Extension of Koopmans’ theorem. II. Accurate ionization energies from correlated wavefunctions for closed-shell atoms

Extended Koopmans’ theorem ionization energies are presented for MC−SCF wavefunctions of the 1s2 2s2 (1S) ground state isoelectronic series, Li− through O4+, and also for some larger CI wavefunctions of Be and B+. Correlation in these reference states reduces the error in the Koopmans’ ionization energy for the 2s electron to approximately 0.01−0.08 eV (1/100−1/20 the SCF Koopmans’ error) in all states except the negative ion, for which the MC−SCF extended Koopmans’ error of 0.25 eV was of the same magnitude but of opposite sign to the SCF error. Our extended Koopmans’ energies for 1s ionization were only slightly better than the corresponding SCF values. Koopmans’ theorem does not yield a 2p ionization energy (1s2 2s2 → 1s2 2p), but the extended Koopmans’ theorem yields an ionization energy whose error is about one−third the SCF 2s error.