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On the nature of the spin exchange interaction in poly (m-aniline)
Chemical Physics 169 ( 1993 ) 8 I-84 God-Holland
On the nature of the spin exchange interaction in poly (m-aniline) M. Baumgarten,
K. MUen,
N. Tyutyulkov
*
Max-Planck-Institutfiir Polymerforschung. Ackermannweg IO, W-6500 Mainz, Germany
and G. Madjarova Faculty ofChemistry,
Vnwersity of Sofia, 1126 Sofia, Bulgaria
Received 6 July 1992
The energy spectra of two infinite 1D models of the poly(meta-aniline) (PMA) namely the neutral and cationic radical forms are theoretically investigated. The band structure is characterized by a wide energy gap with a half-filled band of nearly degenerate molecular orbitals. Different contributions (potential, kinetic, and indirect exchange) to the effective spin exchange between the unpaired electrons in the half-filled band are calculated. The PMA exhibits a net spin exchange of ferromagnetic nature, i.e. the ground state of the PMA is characterized by maximum spin multiplicity. The ferromagnetic interaction is due to the predominant ~ont~bution of the direct (potential) Coulomb exchange.
1. Introduction Recent experimental evidence for the existence of a high-spin ground state of polyanilines has been provided by the investigation of Torrance et al. [ 11, while MacDiarmid et al. [ 21 studied the electron distribution in the conducting state upon doping. Very recently Tanaka and co-workers published [ 3,4] the synthesis of two forms of poly (meta-aniline) (PMA). They proposed the following 1D st~ctures for the Iatter [ 3 ] : dehydrogenated
form
Ferrimagnetic interaction between the unpaired x electrons in the PMA chains has been suggested by ESR and magnetic susceptibility measurements [ 41. Obviously the PMA species belong to the class of pure organic high-spin systems with magnetic ordering. Accordingly, a theoretical understanding of the magnetic properties of PMA is important for the molecular design of new classes of organic ferromagnets. The eiectronic and magnetic properties of the PMA are briefly discussed in refs. [ 3,4]. In ref. [ 41 are reported unpublished results ( f 14 ] ), which show that a ferrimagnetic ground state is more stable than a nonmagnetic in both R and K forms. The “mother” polymer of the R and K polymers is the non-classical alternant 1D polymer M [ 5,6 ] :
cat~on~c form
M /,.(&,Q$,,
K
H Co~es~ndence
to: M. Baum~~en,
H
Max-Pianck-Institut fiir Pol~~o~h~, Acke~annweg IO, W-6500 Mainz, Germany. ’ Permanent address: Academy of Sciences, Institute of Organic Chemistry, 1040 Sofia, Bulgaria. 0301.0104/93/$06.00
8
0
Theoretical inv~tigations f 5,6], based on the method of altemant MOs (AM0 method) show a ferrimagnetic ground state for organic band structures as M and R. The nature of the magnetic inter-
0 1993 Elsevier Science Publishers B.V. All rights reserved.
82
M. Baumgarten et al. /Chemrcal Physics 169 (1993) 8I-84
action between the unpaired A electrons in the halffilled band (HFB ) remained, however, unclear. The aim of the present study is to establish the character of magnetic interaction in PMA. The model chosen for the theoretical considerations is that of the idealized infinite one-dimensional structures R and K proposed in the work of Tanaka [ 3 1. The R and K polymers are isoelectronic; they have an equal, odd number p of R electrons (p= 7) in each elementary unit (EU).
2. Methods of the investigations The calculations of the band structure of the R and K model polymers were carried out within the tightbinding ( JC) approximation, a Htickel version of the Bloch method [ 7,8 1. If for the MOs of the polymers we adopt the Bloch form of wavevector k, k [ - R, n] , the MO energies e(k) are obtained by numerical diagonalization of the Hamiltonian matrix [ 7,8]: H(k)=H+exp(ik)V+exp(-ik)V+,
(1)
where His the matrix of the elementary unit EU, and Vis the interaction matrix between adjacent EUs. The MO energies e(k) have been calculated using the following set of parameters [ 9 1: /lCN = j?CC = P; the Coulomb integrals (Y are taken as [ 9 ] ; a (-N-) =aCC+OSj? for the dehydrogenated forms R, and cx(-N+=) = 1.S/? for the cationic form K. The band structure of the polymers was obtained using a standard value for the resonance integral /I= -2.4 eV [5,6,11-131. In agreement with the calculations of Nath and Taylor [lo] the angle 8 is chosen as 28”. The resonance integral /I( 6) is taken as p( 6) = B cos 8 [ lo]. For a description of the spin correlation within the half-filled band (HFB) it is more convenient to pass from Bloch wavefunctions to Wannier states [ 141. As is seen from table 1, the Wannier functions of R, K and M polymers are largely localized on the elementary unit. Based on the results of Anderson [ 141, it was shown in refs. [ 1 l-l 3 ] that the effective exchange integral (for the quasi-1D systems) J,e in the Heisenberg Hamiltonian can be evaluated by Jea=J+Jkin+Ji*d=J-2t2/(Ug-U,)+J*nd.
