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arXiv · 2110.14445

The tunneling splitting and the Kramers theory of activated processes

Pierpaolo Pravatto·Barbara Fresch·Giorgio J. Moro
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Abstract

The study of tunneling splitting is fundamental to get insight into the dynamics of a multitude of molecular systems. In this paper, a novel approach to the analysis of the ground-state tunneling splitting is presented and explicitly applied to one-dimensional systems. The isomorphism between the Fokker-Planck-Smoluchowski operator and the Born-Oppenheimer quantum Hamiltonian is the key element of this method. The localization function approach, used in the field of stochastic processes to study the Kramers problem, leads to a simple, yet asymptotically justified, integral approximation for the tunneling splitting. The comparison with exact values of the tunneling splittings shows a much better accuracy than WKB semiclassical estimates.

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Pierpaolo Pravatto, Barbara Fresch, Giorgio J. Moro. 2021-10-27. The tunneling splitting and the Kramers theory of activated processes. https://doi.org/10.1016/j.chemphys.2022.111608

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