Open-shell restricted Hartree–Fock perturbation theory: Some considerations and comparisons

A comparative study is presented of the various recently developed open-shell perturbation theories that are based on a restricted Hartree–Fock reference wave function. Included in this study are issues concerning spin contamination, implementational considerations, and numerical comparisons at the second-order of perturbation theory for equilibrium geometries, vibrational frequencies, and singlet–triplet energy differences. Based on all of these considerations, it is concluded that the z-averaged perturbation theory (ZAPT) method is to be preferred over the other recently devised spin–orbital perturbation theories, while the spin-free OPT2 method possesses some advantages and disadvantages relative to the ZAPT method. In particular, it is shown that OPT2 energies are not invariant to rotations among singly-occupied degenerate molecular orbitals.