One-electron density matrices and energy gradients in second-order electron propagator theory

A formalism for evaluation of the effective first-order density matrices associated with second-order electron propagator theory is described. Computer implementation of this formalism affords first-order density properties, such as dipole moments, and energy gradients. Given an initial state with N electrons, this approach enables geometry optimization of the ground and excited electronic states of species with N−1 and N+1 electrons. The performance of the present method is assessed with test calculations on the formyl radical.