Anti-Hermitian Contracted Schrödinger Equation: Direct Determination of the Two-Electron Reduced Density Matrices of Many-Electron Molecules

Two-electron reduced density matrices (2-RDMs) of many-electron molecules are directly determined without calculation of their wave functions by solving the anti-Hermitian contracted Schrödinger equation. Approximation of the 3-RDM in the anti-Hermitian contracted Schrödinger equation by a corrected cumulant expansion Mazziotti, Phys. Rev. A 60, 3618 (1999) permits the direct calculation of the energy and 2-RDM with many high-order correlation effects included. The method is illustrated for the molecules BeH2, H2O, NH3, CH4, and CO as well as the dissociation of BH. Correlation energies are obtained within 95%-100% of full-configuration interaction, and 2-RDMs very nearly satisfy known N-representability conditions.