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Quasi-diabatic electronic states in conjugated polymers
SyntheticMetals101 (1999) 459-460
Quasi-Diabatic Electronic States in Conjugated Polymers H. Nobutoki Advanced Technoloa R&D Center., Mitsubishi Electric Corporation, 8-l-I Hyogo 661-8661, Japan
Tsul;aguchi-Honnlachi, Anzagasaki,
Abstract
A quasi-diabatic crystal orbital theory has been proposedto study the electronic staterepresentingthe diabatic behavior of electrons. The method was applied to nondoped and lithium heavily-doped polyacetylenes. It has been shown that the quasi-diabatic electronic stateis a metallic SDW statefor the doped system,which will causea transition from a soliton stateto a polaron state. k+t~ords: (Semi-empirical models and model calculations. Other phasetransitions, Polyacetylene and derivatives)
r----7
1. Introduction
In conventional electronic band structures, electrons move infinitely slowly on one partially-filled band along the k-space and remains on the same band up to the zone boundary. This behavior of the electron may be called “adiabatic”. On the other hand, if electrons move with a finite velocity, there will be a finite probability that the electron will change from one band to the other vacant bands. This behavior of the electron may be called “diabatic”. Such a diabatic electronic structure might influence chemical and physical properties in heavilydoped polyacetylenes since the metallic properties measured would be associated with the electrons moving with a finite velocity. We previously proposed a quasi-diabatic crystal orbital (CO) theory to study the electronic structure representing the diabatic behavior of electrons [1,2]. In this communication. we present novel characteristics of the quasi-diabatic electronic states in nondoped and lithium heavily-doped tmfjs-polyacetylenes (tPA’s) and discuss the electronic statesfrom a point of electronic correlation. 2. Method of Calculations
Our method is characterized by a quasi-diabatic treatment of the coupling between canonical CO’s due to the derivative operator of crystal momentum. The details of’ the theoretical treatment have already been describedpreviously [1,2]. We refer to this method as the corresponding CO (CCO) method. The calculations have been carried out on the basis of the onedimensional tight-binding SCF-CO method at the level of the CNDOI2 approximation. In this study, the lithium heavily-doped r-PA with an equal bond length chain (a soliton lattice) was employed, as shown in Fig. 1, where the unit cell is surrounded by broken lines, to achieve an idealized metallic state due to the soliton lattice. Geometries of nondoped alternating and model doped t-PA’s were taken from the experimental data of Ref. [3] and from the calculated result of Ref. [4], respectively.
R Li- C= 2.00 A Fig. 1. Geometry of the Li heavily-doped t-PA used in this study, where RLimc standsfor lithium-carbon distance.
3. Results and Discussion
3.1. Electronic Structures The CC0 band structure and the density of states(DOS) for the Li heavily-doped t-PA, calculated by our method, are shown in Fig. 2 [2]. In Fig. 2(a), the bold for 4’1, @z, and 4’3 and dashed lines signify predominantly carbon ‘TCnature and predominantly Li nature, respectively. around the Fermi energy level (EF). The band gap disappearsdue to a band crossing between @t and &. They are partially-filled bands at the EF: there is a finite CCO-DOS at the EF, Table 1 lists the ratio r of the zwitterionic configuration to the biradical configuration, the biradical characteryZ the total spin angular momentum l(S2), and the normalized spin density p(SD) for the Li heavily-doped and the nondoped t-PA’s [l.2]. Much attention should be given to the caseof k = 2Tc/3a.As is seen, at this k-point, a SDW largely emerges.In other words, there exists strong electronic correlation. The large SDW comes from a contribution of the canonical CO h;(k) at the point where the strong crystal momentum coupling happens between the T[ and the Li canonical CO’s. It is deduced, therefore. thatthe large SDW arisesfrom this coupling [2].
