A second-order doubles correction to excitation energies in the random-phase approximation

A computationally tractable doubles correction to excitation energies obtained in the random-phase approximation (RPA(D)) is presented. It gives excitation energies correct through second order in the ground-state fluctuation potential. RPA(D) has been tested for H2O, N2, Ne, CH2, BH and C2 using full configuration interaction (FCI) results as benchmarks. Comparison is made with other existing models of similar complexity. Overall the accuracy of excitation energies calculated using RPA(D) is similar to that obtained in the CC2, CIS(D) and SOPPA methods. The errors of the random-phase approximation excitation energies are typically reduced by a factor of two using the RPA(D) correction. The mean absolute deviation of RPA(D) and FCI excitation energies is 0.51 eV and for the majority of the excitations the RPA(D) results are lower than the FCI results.