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 H₂ has no preference for its orientation. There are thus two equivalent orientations with equal energy separated by a potential-energy barrier. According to quantum mechanics, the molecule can tunnel between these orientations resulting in a tunnelling splitting, which in the case of H₂, is the same as the ortho–para splitting. In this work, we generalise semiclassical instanton theory to calculate the energy splitting of molecules in electric fields in full dimensionality. This goes beyond the rigid-rotor approximation with a perturbative treatment of the field by taking 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 H₂ in a static electric field and then show how it can be applied to larger polar molecules subjected to oscillating electric fields (such as can be achieved with high-intensity lasers), where we find that even large-amplitude heavy-atom tunnelling can lead to observable splittings.