Two new unitary-invariant and size-consistent perturbation theoretical approaches to the electron correlation energy

Two Rayleigh–Schrödinger perturbation methods are proposed. In the first method, the unperturbed Hamiltonian is that part of the second quantization Hamiltonian that retains the number of electrons in the occupied orbital space. In the second method the electron-repulsion integrals (ERIs) with four non-occupied orbitals are substituted by ERIs with four occupied orbitals. Both approaches are size consistent and invariant with respect to unitary orbital transformations. Comparison of electronic energies with full CI, coupled-cluster, and Møller–Plesset results demonstrate that the new approaches are more accurate than Møller–Plesset perturbation theory and comparable with coupled-cluster results.