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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.

Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality. We report tests on several collinear and three-dimensional reactions, in which QTST outperforms FEIT over a range of temperatures below crossover, which can extend down to half the crossover temperature (below which FEIT outperforms QTST). This suggests that QTST-based methods such as ring-polymer molecular dynamics (RPMD) may often give closer agreement with the exact quantum results than FEIT.

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.