Dynamical pseudopotentials

Abstract: Pseudopotential theory has greatly driven first-principles calculations in materials, replacing the explicit treatment of the chemically inert core electrons with an effective potential acting only on the valence states. This is inherently an embedding problem, where tracing out the core electrons can be formulated in terms of a dynamical embedding potential. Motivated by this perspective, we first introduce a framework for dynamical (i.e., energy-dependent) pseudopotentials, showing how this leads to generalized norm-conservation conditions. Then, adopting a sum-over-poles representation, we disentangle the number of reference energies from the number of projectors; this allows to reproduce all-electron scattering at many reference energies with great accuracy and over very extended energy ranges. We further show that these pseudopotentials enter naturally into many-body total energy functionals, leading for the first time to a consistent and unified treatment of the all-electron atom, the pseudo-atom, and the solid within the same electronic-structure theory.