Dual-basis self-consistent field methods: 6-31G*calculations with a minimal 6-4G primary basis

The feasibility of the strongest possible dual-basis approximation to polarized valence double zeta Hartree-Fock and density functional theory calculations is explored. Specifically, to approximate 6-31G* and 6-31+G* calculations, a minimal 6-4G basis is constructed from 6-31G exponents. The self-consistent field calculation is performed in this minimal basis, followed by a single diagonalization step in the target basis. Statistical errors in atomization energies, molecular structures, and harmonic frequencies approach those of the target basis for HF, B3LYP and EDF1, and are far superior to calculations that do not include polarization functions. Speedups of approximately 5-10 are obtained for the energy, with speedups of 2-3 for the gradient, using existing algorithms, with significant potential for future improvements.