电子关联对聚合物中激子和双激子极化性质的影响
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摘要
在有机材料非线性光学性质的理论研究中,极化率的计算是一个关键问题。由于共轭有机分子化学结构具有低维特性,掺杂或光激发可以在分子链中产生孤子,极化子,激子和双激子等元激发。这些元激发的产生对高聚物分子的非线性光学极化率也有非常大的影响。孙鑫等人首先理论研究了聚合物中激子和双激子在外电场下的行为,并发现了双激子态具有反向极化的奇异特性,引起了物理和化学工作者的极大兴趣。电子关联对激子、双激子的物理性质起着非常重要的影响,然而,电子关联效应如何影响激子、双激子的极化特性,目前仍不清楚。
本文将基于紧束缚的Su-Schriefer-Heeger(SSH)模型和扩展Hubbard模型,采用组态相互方法(CI)方法,同时考虑到电子-晶格相互作用和电子关联效应,研究了有机共轭聚合物的基态和激发态(激子态,双激子态)的极化率性质,通过与Hartree-Fock方法的计算结果比较,发现电子关联对体系的极化率性质以及晶格位形有着非常重要的影响。经过计算表明:(1)体系基态的二聚化程度会随着电子相互作用的增强,先增大后减小;(2)同一格点电子相互作用或相邻格点电子相互作用增大会减弱基态的正向极化率;(3)同一格点电子相互作用增大会加强激子态的正向极化率,而相邻格点电子相互作用增大会减弱激子态的正向极化率;在双激子态中,体系的极化率为负,同一格点电子相互作用增大会增强双激子态的负向极化率,相邻格点电子相互作用增大则减弱双激子态的负向极化率
A key point in the theory study of the nonlinear optical(NLO) properties of the organic materials is the calculation of polarizability.Due to the low-dimension structure of the conjugated organic molecules,many sorts of elementary excitations through doping or photoexcitation will be induced in the chain,such as soliton,polaron,exciton and biexciton. These excitations will affect the NLO polarizability of polymer molecular.Xin Sun found that the biexciton showed the negative polarization under the external electric fields.This attracted many physical and chemical researchers.The effect of electron correlation on the properties of exciton and biexciton is very important.But we still don't know how the correlation affect the polarization properties at present.
In this paper,based on the tight-binding Su-Schrieffer-Heeger(SSH) model and the Extended Hubbard model,by using the Configuration interaction method,to consider the electron-lattice interaction and electron-correlation,we have investigated the polarizability of the ground state and excitation state(exciton,biexciton) of the organic conjugated polymer. After taking account into electron correlation,it has been found that(1) the electron-electron interactions enhance the dimerization of the ground state in weak electron correlation region, and then decrease in strong correlation.(2) The on-site and nearest-neighbor electron interactions suppress the polarization of ground state.(3) For the exciton state the on-site electron interactions enhance the polarization while the nearest-neighbor electron interaction suppresses the polarization;in addition,for the biexciton the on-site electron interactions will increase the negative polarization and nearest-neighbor electronic interactions suppress the negative polarization
Compared with the result of Hartree-Fock method,our results demonstrated that the electron-correlation can not be neglect at stronger electron interaction system and is very important for the polarization of the excited state.
本文将基于紧束缚的Su-Schriefer-Heeger(SSH)模型和扩展Hubbard模型,采用组态相互方法(CI)方法,同时考虑到电子-晶格相互作用和电子关联效应,研究了有机共轭聚合物的基态和激发态(激子态,双激子态)的极化率性质,通过与Hartree-Fock方法的计算结果比较,发现电子关联对体系的极化率性质以及晶格位形有着非常重要的影响。经过计算表明:(1)体系基态的二聚化程度会随着电子相互作用的增强,先增大后减小;(2)同一格点电子相互作用或相邻格点电子相互作用增大会减弱基态的正向极化率;(3)同一格点电子相互作用增大会加强激子态的正向极化率,而相邻格点电子相互作用增大会减弱激子态的正向极化率;在双激子态中,体系的极化率为负,同一格点电子相互作用增大会增强双激子态的负向极化率,相邻格点电子相互作用增大则减弱双激子态的负向极化率
A key point in the theory study of the nonlinear optical(NLO) properties of the organic materials is the calculation of polarizability.Due to the low-dimension structure of the conjugated organic molecules,many sorts of elementary excitations through doping or photoexcitation will be induced in the chain,such as soliton,polaron,exciton and biexciton. These excitations will affect the NLO polarizability of polymer molecular.Xin Sun found that the biexciton showed the negative polarization under the external electric fields.This attracted many physical and chemical researchers.The effect of electron correlation on the properties of exciton and biexciton is very important.But we still don't know how the correlation affect the polarization properties at present.
