Two-dimensional model of a double-well potential: Proton transfer upon hydrogen bond deformation

Proton tunneling in a hydrogen bond can only take place if the potential energy surface has two minima; this is known as a double-well potential. The aim of this work was (i) to present a simple enough 2D model of H-bond double-well potential in harmonic approximation and (ii) to assess how proton transfer therein is affected by H-bond deformations (shifts and turns such as result from conformational motion of molecular structures carrying the donor and the acceptor). It is shown that even small stretching of the H-bond and reorientation of its covalent part (‘bending’) increase the characteristic time of proton tunneling by orders of magnitude. On the other hand, the model, being two-dimensional, demonstrates that different types of deformation not only can aggravate each other but in some cases can be mutually compensatory in terms of proton transfer efficiency. The properties of the model and some implications of the results are discussed.