Quantum dynamics of [1,7] hydrogen shift in Z,Z-1,3,5-heptatriene: Implications for kinetic isotope effects and Swain-Schaad exponents

ORGN 290

John D. Thoburn, Department of Chemistry, Department of Chemistry, Randolph Macon College, Ashland, VA 23005
Variational transition state theory with multidimensional tunneling is used to calculate rates, kinetic isotope effects, and Swain-Schaad exponents for the [1,7] antarafacial hydrogen shift in Z,Z-1,3,5-heptatriene (1) and Z,Z-7-methyl-1,3,5-octatriene (2). Rates were calculated at the B3LYP/6-31G* level using GAUSSRATE/POLYRATE. Tunneling corrections were incorporated into the transmission coefficients (k) using a one-dimensional tunneling model (ZCT) as well as a multi-dimensional tunneling model (SCT) that allowed for “corner-cutting”. The effect of tunneling on the KIE was found to be moderate, in line with experimental results. Interestingly, “inverse” secondary KIEs become positive when tunneling is included. Inclusion of tunneling actually deflates the Swain-Schaad exponent in some cases, in contrast to the commonly held belief that tunneling should always inflate the exponent. An analysis that rationalizes both deflation and inflation is presented. The origin of the misconceptions regarding the relation between tunneling and the Swain Schaad exponents is discussed.