In this paper,based on the tight-binding Su-Schrieffer-Heeger(SSH) model and the Extended Hubbard model,by using the Configuration interaction method,to consider the electron-lattice interaction and electron-correlation,we have investigated the polarizability of the ground state and excitation state(exciton,biexciton) of the organic conjugated polymer. After taking account into electron correlation,it has been found that(1) the electron-electron interactions enhance the dimerization of the ground state in weak electron correlation region, and then decrease in strong correlation.(2) The on-site and nearest-neighbor electron interactions suppress the polarization of ground state.(3) For the exciton state the on-site electron interactions enhance the polarization while the nearest-neighbor electron interaction suppresses the polarization;in addition,for the biexciton the on-site electron interactions will increase the negative polarization and nearest-neighbor electronic interactions suppress the negative polarization
Compared with the result of Hartree-Fock method,our results demonstrated that the electron-correlation can not be neglect at stronger electron interaction system and is very important for the polarization of the excited state.
引文
[1]孙鑫,物理学新进展,5(1985),469
[2]Yu.A.Firuv and V.N.Prigodin,Phys.Rev,126(1985),245
[3]M.A.D.Y.W.Park,A.J.Heeger and A.G.MacDiarmid.Electrical transport in doped polyacetyleneQ].J.Chem.Phys,1980,73:946.
[4]J.S.W.P.Su and A.J.Heeger.Soliton in polyacetylene[J].Phys.Rev.Lett.,1979,42:1698.
[5]J.S.W.P.Su and A.J.Heeger.Soliton excitations in polyacetylene[J].Phys.Rev.B.,1980.22:2099-2111.
[6]A.J.Heeger,S.Kivelson,J.R.Schrieffer et al.,Solitons in conducting polymers[J].Rev.Mod.Phys,1988,781-850,and reference therein.
[7]D.K.Campbell,and A.R.Bishop,Solitons in polyacetylene and relativistic-field-theory models[J].Phys.Rev.B,1981,24:4859.
[8]C.L.Wang,Z.B.Su,and F.Martino,Bipolaron dynamics in nearly degenerate quasi-one-dimensional polymersQ].Phys.Rev.B,1986,33:1512-1515.
[9]J.L.Bredas,C.Adant,P.Tackx,A.Persoons and B.M.Pierce,Chem.Rev.94,243 (1994)
[10]V.M.Geskin and J.L.Bredas,Evolution of the third-order molecular polarizability in polyenes:A local view from atomic charge derivatives[J].J.Chem.Phys,1998,109:6163.
[11]D.N.Beratan,J.N.Onuchic and J.W.Perry,J.Phys.Chem,1987,91:2696.
[12]T.L.Fonseca,C.P.de Melo and B.Kirtman,Synth.Met,1995 71:1695.
[13]Z.Shuai and J.L.Bredas,Static and dynamic third-harmonic generation in long polyacetylene and polyparaphenylene vinylene chains [J].Phys.Rev.B,1991,44:5962.
[14]J.Yu and W.P.Su,Nonlinear optical susceptibilities of many-electron systems Phys.Rev.B,1991,44:13315.
[15]Z.Shuai and J.L.Bredas,Static and dynamic optical nonlinearities in conjugated polymers:Third-harmonic generation and the dc Kerr effect in polyacetylene,polyparaphenylene vinylene,and polythienylene vinylene[J].Phys.Rev.B,1992,46:4395.
[16]C.P.de Melo and R.Silbey,Non-linear polamzabilities of conjugated chains:regular polyenes,solitons,and polarons[J].Chem.Phys.Lett,1987,140:537-541.
