Advanced Computational Strategies in the Dirac-Kohn-Sham Framework: Optical Properties in the Strong Spin-Orbit Coupling Regime and Strong Fields

Relativistic effects, arising from the fast motion of the core electrons and propagating into the valence region, become very important for the chemical bonding and determine the optical properties of systems containing heavy atoms. The most rigorous way to include relativity in the modeling of molecular systems is to use the full 4-component (4c) formalism derived from the Dirac equation. In this Thesis we treat electronic correlation and relativistic effects on same footing employing a 4c Dirac-Kohn-Sham (DKS) relativistic framework as implemented in the BERTHA program. The interaction of molecular systems with electromagnetic fields can be treated employing time-dependent density functional theory (TDDFT), which is a widely used method to compute molecular dynamics properties such as excited state energies. In the weak field regime, the approach based on the linear response theory in the frequency domain is adequate. However, a first order method is insufficient in many circumstances, for example to study atoms or molecules in intense laser fields. In the real-time approach one seeks to solve the (Dirac-)Kohn-Sham equation directly in the real-time (RT) domain, resulting in a methodology suitable for both the weak and strong field regime. Several non-relativistic implementations of RT-TDDFT have been presented since the last decade. The RT methodology has been used with increasing success in the investigation of several linear and non-linear molecular properties and phenomena. The application of a RT propagator scheme within the 4c Dirac-Kohn-Sham model has only recently started and has been only partially explored and understood. In this Thesis we tackle the implementation of RT-TDDFT both in the non-relativistic and relativistic framework, with special emphasis on the latter: our primary aim is to provide a sound framework to study optical properties in the strong spin-orbit coupling regime and strong fields. The real-time methodology has been further extended to include environmental effects employing Frozen Density Embedding (FDE) schemes. This Thesis is the result of an international joint supervision PhD with the Vrije Universiteit Amsterdam, under the supervision of Prof. Dr. Lucas Visscher. The outline of the Thesis is as follows. In Chapter 1 we set up a unifying framework based on the time-dependent quantum theory: making use of few key concepts we derive the most relevant equations of motion, with particular attention to mean-field theories. In Chapter 2 we review the most recent computational advances in the BERTHA code. In Chapter 3 the implementation of RT propagation both in the non-relativistic and relativistic frameworks is presented. We proceed from the study of the two-level model system to realistic systems: group-12 atom excitation energies are investigated in the 4c relativistic framework. In particular, we provide a detailed analysis of our data in comparison to similar calculations reported in the literature. In Chapter 4 the extension of FDE to real-time method is presented. Environmental effects on the electronic structure of the ground state are suitably described within FDE theory. Merging real-time propagation and Frozen Density Embedding allows us to include environmental effects on electronic excitations. We tested several systems of increasing complexity, ranging from the water-ammonia adduct to the acetone molecule embedded in a realistic water cluster. A critical review of methods for the analysis of excited states is carried out in Chapter 5: we elucidate differences and analogies between the presented methods, showing that not all methods are equally effective in describing the nature of electronic excitations. In Chapter 6 our implementation of some meaningful methods for excited state characterization is described in a common computational framework. Finally, in the closing chapter we recapitulate the highlights of the Thesis, giving a perspective on possible developments.