Energy gap equation of 1D polyconjugated π-systems in the Hubbard approximation

Abstract

It is shown that the energy gap of an arbitrary homonuclear or heteronuclear alternant or nonalternant π-conjugated system, having a singlet ground state, is given by the formula Δ E σ={Δ 2 1(σ) corr+[Δ 2(σ) corr+Δ top+Δ geom] 2} 1 2 , where Δ top and Δ geom are factors depending on the molecular topology and geometry, respectively. In the general case, the correlation corrections Δ 1 (σ) and Δ 2(σ) differ for MOs with different spin (σ=α,β) and Δ E β≠Δ E β. In some particular cases Δ E α= Δ E β. The correlation correction Δ 2(σ) corr corresponds to a non-uniform charge distribution in the π-system. In the case of homo-nuclear alternant systems Δ 2(σ) corr=0. The investigations are carried out using the method of alternant molecular orbitals (AMO) in the Hubbard approximation. The band structure of the fully oxidized form of 1D poly(para-aniline)-poly(para-phenyleneimine), has been studied.