta basis set. 2. METHODOLOGY The band structure calculations of the (Y- (Y’ linked PTMO and PTDO were performed using their energetically optimised geometry [9] in the framework of the ab initio Hartree-Fock crystal orbital method [lo, 111. In this method, one solves the pseudoeigen-
943
944
PROPERTIES
OF OXY-DERIVATIVES
OF POLYTHIOPHENE
Vol. 94, No. 11
-cII’,:,I
(7)
respectively with PTOO
PTMO
PTP
p$ = c M
Fig. 1. Structures of the unit cells of (a) polythiophene (PTP), (b) polythiophenemonoxide (PTMO), (c) polythiophenedioxide (PTDO).
c exP (-jk(&
(8)
- R,)C~,,&&,
k
and the two electron integral is given by
value equation for different k values in the Brillouin zone. F(k) and are the Fock and Overlap matrices in the k representation. The index n denotes the band while N is the number of neighboring cells explicitly taken into account. The Fock and Overlap matrix elements are given by S(k)
Fob(k) = 5
exp -(ikRi)
-fz,
(2)
j=-N
s,,(k)
= 2
exp(-ikRj)Sjljb,
(3)
j=-N
where s$ = (&)]x’b(r))
(4)
f SJ’b= ho’ + go’ ab
(5)
ab’
In equation (5), the one electron term (h$,) and the two electron term g$ are given by h$ = -1/2(xjl]A]x’b(r)) +
~~(-&‘+a//‘. h
_xi is the bth atomic basis function in the unit cell denoted by the upper index j; Z, and R, are the charge and position of the oth nucleus and Cd,,,(k) are the components of the mth eigenvector of equation (1). The first summation in equation (8) runs over all doubly filled bands and the second runs over the Brillouin zone. The eigenvalues e,(k) give the band structure of the polymer. All the computations were performed using Clementi’s double-zeta basis set [12] (75 basis functions for PTMO and 85 basis functions for PTDO). All the multicentre two electron integrals larger than the threshold value of lo-‘a.u. were calculated and the interactions up to second neighbors were taken into account.
Rh
- R&(r))
(6)
0
and
3. RESULTS AND DISCUSSION The most important electronic properties such as the IP (corresponding to the top of the valence band), EA (corresponding to the bottom of the conduction band), the band gap and the total energy per unit cell of PTMO and PTDO are given in Table 1. Also given in this table are the corresponding results of PTP [ 161 obtained using the same method and the same basis set. Both the highest occupied and the lowest unoccupied bands in each system are found to be r bands. PTMO and PTDO are found to have
Table 1. Calculated electronic properties (in electron volts) of polythiophenemonoxide (PTMO), polythiophenedioxide (PTDO) and polythiophene (PTP)
PTMO Ionisation potential Electron affinity Valence bandwidth Conduction bandwidth Band gap Scaled value of band gap Total energy per unit cell (a.u.)
8.093 3.951 4.04 1 5.088 4.142 1.14 -1317.107634
PTDO 11.156 5.611 3.953 4.358 5.545 1.53 - 1644.65602 1
PTP 7.749 0.145 3.413 2.937 7.604 2.1 -1174.301889
Vol. 94, No. 11
PROPERTIES
OF OXY-DERIVATIVES
much smaller band gap than PTP and are therefore expected to be less insulating than PTP. The calculated order of band gap is PTMO < PTDO < PTP. This order is not in agreement with the order PTDO < PTMO < PTP obtained by Tanaka et al. [93 using the CNDOj2 crystal orbital method. The calculated values of band gap for all the systems are found to be very large. This is the well known overestimation of the band gap in the Hartree-Fock method. Using better basis sets and taking into account electron correlation effects the calculated band gap values will come closer to the experimental ones as has been observed earlier in the case of trans-PA [14]. If we divide our DZ band gap values for the systems by 3.62 (the factor between theoretical and experimental gap in the case of PTP), we obtain values of 1.14 and 1.53 for PTMO and PTDO respectively. The smaller band gap of oxy-derivatives of PTP as compared to that of PTP is the result of increase in both EA and IP values. The calculated trend for both electron affinity and ionization potential values is PTDO > PTMO > PTP. It. therefore, means that PTDO is expected to have the largest capacity to form highly conducting materials on doping with electron donors (n-doping) while PTP is expected to be the best candidate for formingp-doped conducting materials (i.e. with electron acceptors). The CND0/2 calculations, on the other hand, predict PTDO to be the most promising candidate for both p- and n-doping. The Bloch wavefunctions corresponding to the top of the valence band and the bottom of the conduction band for PTP, PTMO and PTDO are depicted schematically in Fig. 2. An analysis of these wavefunctions shows that in both PTP and PTMO, the contributions to the top of the valence band come only from the p_ orbitals of the backbone carbon atoms and not at all from the pz orbitals of the heteroatoms whereas in PTDO the p._ orbitals of the
945
OF POLYTHIOPHENE
