Convergence properties of the effective Hamiltonian for the excitation energies in closed-shell systems

Abstract

Methods for calculations of the effective Hamiltonian for particle–hole excitations of closed shell molecular systems, based on the linked-diagram expansions of the Rayleigh–Schrödinger (the folded diagram expansion) and Brillouin–Wigner (the Bloch–Horowitz diagram expansion) perturbation schemes for a quasidegenerate multiconfigurational model space, are studied. The convergence properties of these perturbative methods up to third order, in particular paying attention to the presence of a crossing of levels, are numerically studied for excitation energies of a π-electron system of trans-butandiene. The Padé approximant consistent with the continued fraction approach is applied to the folded diagram expansion treatment. The results of the low-order Padé approximants are similar to those of the Bloch–Horowitz diagram expansions. The singularity of the [2/1] Padé approximant is not necessarily related to the crossing of levels. A strong energy dependence of the effective interaction is shown to be attributed to the crossing of levels.