Christopher Daggett | Searcharxiv

arXiv2026

Symmetry and Topology in Wavepacket Dynamics near Conical Intersections

Whether topology directly shapes chemical dynamics remains an open question in theoretical chemistry. The issue arises because degeneracies of adiabatic electronic states can generate nontrivial topological structure, and such degeneracies are common in polyatomic molecules. Existing work has largely emphasized static characterizations and dynamical studies of low-energy, highly symmetric models. Here we develop a symmetry-based analysis of nonadiabatic dynamics in two-state conical-intersection models that is predictive without invoking topological invariants. We show that the nodal-line structures associated with dynamics near a conical intersection are robust in highly symmetric settings, but should not in general be expected to persist once the relevant symmetry is broken.

physics.chem-ph↗

arXiv2023

Towards a Topological Classification of Nonadiabaticity in Chemical Reactions

The application of topology, a branch of mathematics, to the study of electronic states in crystalline materials has had a revolutionary impact on the field of condensed matter physics. For example, the development of 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 frequency of energy level crossings on the potential energy surface in molecules, the applicability of these concepts to molecular systems could be of great interest for our understanding of reaction dynamics. However, challenges arise due to differing quantum mechanical descriptions of solids and molecules. Out work aims to bridge the gap between topological band theory and molecular chemistry. We propose that the Euler Class, a topological invariant, can be used to categorize and analyse the distribution of nonadiabatic couplings on the potential energy surface. To exemplify this connection, we introduce a model system with two distinct regimes that are characterized by different values of the Euler Class, yet identical potential energy surfaces. Contrary to expectations set by the Born-Oppenheimer approximation, we propose that these two regimes don't exhibit identical dynamics, due to a qualitatively distinct distribution of nonadiabatic couplings.

cond-mat.mtrl-sci↗