Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations

It is customary in molecular quantum chemistry to adopt basis set libraries in which the basis sets are classified according to either their size (triple-ζ, quadruple-ζ, ...) and the method/property they are optimal for (correlation-consistent, linear-response, ...) but not according to the chemistry of the system to be studied. In fact the vast majority of molecules is quite homogeneous in terms of density (i.e., atomic distances) and types of bond involved (covalent or dispersive). The situation is not the same for solids, in which the same chemical element can be found having metallic, ionic, covalent, or dispersively bound character in different crystalline forms or compounds, with different packings. This situation calls for a different approach to the choice of basis sets, namely a system-specific optimization of the basis set that requires a practical algorithm that could be used on a routine basis. In this work we develop a basis set optimization method based on an algorithm-similar to the direct inversion in the iterative subspace-that we name BDIIS. The total energy of the system is minimized together with the condition number of the overlap matrix as proposed by VandeVondele et al. [VandeVondele et al. J. Chem. Phys. 2007, 227, 114105]. The details of the method are here presented, and its performance in optimizing valence orbitals is shown. As demonstrative systems we consider simple prototypical solids such as diamond, graphene sodium chloride, and LiH, and we show how basis set optimizations have certain advantages also toward the use of large (quadruple-ζ) basis sets in solids, both at the DFT and Hartree-Fock level.