Pseudorotations in Molecules: Electronic Orbital Triplets

TL;DR

This paper employs topological and geometrical methods to analyze the pseudorotational vibronic spectra of electronic triplets in symmetric molecules, revealing the influence of Jahn-Teller effects and related geometries.

Contribution

It introduces a novel geometric framework based on isoparametric geometry and connection Laplacians to study pseudorotational spectra in molecules affected by Jahn-Teller distortions.

Findings

Jahn-Teller effect induces a specific geometric structure related to E. Cartan's isoparametric geometry.

Pseudorotational spectra are linked to spectra of connection Laplacians on nontrivial line bundles.

The isoparametric submanifolds form a totally geodesic foliation of S^4, with computed spectral flow.

Abstract

Topological and geometrical methods are used to calculate the pseudorotational part of the vibronic spectrum for an electronic triplet of an octahedral, tetrahedral, or icosahedral molecule. The calculations take into account the nontrivial geometry inherent in the Jahn-Teller effect. It is shown that the Jahn-Teller effect gives rise to a geometry, which is related to the isoparametric geometry of E. Cartan. The pseudorotational spectra correspond to the spectra of connection Laplacians on nontrivial line bundles over base spaces with this geometry. Globally, the isoparametric submanifolds form a totally geodesic foliation of S^4 and the spectral flow of these connection Laplacians on this foliation is computed.