[17]C.P.de Melo and R.Silbey,Variational-perturbational treatment for the polarizabilities of conjugated chains.I.Theory and linear polarizabilities results for polyenes[J].J.Chem.Phys,1988,88:2558.
[18]S.Mukamel,A.Takahashi,H.X.Wang,and G.H.Chen,Science,1994,266:250.
[19]B.Kirtman,Convergence of finite chain approximation for linear and non-linear polarizabilities of polyacetylene [J].Chem.Phys.Lett,1988,143:81.
[20]H.A.Kurtz,Int.J.Quantum Chem.,Quantum Chem.Symp.24,791 (1990).
[21]G.P.Das and D.S.Dudis,An approximate ab initio study of the polarizability and hyperpolarizabilities of organic molecules[J].Chem.Phys.Lett,1991,185:151.
[22]G.P.Das and D.S.Dudis,Synth.Met,1992,49/50:211.
[23]G.J.B.Hurst,M.Dupuis and E.Clementi,Ab initio analytic polarizability,first and second hyperpolarizabilities of large conjugated organic molecules:Applications to polyenes C4H6 to C22H24 J.Chem.Phys,1988,89:385.
[24]B.Kirtman,J.L.Toto and M.Hasan,Ab initio finite oligomer method for nonlinear optical properties of conjugated polymers.Hartree-Fock static longitudinal hyperpolarizability of polyacetylene[J].J.Chem.Phys,1995,102:5350.
[25]K.A.Robins,S.-J.Kim,J.L.Toto,M.Hasan,T.T.Toto,C.P.de Melo and B.Kirtman,Synth.Met.71,1671 (1995).
[26]T.T.Toto,J.L.Toto,C.P.de Melo,M.Hasan and B.Kirtman,Ab initio finite oligomer method for nonlinear optical properties of conjugated polymers.Effect of electron correlation on the static longitudinal hyperpolarizability of polyacetylene[J].Chem.Phys.Lett,1995,244:59-64.
[27]X.Sun,R.L.Fu,Yonemitsu.K et al,Photoinduced Polarizarization Inversion in a Polymeric Molecule[J].Phys.Rev.Lett,2000,84(13):2830-2832.
[28]K.Chen,X.Sun and L.H.Tang,Polarizability of polaron in conjugated polymer[J].Phys.Lett.A,2002,294:113-116.
[29]“Primary photoexcitation in conjugated polymers” Ed.N.S.Sarifcific (1997 world scientific).
[30]A.H.Zewial,“Femtochemistry” Ed.M.Chergui (1996 world scientific).
[31]B.S.Hudson and B.E.Kohler,Polyene spectroscopy:The lowest energy excited singlet state of diphenyloctatetraene and other linear polyenes [J].J.Chem.Phys,1973,59.-4984.
[32]See,for example,B.S.Hudson,B.E.Kohler,and K.Schulten,in Excited States,edited by E.C.Lim (Academic,New York,1982),Vol.6,p＞1,and references therein.
[33]A.A.Ovchinnikov,I.I.Ukrainski,and G.V.Kuentsel,lisp.Fiz.Nauk 108,81 (1972)[Sov.Phys.Usp.15,575 (1973)],and references therein.
[34]K.Schulten,I.Ohmine,and M.Karplus,Correlation effects in the spectra of polyenes[J].J.Chem.Phys.1976,64:4422.
[35]K.Schulten,U.Dinur,and B.Honig,The spectra of carbonium ions,cyanine dyes,and protonated Schiff base polyenes [J].J.Chem.Phys,1980,73:3927.
[36]Z.G.Soos and S.Ramasesha,Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models[J].Phys.Rev.B,1984,29:5410-5422.
[37]P.Tavan and K.Schulten,Electronic excitations in finite and infinite polyenes[J].Phys.Rev.B,1987,36:4337-4358.
[38]J.L.Toto,T.T.Toto and C.P.de Melo,A comparative study of the effect of electron correlation in the hyperpolarizability of polyyne,polyacetylene andpolypyrrole oligomers [J].Chem.Phys.Lett,1995,245(10) :660-664.
