Hybrid finite element / multipole expansion method for atomic Kohn-Sham density functional theory calculations

A numerical framework is developed for aspherical atomic Kohn-Sham density functional theory calculations. The framework invokes higher-order finite elements as a radial discretization in combination with a multipole expansion for controlling the spherical resolution. Both all-electron and nonlocal pseudopotential calculations are addressed in a unified setting. The overall approach is validated through a range of numerical examples which demonstrate the systematic convergence of the radial and spherical discretizations as well as the outstanding accuracy that can be efficiently obtained in the presence of strong aspherical external fields. Overall, the presented approach offers a route to adaptive local enrichment for electronic structure calculation in the context of the finite element method. •Real-space aspherical atomic electronic structure calculation framework is developed.•All-electron and nonlocal pseudopotential Kohn-Sham density functional theory is targeted.•Finite element method is invoked together with multipole expansion.•The ability to efficiently capture significantly aspherical solutions is demonstrated.•The framework is validated through systematic convergence at optimal rates.