Advancing relativistic electronic structure methods for solids and in the time domain

Abstract

Effects arising from the special theory of relativity significantly influence the electronic structure and properties of molecules and solid-state materials containing heavy elements. At the same time, the inclusion of the relativistic effects in theoretical and computational models increases their methodological complexity and the computational cost. In the solid state, additional challenges to the mathematical and algorithmic robustness of methods arise due to the infinite extent of the systems.

In this thesis, I present two extensions of quantum-chemical relativistic methods based on Gaussian-type basis functions in the study of the electronic ground-state of molecules: band-structure calculations of materials in the solid state, and simulations of the response of molecules that are subjected to an external time-dependent field by propagating their perturbed state in real time. The development of the relativistic methods for solids was preceded by an independent implementation of the theory at the nonrelativistic level. In comparison to methods based on plane waves, the use of Gaussian-type basis functions in the solid-state community is limited. The relativistic method presented here is the first ever implementation of the Dirac-type equations using Gaussian-type basis functions for solid-state systems, and can be used to study one-, two-, and three-dimensional periodic systems on an equal footing for the entire periodic table. The time propagation method is a technically simpler alternative to perturbation approaches, and is applied here to probe relativistic effects on absorption and X-ray spectra, and nonlinear optical and chiroptical properties of molecules. Our work in the both areas provides a technology with the potential to predict properties of novel materials, and to support the interpretation of experiments.