Møller–Plesset expansion of the dispersion energy in the ring approximation

Coupled‐cluster equations for the calculation of the nonexpanded (fully damped) dispersion energy are derived. These equations are solved in the ring approximation using the Møller–Plesset expansion in terms of the fluctuation potentials WA and WB for the individual molecules. Numerical results of high‐order perturbative calculations for the He, H2, LiH, H2O, and HF dimers are presented and compared with the converged results computed using the same basis sets. It is found that the convergence of the Møller‐Plesset expansion of the dispersion energy in the ring approximation is very fast. The padé approximants still accelerate this already good convergence. For all complexes studied in this paper, the sum of the corrections through the second‐order in WA + WB reproduces over 99% of the converged value. The sum of third‐ and higher‐order corrections in the ring approximation is found to be one or two orders of magnitude smaller than the sum of second‐order terms not included in the ring approximation and, therefore, may be safely neglected. Thus, it appears that a second‐order calculation, which does not require iterating coupled‐cluster equations or solving random phase approximation equations, offers the best compromise between accuracy and computational requirements.