Theory and applications of spin-restricted open-shell Møller-Plesset theory

Abstract

Formulae in terms of integrals and orbital energies are presented for the evaluation of the second-, third- and fourth-order energies in open-shell spinrestricted Møller-Plesset (RMP) perturbation theory. The performance of RMP theory is evaluated by calculating equilibrium structures and harmonic vibrational frequencies of a large number of open-shell systems and by calculating energies of reactions which have been shown to be poorly described by spinunrestricted Møller-Plesset (UMP) theory. RMP theory removes the spin contamination present in the unrestricted Hartree-Fock (UHF) reference of UMP theory. In cases where the spin contamination gives rise to large errors in UMP calculations, such as for the harmonic frequencies of NO, CN, CO⁺ and FO₂ and the energies of reactions involving CN and FO₂, RMP theory is shown to offer a substantial improvement. In cases where the Møller-Plesset series exhibits large oscillations, such as for O₂, O⁺ ₂ and F⁺ ₂, RMP theory is shown to offer no improvement over UMP theory; in these cases good results are achieved with higher-order methods such as quadratic configuration interaction and coupled-cluster theory.