Manifestations of Spin–Orbit Coupling in Molecular Systems

Abstract

Quantum chemistry traditionally focuses on solving the non-relativistic Schrödinger equa-tion to model chemical systems. Although the Schrödinger equation can be quite accurate for systems composed of light atoms, special relativity must be considered in the presence of heavy elements where electrons approach the speed of light or in spin-driven processes. While many-body methods developed for the Schrödinger equation have been adapted for the Dirac equation, solving the latter is more computationally demanding. To mitigate this chal- lenge, approximations have been introduced to reduce the complexity of the Dirac problem. Additionally, Dirac-derived perturbative corrections to the Schrödinger equation have been developed to selectively account for key relativistic effects. This Thesis explores the motiva- tions behind different approximations to the many-body Dirac equation. In particular, the state interaction method for approximating vector relativity is examined within configura- tion interaction and linear response time-dependent density functional theory. A benchmark study comparing state interaction and fully variational treatments of vector relativity is also presented. Beyond exploring the theoretical foundations and performance of these methods, this Thesis highlights the chemical relevance of relativistic effects. Specifically, it presents the application of relativistic methods to elucidate the UV-vis spectra of Au25 nanoparticles. Ad- ditionally, it investigates the intersystem crossing mechanism of an organic photosensitizer, underscoring the necessity of special relativity even for light elements.