Correlation energy of open-shell systems. Application of the many-body Rayleigh-Schrödinger perturbation theory in the restricted Roothaan-Hartree-Fock formalism

Correlation energy of doublet and triplet electronic states is formulated in terms of many-body diagrammatic perturbation theory through third order. Applications are presented for B${\mathrm{H}}_2$ and N${\mathrm{H}}_2$ radicals and the computed correlation energies are compared with data obtained with the same basis set from configuration-interaction treatments covering singly and doubly excited configurations. It is shown that the two approaches give correlation energies close in absolute value.