(2)
Table 1 Energy characteristics (m eV) of the half-occupied band of the model polymers. e(O)=e(k=O), e(x)=e(k=n); Ae=e(x)e(0) is the band width. The results are obtained with p= -2.4 eV, and a value of the dihedral angles 0= 28”. L is the normalized localization of the Wannier function Polymer
e(0)
-e(x)
de
La’
R K M
0.657 1.609 0.0
0.458 1.178 0.0
0.199 0.431 0.0
0.713 b’ 0.617 b’ 0.751 b’
a) Let us denote the Bloch functions of the HPB by 1k) = N -” x I., 2, exp (ikp) C,( k) 1p, r) , where y marks the unit, r labels the atoms of the unit, and 1m,k) is given by the expression In)=N-“*~exp(-iku)Ik)=~,C,ar(~-v)IH r). In the limit of N+co the orbital coefftcients of the Wannier functions in the A0 basisarea,(~-v)=~xl”_n exp[i@-v)k]C,(k) dk. The norm of localization L is defined as L= 1, Ia,( 0) 1’. b, Mataga-Nishimoto approximation with one-center Coulomb integral y= 10.84 eV and screening constant D= 1 (see eq. (3)).
The following relevant parameters characterizing the spin interaction within the HFB, given by eq. (2), have been calculated with Wannier functions: J= Coulomb exchange integral of two electrons residing at adjacent Wannier states. U,=Coulomb repulsion integral of two electrons occupying the same Wannier state (Hubbard parameter [ 15,161). U, =Coulomb repulsion integral of two electrons residing at adjacent Wannier states. U1 has a screening effect on U,, leading to a renormalized Hubbard parameter U= U, - U, . t= transfer (hopping) parameter between adjacent Wannier states. Jlnd= magnitude of the indirect exchange interaction between unpaired electrons via K electrons delocalized along the polymer chain [ 11,12,17 1. The character of the ground state is determined by the sign of Jes. If Jen> 0, the interaction (ferromagnetic) favors the localized high-spin state. If Jeff
M. Baumgarten et al. /Chemical Physics 169 (1993) 81-84
83
Table 2 Calculated values (in eV) of the different ~nt~butio~ to the efktive spin exchange between the unpaired electrons in the haif-occupied band. The results have been obtained with B= - 2.4 eV and Mataga-Nishimoto approximation (see eq. ( 3) ) by different values of the one-center Coulomb integral -yO, and with different values of the screening constant D. a: yO= 10.84 eV, D= 1. b: y,=9.0 eV, D= 1. c: yo= 10.84 eV, D=2 Polymer
u0
D,
f
J tn*
Jki,
J
Jar
Ra Rb Rc Kit Kb Kc Ma Mb MC
5.088 4.961 4.070 4.284 3.862 3.134 5.107 4.648 4.307
2.662 2.497 1.647 2.708 2.534 1.698 2.672 2.488 1.635
- 0.048 - 0.049 -0.049 -0.106 -0.106 -0.106 0.000 0.000 0.000
0.06 1 0.038 0.081 0.026 0.016 0.033 0.070 0.041 0.089
- 0.003 -0.002 -0.002 -0.014 -0.017 -0.016 0.000 0.000 0.000
0.184 0.144 0.219 0.196 0.153 0.235 0.199 0.140 0.215
0.242 0.180 0.298 0.208 0.152 0.252 0.269 0.181 0.304
where ~1=e2/2 (r,,i- yyy). If the screening parameter L)= 1, eq. (3) is identical with the Mataga-Nishimoto approximation [ 18 1.