[39]D.Jacquemin,B.Champagne and J.M.Andr(?),Int.J.Quantum Chem.1997,65:679.
[40]D.Jacquemin,B.Champagne,J.M.Andr(?),Mφller-Plesset evaluation of the static first hyperpolarizability of polymethineimine[J].Chem.Phys.Lett,1998,284(20):24-30.
[41]Rou-li Fu,Guang-yu Guo,Xin Sun,Effects of the electric field on the self-trapping excited states in conjugated polymers[J].Phys.Rev.B,2000,32(23):15735-15744.
[42]J.Hubbard,Proc.R.Soc.London A.1963,276:238
[43]孙鑫,吴长勤,刘晶南,傅柔励.低维体系的不稳定性和电子关联物[J].理学进展,1990,10(4):441-469.
[2]Yu.A.Firuv and V.N.Prigodin,Phys.Rev,126(1985),245
[3]M.A.D.Y.W.Park,A.J.Heeger and A.G.MacDiarmid.Electrical transport in doped polyacetyleneQ].J.Chem.Phys,1980,73:946.
[4]J.S.W.P.Su and A.J.Heeger.Soliton in polyacetylene[J].Phys.Rev.Lett.,1979,42:1698.
[5]J.S.W.P.Su and A.J.Heeger.Soliton excitations in polyacetylene[J].Phys.Rev.B.,1980.22:2099-2111.
[6]A.J.Heeger,S.Kivelson,J.R.Schrieffer et al.,Solitons in conducting polymers[J].Rev.Mod.Phys,1988,781-850,and reference therein.
[7]D.K.Campbell,and A.R.Bishop,Solitons in polyacetylene and relativistic-field-theory models[J].Phys.Rev.B,1981,24:4859.
[8]C.L.Wang,Z.B.Su,and F.Martino,Bipolaron dynamics in nearly degenerate quasi-one-dimensional polymersQ].Phys.Rev.B,1986,33:1512-1515.
[9]J.L.Bredas,C.Adant,P.Tackx,A.Persoons and B.M.Pierce,Chem.Rev.94,243 (1994)
[10]V.M.Geskin and J.L.Bredas,Evolution of the third-order molecular polarizability in polyenes:A local view from atomic charge derivatives[J].J.Chem.Phys,1998,109:6163.
[11]D.N.Beratan,J.N.Onuchic and J.W.Perry,J.Phys.Chem,1987,91:2696.
[12]T.L.Fonseca,C.P.de Melo and B.Kirtman,Synth.Met,1995 71:1695.
[13]Z.Shuai and J.L.Bredas,Static and dynamic third-harmonic generation in long polyacetylene and polyparaphenylene vinylene chains [J].Phys.Rev.B,1991,44:5962.
[14]J.Yu and W.P.Su,Nonlinear optical susceptibilities of many-electron systems Phys.Rev.B,1991,44:13315.
[15]Z.Shuai and J.L.Bredas,Static and dynamic optical nonlinearities in conjugated polymers:Third-harmonic generation and the dc Kerr effect in polyacetylene,polyparaphenylene vinylene,and polythienylene vinylene[J].Phys.Rev.B,1992,46:4395.
[16]C.P.de Melo and R.Silbey,Non-linear polamzabilities of conjugated chains:regular polyenes,solitons,and polarons[J].Chem.Phys.Lett,1987,140:537-541.
[17]C.P.de Melo and R.Silbey,Variational-perturbational treatment for the polarizabilities of conjugated chains.I.Theory and linear polarizabilities results for polyenes[J].J.Chem.Phys,1988,88:2558.
[18]S.Mukamel,A.Takahashi,H.X.Wang,and G.H.Chen,Science,1994,266:250.
[19]B.Kirtman,Convergence of finite chain approximation for linear and non-linear polarizabilities of polyacetylene [J].Chem.Phys.Lett,1988,143:81.
[20]H.A.Kurtz,Int.J.Quantum Chem.,Quantum Chem.Symp.24,791 (1990).
[21]G.P.Das and D.S.Dudis,An approximate ab initio study of the polarizability and hyperpolarizabilities of organic molecules[J].Chem.Phys.Lett,1991,185:151.
