title: Shallow-tunnelling correction factor for use with Wigner-Eyring transition-state theory.
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.
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. sca10@cam.ac.uk.
authors.forename: Yanchuan
authors.initials: Y
authors.lastname: Zhang
authors.forename: Judith B
authors.initials: JB
authors.lastname: Rommel
authors.forename: Marko T
authors.initials: MT
authors.lastname: Cvitaš
authors.forename: Stuart C
authors.initials: SC
authors.lastname: Althorpe