Efficient treatment of relativistic effects with periodic density functional methods: Energies, gradients, and stress tensors

The implementation of an efficient self-consistent field (SCF) method including both scalar-relativistic effects and spin-orbit interaction in density functional theory (DFT) is presented. We make use of Gaussian-type orbitals and all integrals are evaluated in real space. Our implementation supports density functional approximations up to the level of meta-generalized gradient approximations for SCF energies and gradients. The latter can be used to compute the stress tensor and consequently allow us to optimize the cell structure. Considering spin-orbit interaction requires the extension of the standard procedures to a two-component formalism and a noncollinear approach for open-shell systems. Here, we implemented both the canonical and the Scalmani-Frisch noncollinear DFT formalisms, with hybrid and range-separated hybrid functionals being presently restricted to SCF energies. We demonstrate both efficiency and relevance of spin-orbit effects for the electronic structure of discrete systems and systems periodic in one to three dimensions.