Interaction-induced localisation of protons in hydrogen bonds at superfluid helium temperatures

Abstract

It is common wisdom to expect that protons are more delocalised than much heavier nuclei due to quantum effects, for instance, in hydrogen bonds D−H⋆ ⋅ ⋅ ⋅ A, where the shared proton H⋆ is suspended in between the donor and acceptor heavy sites. Here, we demonstrate that this simple quasi-classical perspective fails at sufficiently low temperatures as a result of intramolecular covalent bonding accompanied by the non-covalent intermolecular interactions which induce strong localisation in the deep quantum regime. Using the water dimer as well as H2O ⋅ ⋅ ⋅ HCl as generic models, path integral simulations at temperatures characteristic to superfluid helium conditions (about 1 K) reveal that the shared proton in such hydrogen bonds gets extremely confined to a spatial region that is comparable to – or even smaller than – that of the heavy atoms. This counter-intuitive so-called interaction-induced localisation phenomenon is also effective for the heavier nuclei, although to a much lesser extent. It is the elevated temperature (about 100 K) that restores the familiar quasi-classical picture, in which atomic spread follows the usual mass dependence of de Broglie wavelength.