期刊
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
卷 16, 期 44, 页码 24292-24300出版社
ROYAL SOC CHEMISTRY
DOI: 10.1039/c4cp03235g
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资金
- British Council in New Zealand
- University of Cambridge
- Humboldt foundation
- Cambridge Newton Trust
- Engineering and Physical Sciences Research Council [EP/G055629/1] Funding Source: researchfish
- EPSRC [EP/G055629/1] Funding Source: UKRI
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.
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