Search

Department of Chemistry, Rishi Bankim Chandra College, Naihati-743 165, North 24-Parganas, West Bengal, India E-mail : hanrkm1@yahoo.co.in Manuscript received 05 December 2014, accepted 05 February 2015 In this particle, a nonperturbative path-integral quantum transition state (PI-QTST) theory is proposed for estimating quantum effect in reaction dynamics in which the rate of the reaction is successfully modelled as the crossing of quantum particle over the free barrier of the double-well potential. It is well known that the rate essentially depends on the centroid density ρ(x0*) at the top of the barrier x0* dividing the two well representing the two stable configurations and x is defined along the reaction coordinate in one dimension. In path-integral approach to quantum transition state theory (PI-QTST), the quantum effect is estimated by calculating the ratio of the quantum grand partition function constrained to x0*, Zq (x0*) to its classical counterpart Zcl(x0*) and is called quantum correction factor, Γ. The quantum grand partition function Zq (x0*) is computed by using our non-perturbative Path-integral based Thermal Cluster Cumulant (PI-TCC) method. It is also shown that the value of quantum correction factor, Γ tends to unity as the temperature goes high indicating the validity of the theory.

Nuclear tunneling and other nuclear quantum effects have been shown to play a significant role in molecules as large as enzymes even at physiological temperatures. I discuss how these quantum phenomena can be accounted for rigorously using Feynman path integrals in calculations of the equilibrium and kinetic isotope effects as well as of the temperature dependence of the rate constant. Because these calculations are extremely computationally demanding, special attention is devoted to increasing the computational efficiency by orders of magnitude by employing efficient path integral estimators.