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Issue 44, 2014
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Shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory

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Abstract

We obtain a shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory (TST). Our starting point is quantum transition state theory (QTST), which approximates the accurate quantum rate as the instantaneous flux through a delocalised transition-state ensemble of ring-polymers. Expanding the ring-polymer potential to second order gives the well-known Wigner tunnelling-factor which diverges at the cross-over temperature between deep and shallow tunnelling. Here, we show how to remove this divergence by integrating numerically over the two softest ring-polymer normal modes. This results in a modified Wigner correction factor involving a one-dimensional integral evaluated along a straight line on the potential energy surface. Comparisons with accurate quantum calculations indicate that the newly derived correction factor gives realistic estimates of quantum rate coefficients in the shallow-tunnelling regime.

Graphical abstract: Shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory

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Publication details

The article was received on 21 Jul 2014, accepted on 30 Sep 2014 and first published on 30 Sep 2014


Article type: Paper
DOI: 10.1039/C4CP03235G
Author version available: Download Author version (PDF)
Citation: Phys. Chem. Chem. Phys., 2014,16, 24292-24300
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    Shallow-tunnelling correction factor for use with Wigner–Eyring transition-state theory

    Y. Zhang, J. B. Rommel, M. T. Cvitaš and S. C. Althorpe, Phys. Chem. Chem. Phys., 2014, 16, 24292
    DOI: 10.1039/C4CP03235G

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