Correlation Energy Estimators based on Møller-Plesset Perturbation Theory

Some methods for the convergence acceleration of the Møller-Plesset perturbation series for the correlation energy are discussed. The order-by-order summation is less effective than the Feenberg series. The latter is obtained by renormalizing the unperturbed Hamilton operator by a constant factor that is optimized for the third order energy. In the fifth order case, the Feenberg series can be improved by orderdependent optimization of the parameter. Alternatively, one may use Padé approximants or a further method based on effective characteristic polynomials to accelerate the convergence of the perturbation series. Numerical evidence is presented that, besides the Feenberg-type approaches, suitable Padé approximants, and also the effective second order characteristic polynomial, are excellent tools for correlation energy estimation.