Application of the Dyson-type boson mapping for low-lying electron excited states in molecules

Abstract

In this paper, we propose a bosonization method of the system in which a quasi-particle consists of electron-hole pairs. Electron excitation energies of low-lying electron excited states are obtained by finding out the quantized normal mode oscillations around a ground state in the molecular electronic structure. These excited states are approximately considered as the collective motion states of the quasi-particles that correspond to the quantized normal mode oscillations, and each of these quasi- particles consists of the electron-hole pairs. We introduce the quasi-particle operators which create the low-lying electron excited states. These introduced quasi-particle operators, however, do not satisfy the commutation relations as bosons. Therefore, by using the Dyson-type boson mapping method, we transform these operators into those which satisfy exactly the boson commutation relations. We discuss how to map the operators of the fermion space onto the Dyson-type boson space, and obtain the Dyson-type boson representation Hamiltonian. By using this Hamiltonian, we discuss the low-lying excited states as a many-body problem of the boson system. We apply this method to the π-electrons system of the ethylene molecule, and obtain the low-lying electronexcitedstateenergiesintherandom-phaseapproximation(RPA).Inthenextstep,toimprove the accuracy of the these obtained excitation energy values, we carry out additional calculations by