Traditionally, chemistry has focused on reactions in which all electrons remain bound to the nuclei. However, in many settings involving plasma, strong laser fields, or ionizing radiation electrons can enter or leave the system; they are unbound. This often gives rise to reaction pathways that remain inaccessible otherwise. The interaction of unbound electrons with matter is difficult to describe with quantum-chemical methods designed for bound states. An elegant treatment is, however, possible by means of complex-variable techniques such as complex scaling or complex absorbing potentials. Here, unbound electrons are described in terms of resonance states, that is, solutions of the electronic Schrödinger equation with complex-valued energy.

In this talk, I will give an overview of our recent progress about complex-variable electronic-structure methods that enable the accurate treatment of electronic resonances in analogy to bound states. In particular, I will focus on analytic-gradient techniques that have enabled us to explore the high-dimensional complex-valued potential energy surfaces of polyatomic resonances and on ionization rates in strong laser fields that are relevant, for example, for high-harmonic generation.

I will also discuss future extensions of the current methodology that are necessary to treat unbound electrons and electron transport in larger molecules and complex environments. This is relevant for unwanted processes such DNA strand breaks induced by ionizing radiation but also for emerging applications of electrons as reaction agents or catalysts: Processes such as plasmonic catalysis potentially afford higher selectivity and better control over the outcome than conventional approaches where energy is provided in the form of heat but their potential has remained largely unused. Lastly, transport processes where electrons enter a system in one region and leave it in another region as is relevant, for example, for molecular electronics can also potentially be described in terms of complex energies.