Numerical solution of the radial Dirac equation in pseudopotential construction

TL;DR

This paper presents a numerical approach to solving the radial Dirac equation within pseudopotential generation for electronic structure calculations, comparing relativistic and nonrelativistic eigenvalues and discussing implementation details.

Contribution

It introduces a numerical method for solving the radial Dirac equation in pseudopotential construction, integrating relativistic effects into electronic structure calculations.

Findings

Relativistic eigenvalues differ from nonrelativistic ones for one-electron atoms.

The method effectively solves the radial Dirac and Schrödinger equations.

Implementation details facilitate computational application in DFT pseudopotential generation.

Abstract

In the present work we study numerical solution of the radial Dirac equation in a specific case - ab-initio pseudopotential generating process - which is needed within the electronic structure calculations using a Density Functional Theory (DFT) combined with a pseudopotential method. We give a brief introduction to DFT, derive the radial Dirac and Schrodinger equations, show how to solve them both for a given energy and as an eigenvalue problem using a known asymptotic behavior of the solution. Next we compare the nonrelativistic and relativistic eigenvalues for one electron atom. Finally we state a few words about the computer implementation.