The propagation of basis set error and geometry optimization in a b i n i t i o calculations. A statistical analysis of the sulfur d-orbital problem

By generating a sample of 100 random molecular basis sets from a normal distribution centered on the best-energy, fully variational AO basis sets, a statistical analysis has been carried out on the distributions and pair correlations of calculated Hartree–Fock total energies, optimum bond lengths, energy components, and formal atomic charges. Dimethylsulfoxide (DMSO), the calculated geometry of which has been found extremely sensitive to basis variations in an earlier study, has been selected as model compound. The results provide a clear answer to the sulfur d-orbital problem, since no simultaneous reproduction of experimental geometry and an adequate approximation to the variationally optimum total energy have been possible without including d-polarization functions on sulfur.