heteroatoms also contribute to the top of the valence band. The picture is however different in the case of contributions to the bottom of the conducti4n band. Here there are contributions from the p_ odbitals of all the atoms including heteroatoms in case of PTP and PTMO but no contribution from the pi orbitals of the heteroatoms in case of PTDCj. These differences in the Bloch wavefunctions khall be manifested in the nature of K electrons in \iolved in the doping processes, i.e. p-doped PTP and PTMO and n-doped PTDO shall have no involvement of 7~ electrons of the heteroatoms whereas n-doped PTP and PTMO and p-doped PTDO shall have1 involvements of the electrons of all the atoms including heteroatoms. That this is so has already beeh verified through ESR measurements on both p- an n-doped PTP [15] and can be verified in the case of P4 MO and PTDO whenever they are synthesized. 4. POLYMERIC
SUPERLATTICES
An interesting possibility of designing lectronic properties intermediate between those of ewo components is through growing quasi-one di ensional superlattices (or copolymers) which have ta for made properties depending upon the nature o f the two semiconducting components, their relative amounts and their arrangement in the polymer chai d [16]. The band alignments of the pairs PTP-PTMO and PTPPTDO for the superlattices are shown in ig. 3. In both these pairs the top of the valence ba f d of one component lies within the band gap of the ther and the bottom of the conduction band of the s cond lies in the band gap of the first and therefore 1 0th these pairs of superlattices are expected to beldng to the class of Type II-staggered. The calculated1 values of the ratio of the conduction band disconti uity AE, n (which is equal to the difference in the electron affinities of the two components) and the valence band discontinuity AE,, (which is equal to the difference in the ionization potentials of the two
5.611 PTP
PTMO
PTDO
Fig. 2. Orbital patterns of (a) the top of the valence band and (b) the bottom of the conduction band of PTP, PTMO and PTDO. White (black) circles indicate negative (positive) LCAO coefficients. Lined circles indicate oxygen atoms.
8,093
I Fig. 3. Band alignments of the (a) PTP-PTMO (b) PTP-PTDO superlattices.
-11,156 EV
and
946
PROPERTIES
OF OXY-DERIVATIVES
components) are for the pairs PTP-PTMO and PTP-PTDO are 11.07 and 1.60 respectively. One therefore expects, as has been earlier observed in the case of the Type-11 staggered superlattices of polythiophene and polypyrrole too [17], that in both PTP-PTMO and PTP-PTDO superlattices, a higher percentage of either component shall improve the intrinsic conductivity of the copolymer chain. An increase in the percentage of smaller band gap component (PTMO or PTDO) shall make the chain more p-dopantphilic while the n-dopantphilicity of the copolymer chain shall increase with increase in the proportion of larger gap component PTP. 5. CONCLUSIONS In this paper we have investigated the electronic structure and conduction properties of PTMO and PTDO - the two oxy-derivatives of PTP on the basis of ab initio Hartree-Fock crystal orbital method using double-zeta basis set. Our results show that the bonding of oxygen atoms to sulphur atoms through the coordinate bonds in PTMO and PTDO makes them less insulating than PTP. PTMO is predicted to be the most conducting polymer in the intrinsic state with a band gap of the order of 1.1 eV. On the basis of their band alignments, the quasi-one-dimensional superlattices of PTP with both PTMO and PTDO are predicted to belong to the class of Type-II staggered superlattices. The detailed investigations of their electronic structure and conduction properties based on negative factor counting method is in progress and shall be reported later.
OF POLYTHIOPHENE
Vol. 94, No. 11
REFERENCES
5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
A.K. Bakhshi, Annual Reports of Royal Society (Physical Chemistry), Section C, 89, 147 (1992). J.L. Bredas, J. Chem. Phys. 82, 3808 (1985). AK. Bakhshi, J. Ladik & M. Seel, Phys. Rev. B35, 704 (1987). M. Kobayashi, N. Colaneri, M. Boysel, F. Wudl & A.J. Heeger, J. Chem. Phys. 82, 5717 (1985). A.K. Bakhshi & J. Ladik, Solid State Commun. 61, 71 (1987). Y. Ikenoue, F. Wudl & A.J. Heeger, Synth. Met. 40, 1 (1991). C. Taliani, G. Ruani, R. Zamboni, A. Bolognesi, M. Catellani, S. Destri, W. Porzio & P. Ostoja, Synth. Met. 28, C507 (1989). S.A. Jenekhe, Nature 322, 345 (1986). K. Tanaka, S. Wang & T. Yamabe, Synth. Metals 30, 57 (1989). G. Del Re, J. Ladik & G. Biczo’, Phys. Rev. 55, 997 (1967). J.M. Andre, L. Gouverneur & G. Leroy, Znt. J. Quant. Chem. 1,427, 451 (1967). L. Gianolio, R. Pavani & E. Clementi, Gazz. Chim. Ztal. 108, 181 (1992). A.K. Bakhshi, J. Chem. Phys. 96,2339 (1992). S. Suhai, Phys. Rev. B27, 3506 (1983). M. Kobayashi, J. Chen, T.C. Chung, F. Moraes, A.J. Heeger & F. Wudl, Synth. Metals 9, 77 (1984). A.K. Bakhshi, Superlattices and Microstructures 11, 465 (1992). A.K. Bakhshi & J. Ladik, Inr. J. Quant. Chem. 42, 997 (1992).