\textit{In-situ} pseudopotentials for electronic structure theory

TL;DR

This paper introduces a novel in-situ pseudopotential construction method from first-principles calculations, enabling highly accurate reproduction of all-electron eigenvalues and energies in electronic structure simulations.

Contribution

It presents a general, first-principles approach to generate in-situ pseudopotentials directly from all-electron calculations, improving accuracy over standard pseudopotentials.

Findings

In-situ pseudopotentials reproduce all-electron eigenvalues up to sixth significant digit.

The method shows good agreement with all-electron theory and standard pseudopotential approaches.

Application to bcc Na demonstrates the method's effectiveness in real materials.

Abstract

We present a general method of constructing \textit{in-situ} pseodopotentials from first principles, all-electron, full-potential electronic structure calculations of a solid. The method is applied to bcc Na, at equilibrium volume. The essential steps of the method involve (i) calculating an all-electron Kohn-Sham eigenstate. (ii) Replacing the oscillating part of the wavefunction (inside the muffin-tin spheres) of this state, with a smooth function. (iii) Representing the smooth wavefunction in a Fourier series, and (iv) inverting the Kohn-Sham equation, to extract the pseudopotential that produces the state generated in steps (i)-(iii). It is shown that an \textit{in-situ} pseudopotential can reproduce an all-electron, full-potential eigenvalue up to the sixth significant digit. A comparison of the all-electron theory, \textit{in-situ} pseudopotential theory and the standard nonlocal pseudopotential theory demonstrates good agreement, e.g., in the energy dispersion of the 3$s$ band state of bcc Na.