On the efficient path integral evaluation of thermal rate constants within the quantum istanton approximation

摘要

We present an efficient path integral approach for evaluating thermal rate constants within the quantum instaton (QI) approximation that was recently introduced to overcome the quantitative deficiencies of the earlier semiclassical instaton approach [Miller,Zhao,Ceotto,and Yang,J.Chem.Phys.119,1329 (2003)].Since the QI rate constant is determined solely by properties of the (quantum) Boltzmann operator (specifically,by the zero time properties of the flux-flux and delta-delta correaltion functions),it can be evaluated by well-established techniques of imaginary time path integrals even for quite complex chemical reactions.Here we present a series of statistical estimators for relevant quantities which can be evaluated straightforwadly with any nonlinear reaction coordinates and general Hamiltonians in Cartesian space.To facilitate the search for the optimal dividing surfaces required by the QI approximation,we introduce a two-dimensional quantum free energy surface associated with the delta-delta correlation function and describe how and adaptive umbrella sampling can be used effectively to construct such a free energy surface.The overall computational procedure is illustrated by the application to a hydrogen exchange reaction in gas phase,which shows excellent agreement of the QI rates with those obtained from quantum scattering calculations.