Electronic Spectra of Open-Shell Heavy Element Systems

Abstract

After about a hundred years since the introduction of both the Schrödinger and Dirac equations, retrieving the atomic or molecular electronic wave function, together with its energy, is still a challenging task. This especially holds for chemical systems with unpaired electrons – known as open-shell systems – as the spins of these electrons give rise to a more complex interplay. In the case of a system that contains heavy elements, spin-orbit coupling (SOC) becomes important as well. This relativistic interaction breaks certain spin-symmetries, which complicates the retrieval of the wave function even further. In the case of ground states, one way of simplifying the problem is by means of density functional theory (DFT). In this framework, one seeks the density that belongs to the electronic ground state. In this case, one only retrieves the density and the corresponding energy. Usually, this is done within the Kohn-Sham (KS) framework. Excited states can also be retrieved within the time-dependent (TDKS) framework, resulting in the KS-TD-DFT approach. A disadvantage of this approach is the fact that describing the correct spinsymmetries of open-shell systems is not well-defined. However, in practice, one can impose these symmetries in the same way as one would do in the case of the true electronic wave function. The resulting methods still cannot describe certain important low-lying electronic transitions (e.g., spin-flip-down transitions), because they do not incorporate double and/or triple spin-orbital excitation w.r.t. the KS ground state. Yet, in this dissertation, we have presented approximate KS-based methods that can incorporate these transitions too, albeit that the exploited KS framework is imposed in a rather ad hoc manner. This, in turn, led to the possibility of also accounting for SOC corrections on top of these spin-adapted scalar relativistic excited states. This newly devised approach has been implemented in the ADF code as a part of the AMS computational chemistry package. Compared to traditional wave function-based methods, the KS nature of this approach makes the calculation of these open-shell SOC-split electronic states more efficient and leads to results that are easier to interpret. The latter, in turn, allows inexperienced researchers (e.g., experimental chemists) to use this implementation to retrieve theoretical insights into the optical properties of these types of open-shell systems.