The Entropic Barrier around the Conical Intersection Seam

TL;DR

This paper reveals a fundamental statistical-mechanical barrier preventing classical trajectories from reaching conical intersections, explaining why mixed quantum-classical simulations effectively model nonadiabatic transitions without exact degeneracy sampling.

Contribution

It analytically derives the free energy barrier around conical intersections and confirms this with molecular dynamics simulations, clarifying the sampling limitations of MQC methods.

Findings

Infinite free-energy barrier near the CI seam.

Trajectories approach but do not reach the CI.

MQC methods capture nonadiabatic effects without degeneracy sampling.

Abstract

Conical intersections (CIs) are seen as the main mediators of nonadiabatic transitions; yet, mixed quantum-classical (MQC) simulations rarely, if ever, sample geometries with exactly degenerate electronic energies. Here we show that this behavior arises from a fundamental statistical-mechanical constraint. Using a linear vibronic coupling model, we derive the free energy along the adiabatic energy gap and demonstrate analytically that as the gap approaches zero, an infinite free-energy barrier arises around the CI seam. Molecular dynamics simulations of the methaniminium cation on the S$_1$ surface confirm this prediction: trajectories can approach regions with small adiabatic gaps, but never reach the CI seam, even if the CI corresponds to a region of lowest potential energy. These results clarify why MQC methods successfully capture nonadiabatic behavior without sampling exact degeneracies and agree with recent findings that classical trajectories can sense the presence of CIs without visiting them.