All-electron pseudopotentials

We present an ab initio procedure for the construction of pseudopotentials accommodated to a crystal environment under study, which takes into account the response of the core charge density to the valence electrons of an atom in a bond. Within pseudopotential methodology, core electrons are treated differently from valence electrons; however, the core electrons are considered as ``frozen'' in space and independent of the atom's valence electrons after they were relaxed and adapted to a crystal-valence charge density. In this way the frozen-core approximation is removed despite the fact that the frozen-core technique is still used and no all-electron solid-state calculation is required. Since the all-electron core-valence response is taken into account properly, the treatment of nonlinear properties of exchange-correlation functionals is naturally included and corrections using model core charges for nonlinear functionals are eliminated. Contrary to standard pseudopotentials based on the atomic charge density of a free atom, the new all-electron pseudopotentials are functionals of the crystal charge density. Consequently, the intuitive ad hoc choice of occupation numbers, which is necessary for the construction of pseudopotentials by existing methods, is avoided and energy windows for pseudopotentials are put at optimum positions. In this paper, core-level shifts were calculated within the pseudopotential framework. The results of test calculations for diamond, silicon, nonmagnetic fcc $\ensuremath{\beta}$-Co, cubic TiC, and hexagonal ${\mathrm{TiS}}_{2}$ are presented.