Restricted self-consistent field method for excited states

Abstract

A restricted self-consistent field method for excited states is proposed. Assuming that the excited-state Hartree–Fock space is divided into three subspacies orthogonal to each other, we minimize the energy of a single configuration excited state. By using the ground-state Hartree–Fock orbitals as the basis functions, the three coupled pseudoeigenvalue equations obtained from the minimization reduce to the simple secular equations, only two of which are solved iteratively. The optimized excited state guarantees the orthogonality with the HF ground state and the Brillouin-type theorems satisfied in EHP method of Morokuma and Iwata. In addition, the method guarantees two other important Brillouin-type theorems. With an additional assumption this method reduces to Huzinaga’s method. In order to demonstrate the usefulness of this theory in the perturbation treatment, we examine the contribution to the transition probability beyond the independent-particle model using the excited-state wavefunction obtained from the restricted SCF method as the unperturbed wavefunction of the excited state. An approximate expression for the off-diagonal matrix element which determines the theoretical electronic transition probability taking into account the electron correlation is given.