Multireference many-electron correlation energies from two-electron reduced density matrices computed by solving the anti-Hermitian contracted Schrödinger equation

Two-electron reduced density matrices (2-RDMs) have recently been directly calculated by solving the anti-Hermitian contracted Schrödinger equation (ACSE) to obtain 95–100 % of the ground-state correlation energy of atoms and molecules with the accuracy increasing with the size of the one-electron basis set [ Mazziotti Phys. Rev. Lett. 97 143002 (2006).] In this paper, the ACSE method is extended to treat strong multireference correlation effects that are often important at nonequilibrium molecular geometries. While previous ACSE calculations have employed an initial 2-RDM from the Hartree-Fock method, we initialize the solution of the ACSE with a 2-RDM guess from a multiconfiguration self-consistent field calculation. Applications are made to multireference correlation in the potential energy surfaces of the molecules HF, H₂O, and C₂ in polarized valence double-zeta basis sets while N₂ is treated in polarized valence double- and triple-zeta basis sets. Accurate ground-state energies and 1-RDM occupation numbers are obtained at both equilibrium and nonequilibrium geometries where the energies are within a few millihartrees of those from full configuration interaction.