Entanglement Effect and Angular Momentum Conservation in a Non-separable Tunneling Treatment

TL;DR

This paper derives a new rate expression for quantum tunneling in non-separable systems, incorporating entanglement and angular momentum conservation, and provides a model to interpret tunneling effects near the crossover temperature.

Contribution

It introduces a novel entanglement factor into the tunneling rate expression and extends it to include angular momentum conservation in non-separable systems.

Findings

Derived a closed-form tunneling rate expression with an entanglement factor.

Extended the expression to account for angular momentum conservation.

Provided a model explaining the quantum bobsled effect.

Abstract

The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for non-separable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for non-separable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and $E$-resolved rate constants over broad ranges of temperatures and energies.