Efficient Structural Relaxation Based on the Random Phase Approximation: Applications to Water Clusters.

We report an improved implementation for evaluating the analytical gradients of the random phase approximation (RPA) electron-correlation energy based on atomic orbitals and the localized resolution of the identity scheme. The more efficient RPA force calculations allow us to relax the structures of medium-sized water clusters. Particular attention is paid to the structures and energy orderings of the low-energy isomers of (H₂O)_n clusters with n = 21, 22, and 25. It is found that the RPA energy ordering of the low-energy isomers of these water clusters is rather sensitive to the basis set used. For the five low-energy isomers of (H₂O)₂₅, the RPA energy ordering still undergoes a change by increasing the basis set to the quadruple to quintuple level. The standard RPA underbinds the water clusters, and this underbinding behavior becomes more pronounced by increasing the basis size to the complete basis set (CBS) limit. The renormalized single excitation (rSE) correction remedies this underbinding, giving rise to a noticeable overbinding behavior at finite basis sets. However, as the CBS limit is approached, RPA+rSE yields an accuracy for the binding energies that is comparable to that of the best available double hybrid functionals, as demonstrated for the WATER27 test set.