PASPT2: a size-extensive and size-consistent partial-active-space multi-state multi-reference second-order perturbation theory for strongly correlated electrons

A partial-active-space (PAS) multi-state (MS) multi-reference second-order perturbation theory (MRPT2) for the electronic structure of strongly correlated systems of electrons, dubbed PASPT2, is formulated by linearizing the intermediate normalization-based general-model-space state-universal coupled-cluster theory with singles and doubles [IN-GMS-SU-CCSD; J. Chem. Phys. 119, 5320 (2003)]. At variance with the existence of disconnected terms in the IN-GMS-SU-CCSD amplitude equations, the disconnected terms in the PASPT2 amplitude equations can be avoided completely by choosing a special reference-specific zeroth-order Hamiltonian. The corresponding effective/intermediate Hamiltonian can also be made connected and closed, so as to render the energies obtained by diagonalization fully connected. As such, PASPT2 is strictly size-extensive, in sharp contrast with the parent IN-GMS-SU-CCSD. It is also size-consistent when the PAS of a supermolecule is chosen to be the direct product of those of the physically separated, non-interacting fragments. Prototypical systems are taken as showcases to reveal the efficacy of PASPT2.