3. Results and discussion
4. Conclusion
The model polymers Rand K feature an energy gap of AE=2p (jY=-2.4 eV). The HFB is narrow, its width does not exceed 0.43 eV (see table 1). This is not a surprising result, since HFB originates from the non-bonding MO of the corresponding non-classical alternant homonuclear polymer M. If we denote the Coulomb integral of the nitrogen atom by cuN= h& the characteristic polynomial of the R and K polymers reads P(X, cos k) = (x2- 1 )(x[x4-
result is due to the predominant role of the direct Coulomb (potential) exchange interaction. The netexchange coupling between the unpaired electrons in the HFB of polymer M is also of ferromagnetic nature.
(5+2$*)x2+4
+6~~-22s~cosk]+h(x~-55~~-4)). The MO energies e(k) are related to the roots of the characteristic polynomial x(k) according to x(k)=[a-e(k)]/j?=e(k)/p.Ifh=O,theabovepolynomial transforms into the polynomial of polymer M, which has an infinite band at e(k) = 0 (NBMO) and two degenerate bands at e(k) = rf:8. Table 2 presents the calculated values of the different contributions to the effective spin exchange between the unpaired electrons in the HFB of the investigated polymers. The model polymers R and K exhibit a net spin exchange of fe~omagneti~ nature, i.e. Jtn> 0, and this
The numerical results for the spin exchange in the HFB of the investigated polymers show that the model polymers R and K have a high-spin ground state. The direct Coulomb interaction is the main contribution to the spin exchange. The role of the indirect exchange interaction is small and the kinetic term is J km -0. *
The results lead to the qualitative conclusion, that poly (meta-aniline) possessing the structural units comparable to the elementary units of the 1D-models R and K, are candidates for pure organic high-spin systems with magnetic ordering. The difference in Jd for the two models is too small to give a preference to one of them, but synthetic approaches may be easier to be realized for the type K polymers. A more extensive study by comparing these results to other aza-analogues of non-classical polymers with other x subunits and nitrogen substituents or with carbazol or N oxide units seems of interest and are currently under study.
84
M. Baumgarten et al. /Chemical Physics 169 (1993) 81-84
References [ 1] J.B. Torrance, S. Oostra and A. Nazal, Synth. Metals 19 (1987) 809. [2]A.G. MacDiarmid, J.C. Chiang, A.F. Richter and A.J. Epstein, Synth. Metals 18 (1987) 285. [ 31 K. Tanaka, K. Yoshisawa, A. Takata, T. Yamabe and J. Yamauchi, Synth. Metals 41-43 (199 1) 3297. [4] K. Yoshisawa, K. Tanaka, T. Yamabe and J. Yamauchi, J. Chem. Phys. 96 (1992) 5516. [5] N. Tyutyulkov, O.E. Polansky and P. Schuster, Theoret. Chim.Acta63 (1983) 211. [ 6 ] N. Tyutyulkov, O.E. Polansky, P. Schuster, S. Karabunarliev and C.I. Ivanov, Theoret. Chim. Acta 67 ( 1985 ) 29 1. [ 7 ] O.E. Polansky and N. Tyutyulkov, Match (Commun. Math. Chem.) 3 (1977) 149.
[ 81 Y. Judo, T. Inagaki and M. Fukutome, Progr. Theoret. Phys. 48 (1972) 808. [9] A. Streitwieser Jr., MO theory (Wiley, New York, 1965). [ 10 ] K. Nath and P.L. Taylor, Mol. Cryst. Liq. Cryst. 205 ( 199 1) 87. [ 111 N. Tyutyulkov and S. Karabunarliev, Intern. J. Quantum Chem. 29 ( 1986) 1325. [ 121 N. Tyutyulkov and S. Karabunarliev, Chem. Phys. 112 ( 1987) 293. [ 13 ] C. Ivanov, N. Tyutyulkov and S. Karabunarliev, J. Magn. Mater. 92 ( 1990) 172. [ 141 P.W. Anderson, Phys. Rev. 79 (1950) 350; 115 (1959) 2. [ 151 J. Hubbard, Proc. Roy. Sot. A 276 ( 1963) 238. [ 161 M.-H. Whangbo, J. Chem. Phys. 70 (1979) 4963. [ 171 N. Tyutyulkov, S. Karabunarliev, K. Milllen and M. Baumgarten, Synth. Metals 52 ( 1992) 71. [ 181 N. Mataga and K. Nishimoto, Z. Physik. Chem. 13 (1957) 170.
