Semiclassical evaluation of kinetic isotope effects in 13-atomic system

Abstract

The semiclassical instanton approach discussed by Kryvohuz [J. Chem. Phys. 134, 114103 (2011)] is applied to calculate kinetic H/D isotope effect (KIE) of intramolecular hydrogen transfer in cis-1,3-pentadiene. All 33 vibrational degrees of freedom are treated quantum mechanically with semiclassical approximation. Nuclear quantum effects such as tunneling under the barrier and zero-point energy are automatically incorporated in the theory, and are shown to be responsible for the observed appreciable kinetic isotope effect in cis-1,3-pentadiene. Over the barrier passage is also automatically included. Numerical calculations are performed on an empirical valence bond potential energy surface and compared with the previous experimental and theoretical studies. An estimation of heavyatom 12 C/ 13 C KIE in the same system is also provided and the factors contributing to it are discussed.

Ring-polymer instanton theory

“…The ring-polymer instanton approach has been applied to a number of gas-phase reactions using both fitted surfaces and on-the-fly calculations for the PES [23,26,70,[87][88][89][90][91][92][93][94]. Some of these calculations have been used to benchmark the instanton approach against more accurate theories, but others have given new insights into physical chemistry.…”

Instanton rate constant calculations close to and above the crossover temperature

“…Recently, a new formulation of instanton theory has been postulated, which, with our modifications, can overcome each of these problems while retaining good agreement with the canonical theory. This implementation of instanton theory sits among others based on either evaluating the imaginary part of the free energy or representing the rate in terms of a flux through a surface .…”

“…The recent formulation is applicable over the full temperature range, above and below the crossover temperature T c. The well‐known problem of canonical instanton theory, that reaction rate constants are overestimated at temperatures close to, but less than T c, is also solved. Of course, the applicability of instanton theory can also be extended above T c by switching to a microcanonic expression …”

Intramolecular Hydrogen Atom Transfer in Aminyl Radical at Room Temperature with Large Kinetic Isotope Effect

“…This is not in line with the typical signature of QMT and it is most likely indicative of thermally (vibrationally) activated tunneling, 25 e.g., analogous to that observed in 1,5-H-shift in derivatives of cyclopentadiene and cis -1,3-pentadiene. 27,28 …”