Quantum Rate Theory: A Path Integral Centroid Perspective

Abstract

The dynamics of many important processes that take place in condensed phase hosts can be described in terms of rate kinetics, with well-defined rate constants. The calculation of such rate constants from first principles has presented theoretical chemistry with an ongoing challenge. Nonequilibrium statistical mechanics provides a framework within which one can derive explicit expressions for those rate constants, via either linear response theory or Fermi’s golden rule. In both cases, one finds that the rate constants are given in terms of equilibrium correlation functions [1, 2, 3, 4, 5, 6]. Those correlation functions can be evaluated with relative ease from classical molecular dynamics (MD) simulations, even for complex anharmonic many-body systems such as molecular liquids and biopolymers. However, classical mechanics is not valid in the case of many important processes, such as electron and proton transfer and vibrational relaxation. In those cases, one needs to compute the quantummechanical correlation functions. A numerically exact calculation of the latter lies far beyond the reach of currently available computer resources, due to the exponential scaling of the computational effort with the number of degrees of freedom [7, 8]. The challenge therefore lies in finding ways to compute quantum mechanical rate constants which are based on either bypassing the explicit simulation of the quantum dynamics (e.g., transition state theory (TST)), or by using reliable and computationally feasible approximate techniques for computing quantitatively accurate quantum mechanical correlation functions.