What is the most efficient way to reach the canonical MP2 basis set limit?

Various ways of reaching the complete basis set limit at the second-order Møller–Plesset perturbation theory (MP2) level are compared with respect to their cost-to-accuracy ratio. These include: (1) traditional MP2 calculations with correlation consistent basis sets of increasing size, with and without the resolution of identity for Coulomb and exchange (RIJK) or the combined RIJ and 'chain of spheres' (RIJCOSX) approximations; (2) basis set extrapolation obtained with the same MP2 variants; and (3) explicitly correlated F12-MP2 methods. The time required to solve the Hartree–Fock equations is part of the evaluation because the overall efficiency is of central interest in this work. Results were obtained for the ISO34, DC9 and S66 test sets and were analysed in terms of efficiency and accuracy for total energies, reaction energies and their effect on the basis set superposition error. Among the methods studied, the RIJK-MP2-F12 and RIJK-MP2-EP1 (where EP1 stands for 'Extrapolation Protocol 1' as explained in the text) methods perform outstandingly well. Although extrapolation is, in general, slightly faster than explicit correlation, it is found that for reaction energies, RIJK-MP2-F12 performs systematically better. This holds especially in combination with a triple zeta basis set, in which case it even outperforms the much more costly extrapolation involving quadruple- and quintuple-zeta correlation consistent basis sets.