SPARC-atomSFE: Spectral finite-element package for atomic structure calculations in density functional theory
Description
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 broad hierarchy of exchange-correlation approximations, spanning local, semilocal, and nonlocal functionals, within a spin-unpolarized, non-relativistic, spherically symmetric atomic framework. The nonlocal functionals include hybrid functionals and the many-body random phase approximation (RPA); for hybrid functionals, we implement both the generalized Kohn–Sham and optimized effective potential (OEP) approaches, while RPA is treated within the OEP framework. SPARC-atomSFE also includes support for fractional orbital occupations and charged atoms. 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-correlation approximations, obtaining results that are in very good agreement with values reported in the literature. We further demonstrate two representative applications: accuracy testing of pseudopotentials for advanced exchange-correlation, and machine learning of the exact exchange OEP potential.