Radial and three-dimensional nonlocal pseudopotential calculations in gradient-corrected Kohn–Sham density functional theory based on higher-order finite element methods

Kohn–Sham density functional theory is an ab initio framework for electronic structure calculation that offers a basis for nonphenomenological multiscale approaches. In this work, higher-order finite element methods are applied in the context of this theory, with a particular focus on the use of nonlocal pseudopotentials. Specifically, an accurate class of pseudopotentials which are based on the generalized gradient approximation of the exchange–correlation functional with nonlinear core corrections are targeted. To this end, the suitable weak formulation of the underlying nonlinear eigenvalue problem is derived and additionally cast in a radial form. The weak forms are discretized through traditional Lagrange elements in addition to isogeometric analysis based on B-splines in order to explore alternative means of achieving faster routes to the solution of the resulting generalized eigenvalue problems with O(106–107) degrees of freedom. Numerical investigations on single atoms and larger molecules validate the computational framework where stringent accuracy requirements are met through convergence at optimal rates.