  A simple yet general method for constructing basis sets for molecular
electronic structure calculations is presented. These basis sets consist of
atomic natural orbitals from a multi-configurational self-consistent field
calculation supplemented with primitive functions, chosen such that the
asymptotics are appropriate for the potential of the system. Primitives are
optimized for the homonuclear diatomic molecule to produce a balanced basis
set. Two general features that facilitate this basis construction are
demonstrated. First, weak coupling exists between the optimal exponents of
primitives with different angular momenta. Second, the optimal primitive
exponents for a chosen system depend weakly on the particular level of theory
employed for optimization. The explicit case considered here is a basis set
appropriate for the Burkatzki-Filippi-Dolg pseudopotentials. Since these
pseudopotentials are finite at nuclei and have a Coulomb tail, the recently
proposed Gauss-Slater functions are the appropriate primitives. Double- and
triple-zeta bases are developed for elements hydrogen through argon. These new
bases offer significant gains over the corresponding Burkatzki-Filippi-Dolg
bases at various levels of theory. Using a Gaussian expansion of the basis
functions, these bases can be employed in any electronic structure method.
Quantum Monte Carlo provides an added benefit: expansions are unnecessary since
the integrals are evaluated numerically.
