Hartree-Fock symmetry breaking around conical intersections

TL;DR

This paper investigates how Hartree-Fock solutions behave near conical intersections, revealing symmetry-breaking solutions that challenge traditional quantum number assignments and providing new diagnostic tools for their characterization.

Contribution

It demonstrates the emergence of symmetry-breaking Hartree-Fock solutions near conical intersections and introduces a magnetization diagnostic for their analysis.

Findings

Coplanar GHF solutions break all symmetries near conical intersections

Symmetry-breaking solutions do not carry good quantum numbers

Diagnostic tools effectively characterize these solutions

Abstract

We study the behavior of Hartree-Fock (HF) solutions in the vicinity of conical intersections. These are here understood as regions of a molecular potential energy surface characterized by degenerate or nearly-degenerate eigenfunctions with identical quantum numbers (point group, spin, and electron number). Accidental degeneracies between states with different quantum numbers are known to induce symmetry breaking in HF. The most common closed-shell restricted HF instability is related to singlet-triplet spin degeneracies that lead to collinear unrestricted HF (UHF) solutions. Adding geometric frustration to the mix usually results in noncollinear generalized HF (GHF) solutions, identified by orbitals that are linear combinations of up and down spins. Near conical intersections, we observe the appearance of coplanar GHF solutions that break all symmetries, including complex conjugation and time-reversal, which do not carry good quantum numbers. We discuss several prototypical examples taken from the conical intersection literature. Additionally, we utilize a recently introduced a magnetization diagnostic to characterize these solutions, as well as a solution of a Jahn-Teller active geometry of H$_8^{+2}$.