Broken-symmetry orbitals for the quasidiabatic electronic states of polymers

Abstract

Broken-symmetry orbitals were developed to study the electronic states representing the diabatic behavior of electrons. It is shown that a closed-shell system with symmetry is represented by the singlet spin-projected unrestricted Hartree᎐Fock Ž . Ž . UHF solution in the quasidiabatic state, which gives rise to a spin-density wave SDW . An analysis is further given to clarify origin of occurrence of the SDW. It is found that the occurrence of the SDW is derived from different orbital interactions, which are the exchange repulsion, the exchange mixing, and the polarization mixing. The appearance of the SDW is discussed from this respect in trans-polyacetylene.

Accurate first-derivative nonadiabatic couplings for the H3 system

“…35 Over the years, a number of formalisms involving ͑quasi͒diabatic basis have also been put forward. [35][36][37][38][39][40][41][42][43][44][45] This paper focuses on the calculation of high quality ab initio ground and first-excited electronic energies and the first-derivative couplings between them. The secondderivative couplings are generally assumed to be negligible as compared to the other terms in the Hamiltonian ͓Eq.…”

Singlet and triplet instability theorems

“…A solution of the HF equation is said to be unstable when the second variation of the associated energy (the stability matrix) is not positive semidefinite. 1,[4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] This theory was pioneered by Thouless 4 and fully developed byČížek and Paldus, 7 culminating in a comprehensive study by Seeger and Pople, 11 who listed 13 types of such instabilities and the corresponding stability matrices. One of the instabilities is that of a real, singlet, restricted Hartree-Fock (RHF) wave function of a closed-shell molecule in the space of real, triplet, unrestricted Hartree-Fock (UHF) wave functions.…”