Topological Transitions in Orbital-Symmetry-Controlled Chemical Reactions

TL;DR

This paper extends topological band theory concepts to strongly correlated molecular reactions using Green's functions, revealing new topological invariants that classify reaction pathways based on orbital symmetry.

Contribution

It introduces a Green's function formalism to classify orbital-symmetry-controlled reactions with strong correlations, identifying zero crossings as symmetry-forbidden pathways.

Findings

Symmetry-forbidden pathways characterized by Green's function zero crossings.

Introduces a topological invariant for reaction pathway classification.

Framework applicable to reactions without spatial symmetry conservation.

Abstract

Topological band theory has transformed our understanding of crystalline materials by classifying the connectivity and crossings of electronic energy levels. Extending these concepts to molecular systems has therefore attracted significant interest. Reactions governed by orbital symmetry conservation are ideal candidates, as they classify pathways as symmetry-allowed or symmetry-forbidden depending on whether molecular orbitals cross along the reaction coordinate. However, the presence of strong electronic correlations in these reactions invalidate the framework underlying topological band theory, preventing direct generalization. Here, we introduce a formalism in terms of Green's functions to classify orbital symmetry controlled reactions even in the presence of strong electronic correlations. Focusing on prototypical 4$\pi$ electrocyclizations, we show that symmetry-forbidden pathways are characterized by crossings of Green's function zeros, in stark contrast to the crossings of poles as predicted by molecular-orbital theory. We introduce a topological invariant that identifies these symmetry protected crossings of both poles and zeros along a reaction coordinate and outline generalizations of our approach to reactions without any conserved spatial symmetries along the reaction path. Our work lays the groundwork for systematic application of modern topological methods to chemical reactions and can be extended to reactions involving different spin states or excited states.