Communication: Analytic gradients in the random-phase approximation

The relationship between the random-phase-approximation (RPA) correlation energy and the continuous algebraic Riccati equation is examined and the importance of a stabilizing solution is emphasized. The criterion to distinguish this from non-stabilizing solutions can be used to ensure that physical, smooth potential energy surfaces are obtained. An implementation of analytic RPA molecular gradients is presented using the Lagrangian technique. Illustrative calculations indicate that RPA with Hartree-Fock reference orbitals delivers an accuracy similar to that of second-order Moller–Plesset perturbation theory.