[22]G.P.Das and D.S.Dudis,Synth.Met,1992,49/50:211.
[23]G.J.B.Hurst,M.Dupuis and E.Clementi,Ab initio analytic polarizability,first and second hyperpolarizabilities of large conjugated organic molecules:Applications to polyenes C4H6 to C22H24 J.Chem.Phys,1988,89:385.
[24]B.Kirtman,J.L.Toto and M.Hasan,Ab initio finite oligomer method for nonlinear optical properties of conjugated polymers.Hartree-Fock static longitudinal hyperpolarizability of polyacetylene[J].J.Chem.Phys,1995,102:5350.
[25]K.A.Robins,S.-J.Kim,J.L.Toto,M.Hasan,T.T.Toto,C.P.de Melo and B.Kirtman,Synth.Met.71,1671 (1995).
[26]T.T.Toto,J.L.Toto,C.P.de Melo,M.Hasan and B.Kirtman,Ab initio finite oligomer method for nonlinear optical properties of conjugated polymers.Effect of electron correlation on the static longitudinal hyperpolarizability of polyacetylene[J].Chem.Phys.Lett,1995,244:59-64.
[27]X.Sun,R.L.Fu,Yonemitsu.K et al,Photoinduced Polarizarization Inversion in a Polymeric Molecule[J].Phys.Rev.Lett,2000,84(13):2830-2832.
[28]K.Chen,X.Sun and L.H.Tang,Polarizability of polaron in conjugated polymer[J].Phys.Lett.A,2002,294:113-116.
[29]“Primary photoexcitation in conjugated polymers” Ed.N.S.Sarifcific (1997 world scientific).
[30]A.H.Zewial,“Femtochemistry” Ed.M.Chergui (1996 world scientific).
[31]B.S.Hudson and B.E.Kohler,Polyene spectroscopy:The lowest energy excited singlet state of diphenyloctatetraene and other linear polyenes [J].J.Chem.Phys,1973,59.-4984.
[32]See,for example,B.S.Hudson,B.E.Kohler,and K.Schulten,in Excited States,edited by E.C.Lim (Academic,New York,1982),Vol.6,p＞1,and references therein.
[33]A.A.Ovchinnikov,I.I.Ukrainski,and G.V.Kuentsel,lisp.Fiz.Nauk 108,81 (1972)[Sov.Phys.Usp.15,575 (1973)],and references therein.
[34]K.Schulten,I.Ohmine,and M.Karplus,Correlation effects in the spectra of polyenes[J].J.Chem.Phys.1976,64:4422.
[35]K.Schulten,U.Dinur,and B.Honig,The spectra of carbonium ions,cyanine dyes,and protonated Schiff base polyenes [J].J.Chem.Phys,1980,73:3927.
[36]Z.G.Soos and S.Ramasesha,Valence-bond theory of linear Hubbard and Pariser-Parr-Pople models[J].Phys.Rev.B,1984,29:5410-5422.
[37]P.Tavan and K.Schulten,Electronic excitations in finite and infinite polyenes[J].Phys.Rev.B,1987,36:4337-4358.
[38]J.L.Toto,T.T.Toto and C.P.de Melo,A comparative study of the effect of electron correlation in the hyperpolarizability of polyyne,polyacetylene andpolypyrrole oligomers [J].Chem.Phys.Lett,1995,245(10) :660-664.
[39]D.Jacquemin,B.Champagne and J.M.Andr(?),Int.J.Quantum Chem.1997,65:679.
[40]D.Jacquemin,B.Champagne,J.M.Andr(?),Mφller-Plesset evaluation of the static first hyperpolarizability of polymethineimine[J].Chem.Phys.Lett,1998,284(20):24-30.
[41]Rou-li Fu,Guang-yu Guo,Xin Sun,Effects of the electric field on the self-trapping excited states in conjugated polymers[J].Phys.Rev.B,2000,32(23):15735-15744.
[42]J.Hubbard,Proc.R.Soc.London A.1963,276:238
[43]孙鑫,吴长勤,刘晶南,傅柔励.低维体系的不稳定性和电子关联物[J].理学进展,1990,10(4):441-469.