Shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory

• Published in: Physical chemistry chemical physics : PCCP 2014-11, Vol.16 (44), p.24292-243
• Main Authors: Zhang, Yanchuan, Rommel, Judith B, Cvitaš, Marko T, Althorpe, Stuart C
• Format: Article
• Language: English
• ISSN: 1463-9076; 1463-9084
• DOI: 10.1039/c4cp03235g

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. We obtain a shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory (TST).