Efficient Treatment of Relativistic Effects with Periodic Density Functional Methods: Energies, Gradients, and Stress Tensors

TL;DR

This paper presents an efficient density functional theory method incorporating relativistic effects, including spin-orbit interaction, enabling accurate calculations of energies, gradients, and stress tensors for periodic systems.

Contribution

The authors develop a computationally efficient SCF approach that includes scalar relativistic and spin-orbit effects within DFT using Gaussian-type orbitals and real-space integrals.

Findings

Efficient implementation of relativistic DFT with spin-orbit interaction for periodic systems.

Support for meta-GGA functionals in SCF energies and gradients.

Demonstrated importance of spin-orbit effects in electronic structure calculations.

Abstract

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 (GTOs) and all integrals are evaluated in real space. Our implementation supports density functional approximations up to the level of meta-generalized gradient approximations (mGGAs) 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 (2c) formalism and a non-collinear approach for open-shell systems. Here, we implemented both the canonical and the Scalmani-Frisch non-collinear 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.