Failure of the random-phase-approximation correlation energy

The random phase approximation (RPA) is thought to be a successful method; however, basic errors have been found that have massive implications in the simplest molecular systems. The observed successes and failures are rationalized by examining its performance against exact conditions on the energy for fractional charges and fractional spins. Extremely simple tests reveal that the RPA method satisfies the constancy condition for fractional spins that leads to correct dissociation of closed-shell molecules and no static correlation error (such as in H-2 dissociation) but massively fails for dissociation of odd electron systems, with an enormous delocalization error (such as H-2(+) dissociation). Other methods related to the RPA, including the Hartree-Fock response (RPAE) or range-separated RPA, can reduce this delocalization error but only at the cost of increasing the static correlation error. None of the RPA methods have the discontinuous nature required to satisfy both exact conditions and the full unified condition (e. g., dissociation of H-2(+) and H-2 at the same time), emphasizing the need to go beyond differentiable energy functionals of the orbitals and eigenvalues.