Extraction of electronic excited states from the ground-state two-particle reduced density matrix

Electronic excited states are computed through a technique for extracting them from a knowledge of the ground-state two-particle reduced density matrix (2-RDM). Diagonalization of the Hamiltonian in the basis set of one-particle excitations, deexcitations, and projections from the ground-state wave function yields those excited states dominated by one-particle excitations; however, explicit evaluation of the Hamiltonian requires a knowledge of the ground-state 4-RDM. Two techniques are developed for evaluating the Hamiltonian elements with only a knowledge of the 2-RDM: (i) the cumulant method in which the higher RDMs are reconstructed from the 2-RDM via cumulant theory and (ii) the Hermitian or anti-Hermitian operator method in which the higher RDMs are eliminated by selecting the basis functions to be Hermitian or anti-Hermitian. These techniques are extendable to the diagonalization of the Hamiltonian in basis sets of m-excitations where m>1. Excited-state energies with an accuracy between 0.1% and 0.001% of their absolute values are determined in illustrative calculations on Be, LiH, H₂O, and BH.