title: Multidimensional tunneling in the [1,5] shift in (Z)-1,3-pentadiene: how useful are Swain-Schaad exponents at detecting tunneling?
abstract: Rates, kinetic isotope effects (KIE), and Swain-Schaad exponents (SSE) have been calculated for a variety of isotopologues for the [1,5] shift in (Z)-1,3-pentadiene using mPW1K/6-31+G(d,p). Quantum mechanical effects along the reaction coordinate were incorporated with the zero-curvature tunneling (ZCT) model and with the multidimensional small curvature tunneling (SCT) model, which allows for coupling of modes perpendicular to the reaction coordinate. The latter model gives the best agreement with experimental rates and primary KIEs. The small quasiclassical primary KIE (2.6) is rationalized in terms of a nonlinear transition state. For sp3 to sp2 rehybridization, the quasiclassical alpha-secondary KIE shows an unusual inverse effect due to compression of the nonbonding hydrogens in the suprafacial transition state. SCT transmission coefficients (kappa) increase the rates by as much as one order of magnitude. Tunneling allows the reactant to evade 1-2.5 kcal/mol of the barrier depending on the isotope. Inclusion of tunneling in the secondary KIE increases it beyond the equilibrium isotope effect and converts the inverse effect (0.95) into a normal KIE (1.12). Tunneling was found to deflate the primary y SSE but by an amount too small to distinguish it from the quasiclassical SSE. On the other hand, when a specific labeling pattern is used, the difference between the quasiclassical secondary SSE (4.1) and the tunneling secondary SSE (2.3) may be sufficiently large to detect tunneling. The mixed secondary SSE shows even larger differences.
authors: Department of Chemistry, Randolph-Macon College, Ashland, Virginia 23005, USA.
authors: Dana N
authors: DN
authors: Peles
authors: John D
authors: JD
authors: Thoburn