Relativistic AB Initio calculations of interaction energies: formulation and application to ionic solids

Abstract

The theory and computational techniques used in a computer program capable of performing fully relativistic ab initio electronic structure calculations for pairs of interacting atomic species are presented. If the species are ions in a crystal, a description of an ionic solid is obtained. If the two species are otherwise free, the program yields a wavefunction for a diatomic molecule. The molecular wavefunction is an antisymmetrized product of core and valence parts. The core is a Hartree product of the Dirac—Fock atomic orbitals of the free atoms. The largest contribution to the energy arises from the inner-core orbitals, each having negligible overlap with all other orbitals. The purely atomic inner-core energy does not contribute to the binding energy of the molecule, thus obviating the need to calculate the largest part of the molecular energy. The outer core consists of those remaining closed subshells of the isolated atoms that are not significantly affected on molecule formation. All the remaining orbitals, including at least the valence Dirac—Fock atomic orbitals of the free atoms plus further atomic functions needed to describe charge density changes upon molecule formation, are used to construct the valence wavefunction. This can be constructed to take account of correlation between the valence electrons. All atomic functions have central field form with the radial parts defined numerically. This method of constructing the molecular wavefunction avoids the need for large basis sets, ensures that the Dirac small components bear the correct relation to the large components and avoids basis set superposition errors. This program is used to initiate a non-empirical study of the properties of ionic solids. The results show that these properties cannot be reliably predicted by using free ion wavefunctions and that the Watson shell model for describing the non-negligible differences between free and in-crystal ion wavefunctions is not satisfactory. The results demonstrate the importance of inter-ionic dispersive attractions but show that it is not satisfactory to neglect the part quenching of the standard long-range form of these attractions arising from overlap of the ion wavefunctions.