Multidimensional tunnelling of molecules aligned by strong electric fields

TL;DR

This paper extends semiclassical instanton theory to calculate quantum tunnelling energy splittings in molecules under electric fields, accounting for full molecular geometry changes, with applications to H2 and larger polar molecules.

Contribution

It introduces a full-dimensional semiclassical approach to compute tunnelling splittings in molecules influenced by electric fields, surpassing perturbative methods.

Findings

Quantum tunnelling splittings can be significant in molecules under electric fields.

The method applies to both static and oscillating electric fields.

Heavy-atom tunnelling may produce observable effects in polar molecules.

Abstract

Strong electric fields can be used to align molecules. However, a non-polar molecule such as H$_2$ has no preference for its orientation. There are thus two equivalent configurations with equal energy separated by a potential-energy barrier. Quantum mechanically, the molecule can tunnel between these configurations resulting in a tunnelling splitting, which in the case of H$_2$, is the same as the ortho--para splitting. In this work, we generalize semiclassical instanton theory to calculate the energy splitting of molecules in electric fields in full dimensionality. This goes beyond a perturbative treatment of the field and takes into account changes in molecular geometry during the tunnelling process which influence its electrical properties and can have a significant impact on the result. We first study the case of H$_2$ in a static electric field and then show how it can be applied to larger polar molecules subjected to oscillating electric fields, where we find that even large-amplitude heavy-atom tunnelling can lead to observable splittings.