Recently developed linear R12-type explicitly correlated methodology promises few-percent basis set errors with small, double-xi quality, Hartree-Fock basis sets. We present an MP2-R12 method which achieves the two-electron basis limit as closely as desired using any finite Hartree-Fock basis set. We found that the two-electron correlation energy can be computed precisely from a very approximate Hartree-Fock function. The error in the two-electron correlation energy due to the finite Hartree-Fock basis set was averaged over a set of 20 small molecules. The mean error was found to be small, at most 1% for a double-xi basis set, and quickly decaying. (c) 2005 Elsevier B.V. All rights reserved.