Effective convergence to complete orbital bases and to the atomic Hartree–Fock limit through systematic sequences of Gaussian primitives

Abstract

Optimal starting points for expanding molecular orbitals in terms of atomic orbitals are the self-consistent-field orbitals of the free atoms and accurate information about the latter is essential for the construction of effective AO bases for molecular calculations. For expansions of atomic SCF orbitals in terms of Gaussian primitives, which are of particular interest for applications in polyatomic quantum chemistry, previous information has been limited in accuracy. In the present investigation a simple procedure is given for finding expansions of atomic self-consistent-field orbitals in terms of Gaussian primitives to arbitrarily high accuracy. The method furthermore opens the first avenue so far for approaching complete basis sets through systematic sequences of atomic orbitals. It is shown that, for expansions of atomic SCF orbitals in terms of even-tempered Gaussian primitives, the energy- optimized exponents are simple analytic functions of the number of primitives used in the expansions.With the help of these formulas, accurate atomic SCF calculations in terms of very large sets of primitives can be carried out without exponent optimization and the energies from such calculations converge to the Hartree–Fock limit on smooth curves. It proves possible to extrapolate to the limit and to give estimates for the error bounds of the extrapolation. Quantitative data are given for all atoms in the first three periods of the periodic system. The Hartree–Fock limits obtained in this manner are equal or superior to previous calculations based on numerical methods or on expansions in terms of exponential type primitives. From the given atomic SCF orbitals, extended basis sets for molecular calculations are easily obtained by Raffenetti’s method.