On the nature of the spin exchange interaction in poly (m-aniline) M. Baumgarten,
K. MUen,
N. Tyutyulkov
*
Max-Planck-Institutfiir Polymerforschung. Ackermannweg IO, W-6500 Mainz, Germany
and G. Madjarova Faculty ofChemistry,
Vnwersity of Sofia, 1126 Sofia, Bulgaria
Received 6 July 1992
The energy spectra of two infinite 1D models of the poly(meta-aniline) (PMA) namely the neutral and cationic radical forms are theoretically investigated. The band structure is characterized by a wide energy gap with a half-filled band of nearly degenerate molecular orbitals. Different contributions (potential, kinetic, and indirect exchange) to the effective spin exchange between the unpaired electrons in the half-filled band are calculated. The PMA exhibits a net spin exchange of ferromagnetic nature, i.e. the ground state of the PMA is characterized by maximum spin multiplicity. The ferromagnetic interaction is due to the predominant ~ont~bution of the direct (potential) Coulomb exchange.
1. Introduction Recent experimental evidence for the existence of a high-spin ground state of polyanilines has been provided by the investigation of Torrance et al. [ 11, while MacDiarmid et al. [ 21 studied the electron distribution in the conducting state upon doping. Very recently Tanaka and co-workers published [ 3,4] the synthesis of two forms of poly (meta-aniline) (PMA). They proposed the following 1D st~ctures for the Iatter [ 3 ] : dehydrogenated
form
Ferrimagnetic interaction between the unpaired x electrons in the PMA chains has been suggested by ESR and magnetic susceptibility measurements [ 41. Obviously the PMA species belong to the class of pure organic high-spin systems with magnetic ordering. Accordingly, a theoretical understanding of the magnetic properties of PMA is important for the molecular design of new classes of organic ferromagnets. The eiectronic and magnetic properties of the PMA are briefly discussed in refs. [ 3,4]. In ref. [ 41 are reported unpublished results ( f 14 ] ), which show that a ferrimagnetic ground state is more stable than a nonmagnetic in both R and K forms. The “mother” polymer of the R and K polymers is the non-classical alternant 1D polymer M [ 5,6 ] :
cat~on~c form
M /,.(&,Q$,,
K
H Co~es~ndence
to: M. Baum~~en,
H
Max-Pianck-Institut fiir Pol~~o~h~, Acke~annweg IO, W-6500 Mainz, Germany. ’ Permanent address: Academy of Sciences, Institute of Organic Chemistry, 1040 Sofia, Bulgaria. 0301.0104/93/$06.00
8
0
Theoretical inv~tigations f 5,6], based on the method of altemant MOs (AM0 method) show a ferrimagnetic ground state for organic band structures as M and R. The nature of the magnetic inter-
0 1993 Elsevier Science Publishers B.V. All rights reserved.
82
M. Baumgarten et al. /Chemrcal Physics 169 (1993) 8I-84
action between the unpaired A electrons in the halffilled band (HFB ) remained, however, unclear. The aim of the present study is to establish the character of magnetic interaction in PMA. The model chosen for the theoretical considerations is that of the idealized infinite one-dimensional structures R and K proposed in the work of Tanaka [ 3 1. The R and K polymers are isoelectronic; they have an equal, odd number p of R electrons (p= 7) in each elementary unit (EU).
2. Methods of the investigations The calculations of the band structure of the R and K model polymers were carried out within the tightbinding ( JC) approximation, a Htickel version of the Bloch method [ 7,8 1. If for the MOs of the polymers we adopt the Bloch form of wavevector k, k [ - R, n] , the MO energies e(k) are obtained by numerical diagonalization of the Hamiltonian matrix [ 7,8]: H(k)=H+exp(ik)V+exp(-ik)V+,
(1)
where His the matrix of the elementary unit EU, and Vis the interaction matrix between adjacent EUs. The MO energies e(k) have been calculated using the following set of parameters [ 9 1: /lCN = j?CC = P; the Coulomb integrals (Y are taken as [ 9 ] ; a (-N-) =aCC+OSj? for the dehydrogenated forms R, and cx(-N+=) = 1.S/? for the cationic form K. The band structure of the polymers was obtained using a standard value for the resonance integral /I= -2.4 eV [5,6,11-131. In agreement with the calculations of Nath and Taylor [lo] the angle 8 is chosen as 28”. The resonance integral /I( 6) is taken as p( 6) = B cos 8 [ lo]. For a description of the spin correlation within the half-filled band (HFB) it is more convenient to pass from Bloch wavefunctions to Wannier states [ 141. As is seen from table 1, the Wannier functions of R, K and M polymers are largely localized on the elementary unit. Based on the results of Anderson [ 141, it was shown in refs. [ 1 l-l 3 ] that the effective exchange integral (for the quasi-1D systems) J,e in the Heisenberg Hamiltonian can be evaluated by Jea=J+Jkin+Ji*d=J-2t2/(Ug-U,)+J*nd.
