Work

Ring-polymer instanton theory for tunneling between asymmetric wells

Year: 2026

Type: article

Abstract: Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in asymmetric double wells, as there is no imaginary-time periodic orbit connecting the two non-degenerate minima. We have, therefore, developed a new formulation of instanton theory based on a projected flux correlation function that is applicable to these asymmetric systems. Comparison with exact quantum-mechanical results in one- and two-dimensional models demonstrates that it has a reasonably high accuracy, similar to that reported for instanton theory in the symmetric case. The theory is then applied to study tunneling between non-degenerate minima in the biomolecule α-fenchol, for which we find good agreement with experiment. Finally, we use the connection to instanton rate theory, which is also derived from flux correlation functions, to discuss the often misunderstood relationship between tunneling splittings and reaction rate constants.

Source: The Journal of Chemical Physics

DOI: 10.1063/5.0310667

Authors: Marit R. Fiechter, Gabriel Laude, Jeremy O. Richardson

Institutions: ETH Zurich, Institute of Molecular Physical Science

Language: English

Topic: Quantum chaos and dynamical systems

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,500

Funders: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Eidgenössische Technische Hochschule Zürich