0379-6779/99/$ - seefront matter0 1999ElsevierScienceS.A. All rightsreserved, PII: so379-6779(98)0
1193-x
460
H. Nobutoki i Synthetic Metals 101 (1999) 459-160
Thus, the occurrence of the large SDW (r = 0.1414) can be attributed to enlargementof the on-site Cotilombic repulsion. This indicates that the electron-electron repulsive interaction becomes large at the &point so that the electron-electron repulsion turns out to be the large SDW. Therefore, the quasidiabatic electronic structure of the heavily-doped f-PA is characterized as the formation of the metallic SDW state, in which the repulsive interaction plays a dominant role [2]. 3.3. A first-order transition -601 n/a
1
3
5
DOS
k
(StatedeVfor unit cd) (a)
(b)
Fig. 2. (a) CC0 band structure and (b) the DOS fordthe Li heavily-doped t-PA. where the bold for &,, @‘2,and 4.3 and dashed lines signify predominantly carbon TI nature and predominantly Li nature, respectively, around the Fermi energy level &).
Table 1 The ratio Y of the zwitterionic configuration to the biradical configuration, the biradical charactery, the total spin angular momentum *(S2): and the normalized spin density p(SD) for the Li heavily-doped and the nondoped t-PA’s. k
Li-doped nondoped
P
Y
‘W
P(SD)
0 0.9844 0.0001 0.0309 0.1759 2E13a 0.1414 0.7228 0.9800 0.9899 nla 0.9998 0.0000 0.0004 0.0200
o x/a
0.9999 0.0000 0.0002 0.0132 0.9113 0.0043 0.1695 0.4117
Kivelson and Heegerproposeda first-order transition from a soliton lattice to a polaronic lattice which is favored by Coulombic and/or interchain effects [6,7], In the first-order transition, Coulombic interactions tend to favor a polaronic lattice: electron-electron repulsion favors the more delocalized charge distribution in a polaron over a soliton [6,7]. This_ suggests that the quasi-diabatic electronic state obtained becomescloser to the polaronic state rather than the soliton state.The polaronic stateis characterizedas a “radical” ion [S], which is due to a half-filled band in the polaronic lattice [6,7], Appearances of the radical and the half-filled band in the polaronic state are similar to those of the SDW (biradical) and the partially-filled band at the EF in the quasi-diabatic electronic state, respectively [2]. It has been further considered that the suppression of the dimerization due to the repulsion will lead to the polaron lattice from the soliton lattice [6] The first-order transition is of a genuine electronic phasetransition, which holds well for the quasi-diabatic electronic structure studied. Therefore, the quasi-diabaticelectronic state will cause polaronic electronic states;in other words. it may in part assist a transition from a soliton lattice to a polaron lattice. 5. Concluding remarks The quasi-diabatic electronic state is the metallic SDW state for the heavily-doped t-PA, which is induced by the electronelectron repulsive interaction. Tt has been considered that the quasi-diabatic electronic state will tend to approach the polaronic state rather than the soliton state; the quasi-diabatic electronic statewould causepolaronic electronic states.
3.2. The SDW states
The nondoped and the used model of the lithium heavilydoped t-PA’s themselvesdo not show a SDW on the adiabatic electronic states since the they are given as a neutral state (closed-shell structure) in this study. However, the quasidiabatic electronic states show a large SDW. Thus, it is very important and interesting to examine origin of the occurrence of the large SDW in order to manifest the quasi-diabatic electronic statesespecially in the heavily-doped t-PA, For this purpose, an analysis of the SDW statewas attempted. The SDW should be derived from the electron-eiectron repulsive interaction. It should be further remarkedthat the r value is equivalent to the ratio of the transfer integral (t) and the on-site Coulombic repulsion (U) in the two-center twoelectron Hiickel-Hubbard model [5].
6. References [l] H. Nobutoki, S. Tsunoda. J. Phys. Chem. 100 (1996) 6189. [2] H. Nobutoki, J. Phys. Chem. 3 101 (1997) 3999. [3] R.H. Baughman, S.L. Hsu, G.P. Pez, A.J. Signorelli, J. 1 Chem.Phys. 68 (1978) 5405. [4] J.L. Brtdas, R.R. Chance, R. Silbey, J. Phys. Chem. 85 (1981) 756. [S] K. Yamaguchi, Y. Yoshioka, T. Takatsuka, T. Fueno, T? Theor. Chim. Acta, 48 (197X) 185. [6] S. Kivelson, A.J. Heeger,Phys. Rev. Lea. 55 (1985) 308. [7] S. Kivelson, A.J. Heeger,Synth. Met. 17 (1987) 183. [8] D.S. Boudreaux, J.L. BrCdas,R. Silbey, Whys. Rev. B28 (1983) 6927.
