Choosing GTO basis sets for periodic HF calculations

We investigate numerical linear dependencies of Gaussian-type orbital basis sets employed in the framework of the Hartree-Fock self-consistent field m ethod for periodic structures, which so far have hampered the use of extend ed basis sets for non-ionic crystals. These linear dependencies occur when diffuse basis functions are included in a basis set in an uncontrolled mann er. We use the condition number of the overlap matrix to lead us in the con struction of extended basis sets for periodic structures which avoid numeri cal linear dependencies. Extended basis sets of high quality are optimized for a number of periodic structures (fcc He, alpha-Be, alpha-BN, and B1 NaF ) with respect to the energy of the constituent atoms or ions. The results obtained with our basis sets, which do not require reoptimization in the cr ystal environment, compare favorably with those obtained with other extende d basis sets reported in the literature.