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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.

Abstract: We present arguments demonstrating that the Miller, Schwartz, and Tromp (MST) correlation function is the only computationally reasonable choice with regard to minimizing the extent of recrossing flux. However, using accurate numerical results, we point out that the MST flux–flux correlation function almost always exhibits non-vanishing negative parts, even for the simplest physical systems. We argue that, in order to best handle the residual recrossing flux, one must not rely on the “no recrossing” assumption in the development of quantum transition state theories. To provide accurate numerical examples, we derive the analytical expressions for the the flux–flux correlation and spectral functions for the symmetric Eckart and rectangular potential barriers. [Copyright &y& Elsevier]