(2)
Table 1 Energy characteristics (m eV) of the half-occupied band of the model polymers. e(O)=e(k=O), e(x)=e(k=n); Ae=e(x)e(0) is the band width. The results are obtained with p= -2.4 eV, and a value of the dihedral angles 0= 28”. L is the normalized localization of the Wannier function Polymer
e(0)
-e(x)
de
La’
R K M
0.657 1.609 0.0
0.458 1.178 0.0
0.199 0.431 0.0
0.713 b’ 0.617 b’ 0.751 b’
a) Let us denote the Bloch functions of the HPB by 1k) = N -” x I., 2, exp (ikp) C,( k) 1p, r) , where y marks the unit, r labels the atoms of the unit, and 1m,k) is given by the expression In)=N-“*~exp(-iku)Ik)=~,C,ar(~-v)IH r). In the limit of N+co the orbital coefftcients of the Wannier functions in the A0 basisarea,(~-v)=~xl”_n exp[i@-v)k]C,(k) dk. The norm of localization L is defined as L= 1, Ia,( 0) 1’. b, Mataga-Nishimoto approximation with one-center Coulomb integral y= 10.84 eV and screening constant D= 1 (see eq. (3)).
The following relevant parameters characterizing the spin interaction within the HFB, given by eq. (2), have been calculated with Wannier functions: J= Coulomb exchange integral of two electrons residing at adjacent Wannier states. U,=Coulomb repulsion integral of two electrons occupying the same Wannier state (Hubbard parameter [ 15,161). U, =Coulomb repulsion integral of two electrons residing at adjacent Wannier states. U1 has a screening effect on U,, leading to a renormalized Hubbard parameter U= U, - U, . t= transfer (hopping) parameter between adjacent Wannier states. Jlnd= magnitude of the indirect exchange interaction between unpaired electrons via K electrons delocalized along the polymer chain [ 11,12,17 1. The character of the ground state is determined by the sign of Jes. If Jen> 0, the interaction (ferromagnetic) favors the localized high-spin state. If Jeff
M. Baumgarten et al. /Chemical Physics 169 (1993) 81-84
83
Table 2 Calculated values (in eV) of the different ~nt~butio~ to the efktive spin exchange between the unpaired electrons in the haif-occupied band. The results have been obtained with B= - 2.4 eV and Mataga-Nishimoto approximation (see eq. ( 3) ) by different values of the one-center Coulomb integral -yO, and with different values of the screening constant D. a: yO= 10.84 eV, D= 1. b: y,=9.0 eV, D= 1. c: yo= 10.84 eV, D=2 Polymer
u0
D,
f
J tn*
Jki,
J
Jar
Ra Rb Rc Kit Kb Kc Ma Mb MC
5.088 4.961 4.070 4.284 3.862 3.134 5.107 4.648 4.307
2.662 2.497 1.647 2.708 2.534 1.698 2.672 2.488 1.635
- 0.048 - 0.049 -0.049 -0.106 -0.106 -0.106 0.000 0.000 0.000
0.06 1 0.038 0.081 0.026 0.016 0.033 0.070 0.041 0.089
- 0.003 -0.002 -0.002 -0.014 -0.017 -0.016 0.000 0.000 0.000
0.184 0.144 0.219 0.196 0.153 0.235 0.199 0.140 0.215
0.242 0.180 0.298 0.208 0.152 0.252 0.269 0.181 0.304
where ~1=e2/2 (r,,i- yyy). If the screening parameter L)= 1, eq. (3) is identical with the Mataga-Nishimoto approximation [ 18 1.
