Multi-reference perturbation theories based on the DOCI wavefunction

We developed an alternative approach to access the full configuration interaction (FCI) energy based on perturbation expansions using the seniority-number basis. In this study, we started from the ground state of the seniority-zero Hamiltonian, also known as the doubly occupied configuration interaction (DOCI) wavefunction, to derive the Rayleigh-Schrödinger perturbation theories up to the fourth-order. We also derived the second-order perturbation theory by taking the DOCI-Fock operator as the zeroth-order Hamiltonian. From demonstrative calculations for small molecules, the DOCI-SCF-RSPT4 and the DOCI-SCF-MP2 quantitatively reproduced the FCI energy. Although solving the DOCI wavefunction is an NP-hard problem in classical computing, connections to the density matrix renormalization group or quantum computing will provide a promising way to accurately solve many-electron problems.