SPARC-atomSFE: Spectral finite-element package for atomic structure calculations in density functional theory

TL;DR

SPARC-atomSFE is a spectral finite-element software package designed for precise atomic structure calculations within density functional theory, supporting various exchange-correlation functionals and advanced numerical methods.

Contribution

It introduces a versatile spectral finite-element framework for atomic DFT calculations, including hybrid functionals and the RPA, with systematic validation and convergence analysis.

Findings

Achieves results within 1 microHartree of literature values.

Supports a wide range of exchange-correlation functionals, including hybrid and RPA.

Demonstrates systematic convergence and accuracy validation.

Abstract

We present SPARC-atomSFE, a spectral finite-element package for accurate and efficient atomic structure calculations within the framework of Kohn-Sham density functional theory. The package supports both all-electron and norm conserving pseudopotential calculations across a comprehensive hierarchy of exchange-correlation approximations, spanning local, semilocal, and nonlocal functionals. The latter includes hybrid functionals and the many-body random phase approximation, for which we implement both the generalized Kohn-Sham approach and the optimized effective potential (OEP) method, with OEP necessary for eigenvalue-dependent functionals. Spatial discretization is based on an adaptive grid with element nodes distributed according to the Legendre--Gauss--Lobatto scheme, high-order $C^{0}$-continuous Lagrange polynomial basis functions, and Gauss--Legendre quadrature for numerical integration. We present systematic convergence studies and identify the computational parameters required to achieve target accuracies. We validate the accuracy of SPARC-atomSFE through representative calculations spanning the various exchange-correlations approximations, obtaining results that generally agree with values in the literature to within $1~\mu\text{Ha}$ or better.