Quantum Tunnelling across Hydrogen Bonds Demonstrates Isotope Effects with Cornell-Type Potential Model

Hydrogen bonds are fundamental to countless processes in biology, physics and chemistry, and quantum tunnelling within these bonds significantly influences their behaviour and stability. Krishna Kingkar Pathak, from Arya Vidyapeeth College, advances understanding of this crucial phenomenon by developing a new theoretical model that explores how the weight of an atom affects tunnelling rates. This research investigates the differences between proton and deuteron tunnelling, essentially, how hydrogen and its heavier isotope, deuterium, move through a hydrogen bond, using a sophisticated, yet interpretable, potential model. The team’s approach yields clear insights into the relationship between atomic mass, barrier shape, and tunnelling speed, offering a valuable framework for studying diverse areas including spectroscopy, enzyme function and the design of new materials.

Dynamic Hydrogen Bonds and Proton Tunneling

Scientists have investigated proton tunneling, a quantum mechanical phenomenon where protons can pass through barriers even without sufficient energy, within dynamically forming and breaking hydrogen bonds. The research focuses on understanding how this tunneling is affected by the mass of the proton, comparing hydrogen and its heavier isotope, deuterium, and how the characteristics of the hydrogen bond itself influence the tunneling rate. The team employed a sophisticated approach, utilizing a Cornell potential to model the hydrogen bonding environment and accurately describe the potential energy landscape. They then performed detailed numerical calculations, solving the Schrödinger equation to determine the energy levels and wavefunctions of the system.

By varying parameters like barrier height and geometry, they simulated different hydrogen bonding scenarios and quantified the impact on tunneling rates, carefully comparing the results for hydrogen and deuterium to reveal the isotope effect. The calculations demonstrate that proton tunneling is significant in strong, short hydrogen bonds, leading to measurable energy differences between quantum states. The results confirm that replacing hydrogen with the heavier deuterium significantly reduces the tunneling rate, as expected due to its increased mass. Furthermore, the study reveals that tunneling rates are highly sensitive to the height and width of the potential barrier, with higher and wider barriers hindering tunneling. Importantly, the calculated tunneling energy differences align with experimental observations in gas-phase hydrogen-bonded molecules, such as malonaldehyde and formic acid dimer. This suggests the findings can explain isotope-sensitive dynamics observed in liquid-phase hydrogen-bonded systems like water and alcohols, offering insights into their unique properties.

Isotope Effects in Quantum Proton Tunnelling

Scientists have developed a theoretical framework to understand quantum tunneling, a crucial phenomenon in hydrogen bonds and various physical and biological processes. This model generates wavefunctions and tunneling energy differences that clearly demonstrate isotope-dependent quantum effects. Researchers meticulously analyzed the influence of barrier width and curvature on tunneling, finding that these parameters significantly impact the rate of proton and deuteron transfer. The team began by constructing a wavefunction that accurately describes the motion of the proton or deuteron within the hydrogen bond.

They then localized the wavefunction to create separate states, separated by the distance between the donor and acceptor atoms, and calculated the overlap integral between these states to estimate the tunneling energy difference. By carefully normalizing the wavefunction and optimizing the model parameters, the researchers systematically investigated how tunneling energy differences scale with isotope mass. The results reveal how the change from proton to deuteron affects tunneling rates and provide insights into the geometric factors that control quantum behaviour. The team validated their model by comparing the results with one-dimensional Schrödinger equation solutions and existing experimental data.

Isotope Mass Dictates Quantum Tunneling Rates

Scientists have achieved a detailed understanding of quantum tunneling, a phenomenon crucial to diverse areas including biology and materials science, by developing a novel theoretical framework for modelling proton and deuteron transfer across hydrogen bonds. This model delivers wavefunctions that transparently capture isotope-dependent quantum effects, allowing for precise analysis of tunneling behaviour. Experiments reveal a clear relationship between tunneling energy differences and isotope mass, demonstrating that heavier isotopes exhibit reduced tunneling probability. The team validated their model by comparing its trends with existing experimental and computational results, confirming its accuracy and predictive power.

This breakthrough delivers explicit relationships for tunneling energy differences with isotope mass, providing a quantitative measure of how mass affects tunneling rates. Scientists derived equations showing that the tunneling energy difference is directly proportional to the inverse square root of the isotope mass, confirming theoretical predictions. Measurements confirm that barrier curvature and width govern the ratio of hydrogen to deuterium tunneling, offering insights into the dynamics of proton transfer reactions.

Isotope Mass Governs Hydrogen Bond Tunnelling

This research presents a detailed investigation into proton and deuteron tunneling across hydrogen bonds, employing a combined theoretical approach that links a Cornell-type potential with a Schrödinger equation framework. By solving the equation, scientists obtain wavefunctions and tunneling energy differences that clearly demonstrate the influence of isotope mass on this quantum mechanical phenomenon. Results show a strong correlation between isotope mass and tunneling energy difference, with heavier isotopes exhibiting significantly reduced tunneling rates, consistent with expectations regarding barrier penetration. The team validated their model by comparing calculated tunneling energy differences with experimental data from systems like malonaldehyde and the formic acid dimer, achieving good agreement in both scale and qualitative behaviour.

Calculations demonstrate that proton tunneling can be substantial in short, strong hydrogen bonds, reaching terahertz scales, while deuteration markedly suppresses these energy differences to the megahertz range or lower. This pronounced isotope effect provides a fundamental explanation for observed kinetic isotope effects in biological processes such as enzymatic catalysis and proton transfer within biomolecules. Future work could focus on refining the model to incorporate more complex potential energy surfaces and exploring the impact of environmental effects on tunneling dynamics. Nevertheless, this study establishes a robust theoretical framework for understanding and predicting tunneling behaviour in hydrogen-bonded systems, offering valuable insights for diverse fields including spectroscopy, catalysis, and materials science.