Basis set convergence studies of Hartree-Fock calculations of molecular properties within the resolution of the identity approximation

Within the resolution of the identity (RI) method, the convergence of the Hartree-Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunning's cc-pVXZ series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlation-consistent polarized valence double zeta to correlation-consistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RI-HF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree-Fock calculations due to the finite basis set.