Lukas Muechler

The integration of topology, a branch of mathematics, into the analysis of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. Topological band theory has delivered new approaches and tools to characterize the electronic structure of materials, resulting in the discovery of new phases of matter with exotic properties. In the framework of topological band theory, the crossings between energy levels of electrons are characterized by topological invariants, which predict the presence of topological boundary states.

Given the common occurrence of energy level crossings on molecular potential energy surfaces, extending these topological concepts to molecular systems holds potential for significantly enhancing our comprehension of reaction dynamics. However, the disparate quantum mechanical frameworks used to describe solids and molecules present substantial challenges.

This talk will present recent efforts of our group to reconcile these two approaches, focusing on the characterization of features of the potential energy surface such as conical intersections and second order saddle points using topological invariants, and exploring their implications on reaction dynamics. We demonstrate our results by studying 4π electrocyclization reactions relevant for photoswitch design. Here, second-order saddle points and changes in invariants are pivotal for understanding the competition between conrotatory and disrotatory pathways.