Finite Element Method in Density Functional Theory Electronic Structure Calculations

Abstract

We summarize an ab-initio real-space approach to electronic structure calculations based on the finite-element method. This approach brings a new quality to solving Kohn Sham equations, calculating electronic states, total energy, Hellmann–Feynman forces and material properties particularly for non-crystalline, non-periodic structures. Precise, fully non-local, environment-reflecting real-space ab-initio pseudopotentials increase the efficiency by treating the core-electrons separately, without imposing any kind of frozen-core approximation. Contrary to the variety of well established k-space methods that are based on Bloch’s theorem and applicable to periodic structures, we don’t assume periodicity in any respect. The main asset of the present approach is the efficient combination of an excellent convergence control of standard, universal basis of industrially proved finite-element method and high precision of ab-initio pseudopotentials with applicability not restricted to periodic environment.