Radial Kohn-Sham problem via integral-equation approach

TL;DR

This paper introduces a numerical tool for solving the spherically-symmetric Kohn-Sham problem using an integral-equation approach, supporting various exchange-correlation functionals and achieving high-precision results for atomic total energies.

Contribution

It presents a novel integral-equation based solver for the Kohn-Sham problem that accurately handles range-separated functionals and provides benchmark data for atomic calculations.

Findings

Achieves 14-digit agreement with reference Hartree-Fock data.

Supports multiple exchange-correlation functionals, including hybrids.

Provides benchmark results for atomic total energies.

Abstract

We present a numerical tool for solving the non-relativistic Kohn-Sham problem for spherically-symmetric atoms. It treats the Schr\"{o}dinger equation as an integral equation relying heavily on convolutions. The solver supports different types of exchange-correlation functionals including screened and long-range corrected hybrids. We implement a new method for treating range separation based on the complementary error function kernel. The present tool is applied in non-relativistic total energy calculations of atoms. A comparison with ultra-precise reference data[Cinal, JOMC 58, 1571 (2020)] shows a 14-digit agreement for Hartree-Fock results. We provide further benchmark data obtained with 5 different exchange-correlation functionals.