Multidimensional tunnelling of molecules aligned by strong electric fields

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.