Crossing conditions in coupled cluster theory

TL;DR

This paper derives crossing conditions for electronic states in coupled cluster theory, highlighting issues with nondefective Jacobians and demonstrating both artifacts and correct descriptions of conical intersections in specific molecules.

Contribution

It establishes the crossing conditions in coupled cluster theory and analyzes the impact of Jacobian defects on conical intersection descriptions.

Findings

Nondefective Jacobians correctly place crossing conditions.

Artifacts occur at accidental same-symmetry intersections.

Proper description achieved in certain symmetry-allowed intersections.

Abstract

We derive the crossing conditions at conical intersections between electronic states in coupled cluster theory, and show that if the coupled cluster Jacobian matrix is nondefective, two (three) independent conditions are correctly placed on the nuclear degrees of freedom for an inherently real (complex) Hamiltonian. Calculations using coupled cluster theory on an $2 {^{1}}A' / 3 {^{1}}A'$ conical intersection in hypofluorous acid illustrate the nonphysical artifacts associated with defects at accidental same-symmetry intersections. In particular, the observed intersection seam is folded about a space of the correct dimensionality, indicating that minor modifications to the theory are required for it to provide a correct description of conical intersections in general. We find that an accidental symmetry allowed $1 {^{1}}A" / 2 {^{1}}A"$ intersection in hydrogen sulfide is properly described, showing no artifacts as well as linearity of the energy gap to first order in the branching plane.