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

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–Schrodinger (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 Pade approximant consistent with the continued fraction approach is applied to the folded diagram expansion treatment. The results of the low‐order Pade approximants are similar to those of the Bloch–Horowitz diagram expansions. The singularity of the [2/1] Pade approximant is not necessarily related to the crossing of levels. A strong energy dependence of the effective interaction is shown to be attribute...