Locally hybridized finite element formulation for Kohn–Sham density functional theory calculations

A novel finite element formulation for Kohn–Sham density functional theory calculations is presented. This formulation employs a background discretization that is overlaid with non-overlapping atomic spheres within which multipole expansions with radial discretizations are invoked as adaptive enrichments. The distinguishing feature of the formulation from typical augmentation schemes is that the overlap between the hybrid and background basis sets facilitates the handling of the continuity requirements. The formulation also deviates from typical enrichment schemes because the radial functions are formulated as part of the solution which enables them to optimally adapt to the requirements of a pseudopotential calculation. The approach is cast in a weak formulation that preserves the variational structure of the energy expression in Kohn–Sham density functional theory. Numerical investigations on atoms and molecules are presented in a non-periodic pseudopotential setting for validation and verification purposes with a particular focus on systematic improvability and accompanying efficiency gains.