Characterizing the E⊗e Jahn–Teller Potential Energy Surfaces by Differential Geometry Tools

Fanica Cimpoesu,Adela Mihai

doi:10.3390/sym14030436

Abstract

The term ‘mathematical chemistry’ is mostly associated with applications of graph theory in topological issues of 3D chemical structures, thought of as a collection of atoms as dots and bonds as lines. We propose here new directions in this field, coming from the side of theoretical chemistry approached with modern computational tools. Possible challenges are proposed in using ancillary tools of differential geometry for examining the potential energy surfaces of certain specific structural prototypes. Concretely, we describe here the geodesics on the surfaces related to the potential energy functions of the so-called E⊗e Jahn–Teller effect, a spontaneous symmetry-breaking phenomenon also known as a case of conical intersection. To illustrate the case, first-principles (ab initio) quantum chemical calculations are performed on the cyclo-propenyl molecular radical C3H3.

Highlights

The Jahn–Teller effect [1] designates a class of molecular problems implying the quantum treatment of electrons and nuclei together with their mutual interactions, such aspects being of interest in specialized branches of the physics of chemistry [2,3]
We describe here the geodesics on the surfaces related to the potential energy functions of the so-called E⊗e Jahn–Teller effect, a spontaneous symmetry-breaking phenomenon known as a case of conical intersection
From a more general perspective, the quantum interplay of nuclei and electron movements is called vibronic coupling [7], an equivalent of the electron–phonon term used in the language of solid-state electronic structures [8]

Summary

Introduction

The Jahn–Teller effect [1] designates a class of molecular problems implying the quantum treatment of electrons and nuclei together with their mutual interactions, such aspects being of interest in specialized branches of the physics of chemistry [2,3]. The molecules are quantum objects, first of all due to their electrons, while the nuclei can often be approximated as classical charges fixed in space, in a manner defining the molecular geometry. This is the so-called Born–Oppenheimer approximation [4] quasi-generally used in applied molecular quantum mechanics, i.e., computational chemistry [5,6]. From a more general perspective, the quantum interplay of nuclei and electron movements is called vibronic coupling (which may occur beyond Jahn–Teller effect cases) [7], an equivalent of the electron–phonon term used in the language of solid-state electronic structures [8].

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Conclusion