Optimization of Gaussian basis sets for density-functional calculations

We introduce a scheme for the optimization of Gaussian basis sets for use in density-functional calculations. It is applicable to both all-electron and pseudopotential methodologies. In contrast to earlier approaches, the number of primitive Gaussians (exponents) used to define the basis functions is not fixed but adjusted, based on a total-energy criterion. Furthermore, all basis functions share the same set of exponents. The numerical results for the scaling of the shortest-range Gaussian exponent as a function of the nuclear charge are explained by analytical derivations. We have generated all-electron basis sets for H, B through F, Al, Si, Mn, and Cu. Our results show that they efficiently and accurately reproduce structural properties and binding energies for a variety of clusters and molecules for both local and gradient-corrected density functionals.