Quasi-Diabatic Electronic States in Conjugated Polymers H. Nobutoki Advanced Technoloa R&D Center., Mitsubishi Electric Corporation, 8-l-I Hyogo 661-8661, Japan
Tsul;aguchi-Honnlachi, Anzagasaki,
Abstract
A quasi-diabatic crystal orbital theory has been proposedto study the electronic staterepresentingthe diabatic behavior of electrons. The method was applied to nondoped and lithium heavily-doped polyacetylenes. It has been shown that the quasi-diabatic electronic stateis a metallic SDW statefor the doped system,which will causea transition from a soliton stateto a polaron state. k+t~ords: (Semi-empirical models and model calculations. Other phasetransitions, Polyacetylene and derivatives)
r----7
1. Introduction
In conventional electronic band structures, electrons move infinitely slowly on one partially-filled band along the k-space and remains on the same band up to the zone boundary. This behavior of the electron may be called “adiabatic”. On the other hand, if electrons move with a finite velocity, there will be a finite probability that the electron will change from one band to the other vacant bands. This behavior of the electron may be called “diabatic”. Such a diabatic electronic structure might influence chemical and physical properties in heavilydoped polyacetylenes since the metallic properties measured would be associated with the electrons moving with a finite velocity. We previously proposed a quasi-diabatic crystal orbital (CO) theory to study the electronic structure representing the diabatic behavior of electrons [1,2]. In this communication. we present novel characteristics of the quasi-diabatic electronic states in nondoped and lithium heavily-doped tmfjs-polyacetylenes (tPA’s) and discuss the electronic statesfrom a point of electronic correlation. 2. Method of Calculations
Our method is characterized by a quasi-diabatic treatment of the coupling between canonical CO’s due to the derivative operator of crystal momentum. The details of’ the theoretical treatment have already been describedpreviously [1,2]. We refer to this method as the corresponding CO (CCO) method. The calculations have been carried out on the basis of the onedimensional tight-binding SCF-CO method at the level of the CNDOI2 approximation. In this study, the lithium heavily-doped r-PA with an equal bond length chain (a soliton lattice) was employed, as shown in Fig. 1, where the unit cell is surrounded by broken lines, to achieve an idealized metallic state due to the soliton lattice. Geometries of nondoped alternating and model doped t-PA’s were taken from the experimental data of Ref. [3] and from the calculated result of Ref. [4], respectively.
R Li- C= 2.00 A Fig. 1. Geometry of the Li heavily-doped t-PA used in this study, where RLimc standsfor lithium-carbon distance.
3. Results and Discussion
3.1. Electronic Structures The CC0 band structure and the density of states(DOS) for the Li heavily-doped t-PA, calculated by our method, are shown in Fig. 2 [2]. In Fig. 2(a), the bold for 4’1, @z, and 4’3 and dashed lines signify predominantly carbon ‘TCnature and predominantly Li nature, respectively. around the Fermi energy level (EF). The band gap disappearsdue to a band crossing between @t and &. They are partially-filled bands at the EF: there is a finite CCO-DOS at the EF, Table 1 lists the ratio r of the zwitterionic configuration to the biradical configuration, the biradical characteryZ the total spin angular momentum l(S2), and the normalized spin density p(SD) for the Li heavily-doped and the nondoped t-PA’s [l.2]. Much attention should be given to the caseof k = 2Tc/3a.As is seen, at this k-point, a SDW largely emerges.In other words, there exists strong electronic correlation. The large SDW comes from a contribution of the canonical CO h;(k) at the point where the strong crystal momentum coupling happens between the T[ and the Li canonical CO’s. It is deduced, therefore. thatthe large SDW arisesfrom this coupling [2].
