Table of Contents
Journal of Theoretical Chemistry
Volume 2014 (2014), Article ID 240491, 11 pages
Research Article

Calculation of the Quantum-Mechanical Tunneling in Bound Potentials

Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, USA

Received 28 January 2014; Accepted 1 April 2014; Published 24 April 2014

Academic Editor: Anton Kokalj

Copyright © 2014 Sophya Garashchuk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The quantum-mechanical tunneling is often important in low-energy reactions, which involve motion of light nuclei, occurring in condensed phase. The potential energy profile for such processes is typically represented as a double-well potential along the reaction coordinate. In a potential of this type defining reaction probabilities, rigorously formulated only for unbound potentials in terms of the scattering states with incoming/outgoing scattering boundary conditions, becomes ambiguous. Based on the analysis of a rectangular double-well potential, a modified expression for the reaction probabilities and rate constants suitable for arbitrary double- (or multiple-) well potentials is developed with the goal of quantifying tunneling. The proposed definition involves energy eigenstates of the bound potential and exact quantum-mechanical transmission probability through the barrier region of the corresponding scattering potential. Applications are given for several model systems, including proton transfer in a HO–H–CH3 model, and the differences between the quantum-mechanical and quasiclassical tunneling probabilities are examined.