Summation approximants improve the accuracy of ab initio calculations of molecular potential-energy hypersurfaces

Full configuration–interaction calculations for BH, HF, and CH3 are used as benchmarks for determining the accuracy of summation approximants for CCSD(T) coupled-cluster theory and fourth-order Møller–Plesset perturbation theory as function of bond distances. A continued-fraction approximant [the CCSD(T)-cf method] reliably improves CCSD(T). The MP4-qλ procedure, in which repartitioned perturbation theory is summed with a quadratic approximant, is much more accurate than conventional MP4 but more sensitive to bond stretching than is CCSD(T)-cf. Diagnostics for estimating the accuracies of the methods, based on singularity analysis of perturbation series, are developed and discussed.