Full-potential relativistic four-component Dirac–Kohn–Sham method for periodic systems using Gaussian-type functions*

I will present a new full-potential all-electron Kohn–Sham theory for obtaining fully-relativistic band structures of spin–orbit-coupled solids. Our method is based on the four-component Dirac–Coulomb Hamiltonian, and all operators are represented compactly in real space using Gaussian-type orbitals (GTOs). The local nature of GTOs allows for explicit handling of one-, two-, and three-dimensional periodic systems avoiding the need to introduce vacuum layers. In combination with a variational treatment of spin–orbit coupling, this makes the method suitable for studying two- and three-dimensional topological insulators as well as spin–orbit-induced splittings of bands. The GTO-based methodology makes no assumptions about the electronic density in the vicinity of nuclei, and can be used to calculate core-related properties, such as nuclear magnetic resonance parameters. Large-scale relativistic calculations of solids containing thousands of heavy atoms in the simulation supercell are possible due to the use of quaternion algebra for the time-reversal-adapted basis and employment of fast-multipole methods.[1]
[1] M. Kadek, M. Repisky, and K. Ruud (to be published)