Quantum Tunnelling Across Hydrogen Bonds: Proton--Deuteron Isotope Effects from a Cornell-Type Potential Model

TL;DR

This paper introduces a semi-analytical model using a Cornell-type potential to study quantum tunnelling and isotope effects in hydrogen bonds, providing clear insights into the physical mechanisms involved.

Contribution

It presents a novel semi-analytical approach combining a Cornell-type potential with a double-well Schrödinger model to analyze isotope-dependent tunnelling effects.

Findings

Tunnelling splittings scale with isotope mass.

Barrier width and curvature significantly influence tunnelling.

Model trends align with experimental and computational data.

Abstract

Hydrogen bonds play a pivotal role in chemistry, biology, and condensed-matter physics, where quantum tunnelling can strongly influence structure and dynamics. Isotope substitution (H $\rightarrow$ D) provides a sensitive probe of such tunnelling, but theoretical descriptions often rely on purely numerical models or simplified potentials that obscure physical interpretation. Here we employ a Cornell-type potential combined with a double-well Schr\"odinger approach to investigate proton and deuteron tunnelling across hydrogen bonds. The model yields semi-analytical wavefunctions and tunnelling splittings that transparently capture isotope-dependent quantum effects. We present scaling behaviour of tunnelling splittings with isotope mass, discuss the influence of barrier width and curvature, and compare model trends with representative experimental and computational results. Beyond hydrogen bonding, the framework provides a general methodology for modelling tunnelling in double-well systems relevant to spectroscopy, enzymatic catalysis, and materials applications.