All-electron fully relativistic Kohn-Sham theory for solids based on the Dirac-Coulomb Hamiltonian and Gaussian-type functions

Abstract

A major challenge in computational solid-state physics is the capability of first-principles theories to treat relativistic effects nonperturbatively when modeling material properties driven by atomic-core regions or the spin-orbit interaction. Such a relativistic approach is mandatory for heavy-element containing materials that often exhibit nontrivial topological properties. Here, the first formulation and implementation of a relativistic full-potential theory for solids solving the four-component Dirac-Kohn-Sham equation within local Gaussian-type bases is presented. Time-reversal symmetry is exploited in a quaternion algebra-based formalism to significantly reduce the methodological and computational complexity of the approach. The results are demonstrated to be well converged with basis sets developed for molecules.