0379-6779/99/$ - seefront matter0 1999ElsevierScienceS.A. All rightsreserved, PII: so379-6779(98)0
1193-x
460
H. Nobutoki i Synthetic Metals 101 (1999) 459-160
Thus, the occurrence of the large SDW (r = 0.1414) can be attributed to enlargementof the on-site Cotilombic repulsion. This indicates that the electron-electron repulsive interaction becomes large at the &point so that the electron-electron repulsion turns out to be the large SDW. Therefore, the quasidiabatic electronic structure of the heavily-doped f-PA is characterized as the formation of the metallic SDW state, in which the repulsive interaction plays a dominant role [2]. 3.3. A first-order transition -601 n/a
1
3
5
DOS
k
(StatedeVfor unit cd) (a)
(b)
Fig. 2. (a) CC0 band structure and (b) the DOS fordthe Li heavily-doped t-PA. where the bold for &,, @‘2,and 4.3 and dashed lines signify predominantly carbon TI nature and predominantly Li nature, respectively, around the Fermi energy level &).
Table 1 The ratio Y of the zwitterionic configuration to the biradical configuration, the biradical charactery, the total spin angular momentum *(S2): and the normalized spin density p(SD) for the Li heavily-doped and the nondoped t-PA’s. k
Li-doped nondoped
P
Y
‘W
P(SD)
0 0.9844 0.0001 0.0309 0.1759 2E13a 0.1414 0.7228 0.9800 0.9899 nla 0.9998 0.0000 0.0004 0.0200
o x/a
0.9999 0.0000 0.0002 0.0132 0.9113 0.0043 0.1695 0.4117
Kivelson and Heegerproposeda first-order transition from a soliton lattice to a polaronic lattice which is favored by Coulombic and/or interchain effects [6,7], In the first-order transition, Coulombic interactions tend to favor a polaronic lattice: electron-electron repulsion favors the more delocalized charge distribution in a polaron over a soliton [6,7]. This_ suggests that the quasi-diabatic electronic state obtained becomescloser to the polaronic state rather than the soliton state.The polaronic stateis characterizedas a “radical” ion [S], which is due to a half-filled band in the polaronic lattice [6,7], Appearances of the radical and the half-filled band in the polaronic state are similar to those of the SDW (biradical) and the partially-filled band at the EF in the quasi-diabatic electronic state, respectively [2]. It has been further considered that the suppression of the dimerization due to the repulsion will lead to the polaron lattice from the soliton lattice [6] The first-order transition is of a genuine electronic phasetransition, which holds well for the quasi-diabatic electronic structure studied. Therefore, the quasi-diabaticelectronic state will cause polaronic electronic states;in other words. it may in part assist a transition from a soliton lattice to a polaron lattice. 5. Concluding remarks The quasi-diabatic electronic state is the metallic SDW state for the heavily-doped t-PA, which is induced by the electronelectron repulsive interaction. Tt has been considered that the quasi-diabatic electronic state will tend to approach the polaronic state rather than the soliton state; the quasi-diabatic electronic statewould causepolaronic electronic states.
3.2. The SDW states
The nondoped and the used model of the lithium heavilydoped t-PA’s themselvesdo not show a SDW on the adiabatic electronic states since the they are given as a neutral state (closed-shell structure) in this study. However, the quasidiabatic electronic states show a large SDW. Thus, it is very important and interesting to examine origin of the occurrence of the large SDW in order to manifest the quasi-diabatic electronic statesespecially in the heavily-doped t-PA, For this purpose, an analysis of the SDW statewas attempted. The SDW should be derived from the electron-eiectron repulsive interaction. It should be further remarkedthat the r value is equivalent to the ratio of the transfer integral (t) and the on-site Coulombic repulsion (U) in the two-center twoelectron Hiickel-Hubbard model [5].
6. References [l] H. Nobutoki, S. Tsunoda. J. Phys. Chem. 100 (1996) 6189. [2] H. Nobutoki, J. Phys. Chem. 3 101 (1997) 3999. [3] R.H. Baughman, S.L. Hsu, G.P. Pez, A.J. Signorelli, J. 1 Chem.Phys. 68 (1978) 5405. [4] J.L. Brtdas, R.R. Chance, R. Silbey, J. Phys. Chem. 85 (1981) 756. [S] K. Yamaguchi, Y. Yoshioka, T. Takatsuka, T. Fueno, T? Theor. Chim. Acta, 48 (197X) 185. [6] S. Kivelson, A.J. Heeger,Phys. Rev. Lea. 55 (1985) 308. [7] S. Kivelson, A.J. Heeger,Synth. Met. 17 (1987) 183. [8] D.S. Boudreaux, J.L. BrCdas,R. Silbey, Whys. Rev. B28 (1983) 6927.