3. Results and discussion
4. Conclusion
The model polymers Rand K feature an energy gap of AE=2p (jY=-2.4 eV). The HFB is narrow, its width does not exceed 0.43 eV (see table 1). This is not a surprising result, since HFB originates from the non-bonding MO of the corresponding non-classical alternant homonuclear polymer M. If we denote the Coulomb integral of the nitrogen atom by cuN= h& the characteristic polynomial of the R and K polymers reads P(X, cos k) = (x2- 1 )(x[x4-
result is due to the predominant role of the direct Coulomb (potential) exchange interaction. The netexchange coupling between the unpaired electrons in the HFB of polymer M is also of ferromagnetic nature.
(5+2$*)x2+4
+6~~-22s~cosk]+h(x~-55~~-4)). The MO energies e(k) are related to the roots of the characteristic polynomial x(k) according to x(k)=[a-e(k)]/j?=e(k)/p.Ifh=O,theabovepolynomial transforms into the polynomial of polymer M, which has an infinite band at e(k) = 0 (NBMO) and two degenerate bands at e(k) = rf:8. Table 2 presents the calculated values of the different contributions to the effective spin exchange between the unpaired electrons in the HFB of the investigated polymers. The model polymers R and K exhibit a net spin exchange of fe~omagneti~ nature, i.e. Jtn> 0, and this
The numerical results for the spin exchange in the HFB of the investigated polymers show that the model polymers R and K have a high-spin ground state. The direct Coulomb interaction is the main contribution to the spin exchange. The role of the indirect exchange interaction is small and the kinetic term is J km -0. *
The results lead to the qualitative conclusion, that poly (meta-aniline) possessing the structural units comparable to the elementary units of the 1D-models R and K, are candidates for pure organic high-spin systems with magnetic ordering. The difference in Jd for the two models is too small to give a preference to one of them, but synthetic approaches may be easier to be realized for the type K polymers. A more extensive study by comparing these results to other aza-analogues of non-classical polymers with other x subunits and nitrogen substituents or with carbazol or N oxide units seems of interest and are currently under study.
84
M. Baumgarten et al. /Chemical Physics 169 (1993) 81-84
References [ 1] J.B. Torrance, S. Oostra and A. Nazal, Synth. Metals 19 (1987) 809. [2]A.G. MacDiarmid, J.C. Chiang, A.F. Richter and A.J. Epstein, Synth. Metals 18 (1987) 285. [ 31 K. Tanaka, K. Yoshisawa, A. Takata, T. Yamabe and J. Yamauchi, Synth. Metals 41-43 (199 1) 3297. [4] K. Yoshisawa, K. Tanaka, T. Yamabe and J. Yamauchi, J. Chem. Phys. 96 (1992) 5516. [5] N. Tyutyulkov, O.E. Polansky and P. Schuster, Theoret. Chim.Acta63 (1983) 211. [ 6 ] N. Tyutyulkov, O.E. Polansky, P. Schuster, S. Karabunarliev and C.I. Ivanov, Theoret. Chim. Acta 67 ( 1985 ) 29 1. [ 7 ] O.E. Polansky and N. Tyutyulkov, Match (Commun. Math. Chem.) 3 (1977) 149.
[ 81 Y. Judo, T. Inagaki and M. Fukutome, Progr. Theoret. Phys. 48 (1972) 808. [9] A. Streitwieser Jr., MO theory (Wiley, New York, 1965). [ 10 ] K. Nath and P.L. Taylor, Mol. Cryst. Liq. Cryst. 205 ( 199 1) 87. [ 111 N. Tyutyulkov and S. Karabunarliev, Intern. J. Quantum Chem. 29 ( 1986) 1325. [ 121 N. Tyutyulkov and S. Karabunarliev, Chem. Phys. 112 ( 1987) 293. [ 13 ] C. Ivanov, N. Tyutyulkov and S. Karabunarliev, J. Magn. Mater. 92 ( 1990) 172. [ 141 P.W. Anderson, Phys. Rev. 79 (1950) 350; 115 (1959) 2. [ 151 J. Hubbard, Proc. Roy. Sot. A 276 ( 1963) 238. [ 161 M.-H. Whangbo, J. Chem. Phys. 70 (1979) 4963. [ 171 N. Tyutyulkov, S. Karabunarliev, K. Milllen and M. Baumgarten, Synth. Metals 52 ( 1992) 71. [ 181 N. Mataga and K. Nishimoto, Z. Physik. Chem. 13 (1957) 170.