AbstractResummation methods can significantly improve the accuracy of ab initio electronic structure computations without increasing the computational cost. For perturbation theories, resummation methods can be designed by constructing approximants to model the known singularity structure of the theory in the complex plane of the perturbation parameter. Quadratic approximants for the fourth‐order Møller–Plesset perturbation theory (MP4) greatly improve the accuracy for the ground‐state energy and provide information about singularity positions that can be used to select an optimal summation method. The Coupled cluster theories CCSD (coupled clusters with single and double excitations), CCSDT (with triple excitations), CCSDTQ (with quadruple excitations), and CCSD(T) (with a triples correction from perturbation theory) can be resummed using approximants that model the empirically observed convergence patterns of the Hartree–Fock (HF), CCSD, CCSD(T) and HF, CCSD, CCSDT, CCSDTQ sequences. Coupling‐constant perturbation theories of molecular vibration and of atoms in external fields, and semiclassical perturbation theories also benefit from appropriate approximants. © 2011 John Wiley & Sons, Ltd.This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods