Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth-order wavefunctions

A method is proposed to calculate the effect of configuration interaction by a Rayleigh-Schrödinger perturbation expansion when starting from a multiconfigurational wavefunction. It is shown that a careless choice of H0 may lead to absurd transition energies between two states, at the first orders of the perturbation, even when the perturbation converges for both states. A barycentric defintion of H0 is proposed, which ensures the cancellation of common diagrams in the calculated transition energies. A practical iterative procedure is defined which allows a progressive improvement of the unperturbed wavefunction ψ0; the CI matrix restricted to a subspace S of strongly interacting determinants is diagonalized. The desired eigenvector ψ0 of this matrix is perturbed by the determinants which do not belong to S. The most important determinants in ψ1 are added to S, etc. The energy thus obtained after the second-order correction is compared with the ordinary perturbation series where ψ0 is a single determinant. For the ground state, this procedure includes, besides the whole second-order correction, the most important terms of the third and fourth orders. The question of orthogonality of excited states is discussed. This technique, hereafter called CIPSI, has been tested on the ground and several excited states of H2, Ne, and MgO, showing both a rapid convergence of the calculated transition energy and the importance of correlation effects on transition energy.