Analytic energy derivatives in the numerical local-density-functional approach

Analytical energy gradients for numerical orbital expansions can be calculated using the same three-dimensional integration methods as for calculating the total energy in the local-density-functional approach. It is shown that in addition to Pulay corrections for expansion functions attached to the atomic sites correction terms for non-self-consistency of the auxiliary density can also be used with benefit. The usefulness of this approach is demonstrated in the calculation of equilibrium geometries of organic and inorganic molecules, radicals, and transition-metal compounds. The calculated structural parameters are in at least as good agreement with experimental data as structures obtained from standard ab initio methods. Excellent basis sets can be used at a comparably low computational cost.