Dynamical pseudopotentials

TL;DR

This paper introduces a new framework for dynamical pseudopotentials that accurately reproduce all-electron scattering over extended energy ranges and integrate seamlessly into many-body total energy calculations.

Contribution

It develops a dynamical pseudopotential framework with a sum-over-poles approach, enabling consistent treatment of all-electron, pseudo-atom, and solid within electronic-structure theory.

Findings

Accurately reproduces all-electron scattering at multiple energies.

Provides a unified treatment of atoms and solids in many-body calculations.

Introduces a generalized norm-conservation condition for 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.