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arXiv · 2605.18488

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

Qihao Cheng·Shubhang Krishnakant Trivedi·Phanish Suryanarayana
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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 $1~μ\text{Ha}$ or better.

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Qihao Cheng, Shubhang Krishnakant Trivedi, Phanish Suryanarayana. 2026-05-18. SPARC-atomSFE: Spectral finite-element package for atomic structure calculations in density functional theory. https://arxiv.org/abs/2605.18488

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