A Method of Calculating Tunneling Corrections for Eckart Potential Barriers

(3) u· = hv·lkT a/ = 21rVihv·, i = 1,2 v· = (l/21rX F·lm)'h The potential has the limiting value of zero when x 00, goes through a single maximum of height VI as x increases, and has a limiting value of VI V2 as x + 00. F· is the second derivative of Vat its maximum. The lower bound Eo in the integral (1) is equal to zero when VI =::;; V2 , and to VI V2 when VI > V2 • The three parameters used by Johnston and Heicklen are aI' a2 , and u·. The Eckart potential function [1]1 is often used to estimate quantum mechanical tunneling corrections to theoretically determined chemical rate constants. The correction factor r· is defined as the ratio of the quantum mechanical to the classical mechanical barrier crossing rate. It can be expressed [2] as in integral over the energy E, r· = exp(VIlkT) rK exp( -E/kT)dE/kT (1) E.