Multireference Møller–Plesset perturbation theory with non-canonical and non-orthogonal orbitals

Using non-orthogonal secondary orbitals and non-canonical (localized) inactive and active orbitals, a second-order multireference perturbation theory is formulated, based on a complete active space self-consistent field (CASSCF) wavefunction. The equations of interest are derived from the first-order Bloch equation by using an approach based on a bi-orthogonal basis and operators expressed in second-quantization.