Scaled Hartree-Fock orbitals for perturbation treatment of ground and excited electronic states

Perturbation theory is a standard method used to calculate electronic correlation effects in atomic and molecular systems. It is able to provide a size-consistent description of electronic energies. Perturbation theory for excited states is often only applicable in a restricted way due to convergence problems (intruder-state problems). The starting point for a perturbation treatment is the decomposition of the total Hamiltonian H into $H_0$+V. The present study is devoted to proper definitions of ${\mathrm{H}}_0$ for a convergent treatment of ground and excited states. We use the scaled Hartree-Fock operator as an unperturbed Hamiltonian. It contains scaling factors to modify the Coulomb and exchange terms. These factors can be chosen in order to improve the convergence properties for the treatment of ground and excited electronic states. As a simple illustrative example, second-order perturbation calculations are reported in complete model spaces for ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ states of the hydrogen molecule. The total energies obtained show an agreement of better than 0.23 eV with the exact results.