Active-Space Pair Two-Electron Reduced Density Matrix Theory for Strong Correlation

An active-space variational calculation of the two-electron reduced density matrix (2-RDM) is derived and implemented where the active orbitals are correlated within the pair approximation. The pair approximation considers only doubly occupied configurations of the wave function, which enables the calculation of the 2-RDM at a computational cost of (r(3)). Calculations were performed both with the pair active-space configuration interaction (PASCI) method and the pair active-space self-consistent field (PASSCF) method. The latter includes a mixing of the active and inactive orbitals through unitary transformations. The active-space pair 2-RDM method is applied to the nitrogen molecule, the p-benzyne diradical, a newly synthesized biscobalt complex, and the nitrogenase cofactor FeMoco. The FeMoco molecule is treated in a [120,120] active space. Fractional occupations are recovered in each of these systems, indicating the presence of strong electron correlation.