A new general approach is developed for obtaining systematic sequences of atomic single-particle basis sets for use in correlated electronic structure calculations of molecules. All the constituent functions are defined as the solutions of variational problems and are of three types: a minimal Hartree-Fock set, additional functions to represent low-lying excited configurations, and general functions for describing electron correlation. The latter are determined to minimize a functional derived from the closed-shell second-order correlation energy expression. Generally-contracted Gaussian expansions are developed to approximate these general functions in the non-relativistic case and within a scalar-relativistic approximation. (c) 2005 Elsevier B.V. All rights reserved.