Spin-Orbit Coupling nei Solidi Tramite un Approccio Perturbativo: Accuratezza ed Efficienza Computazionale nelle Implementazioni del codice CRYSTAL

This Master thesis was developed at the theoretical chemistry group of the University of Turin that created and develops the worldly-distributed quantum ab initio software called Crystal. In particular, this work follows from a branch of research started in the last few years that is dedicated to the analysis of non-scalar relativistic effects, namely the spin-orbit coupling (SOC), in molecules but most importantly in solids. As the name suggests, the spin-orbit coupling (or spin-orbit interaction) is an interaction between the electronic magnetic momentum and its angular momentum, which brakes the electronic symmetries of the system and generates new energy levels; but is also responsible for very sophisticated and fine phenomena. The focus of this thesis is the analysis of two algorithms present in Crystal to calculate scalar and non-scalar relativistic effects: the two-component self-consistent field (2c-SCF) and the coupled-perturbed Kohn-Sham (CPKS) approach. The first one is the most complete one, it offers high accuracy but at the cost of a big computational effort; the second one is a recently developed perturbative approach that has the advantage of drastically reducing the cost and time of the calculation, hopefully without renouncing the quality of the description. In particular, we want to benchmark this CPKS algorithm, that has proved to work really well in molecules, and compare it with the 2c-SCF one, this time in solids. In other words, we test CPKS strengths, limitations and potential applications. In order to do that we selected a series of layered transition metal dichalcogenides featuring tungsten with brute formula WX2 (where X = Se, Te, Po and Lv) where we expect to see a fundamental increase in the SOC contribution going down the periodic table. We especially choose to treat a single layer of these crystals both because it is less computationally demanding than a 3D system but also because the lack of inversion symmetry induces a peculiar characteristic that is able to be compared with experimental results: a giant Rashba spin-splitting throughout the M-K-Γ path in the first Brillouin zone.