Time correlation function, transition path

Path Integral Methods Reaction Path Hamiltonian and its Use for Investigating Reaction Mechanisms Reactive Scattering of Polyatomic Molecules State to State Reactive Scattering Statistical Adiabatic Channel Models Time Correlation Functions Transition State Theory Unimolecular Reaction Dynamics. 

The slope of (7(f) in the time regime rmoi < f forward reaction rate constant. Thus, for the calculation of reaction rate constants it is sufficient to determine the time correlation function (7(f). In the following paragraphs we will show how to do that in the transition path sampling formalism. 

Finally, in Sect. 7.6, we have discussed how various free energy calculation methods can be applied to determine free energies of ensembles of pathways rather than ensembles of trajectories. In the transition path sampling framework such path free energies are related to the time correlation function from which rate constants can be extracted. Thus, free energy methods can be used to study the kinetics of rare transitions between stable states such as chemical reactions, phase transitions of condensed materials or biomolecular isomerizations. 

To evaluate the time correlation function C(f) in the transition path sampling framework we rewrite it in terms of sums over trajectories ... 

Having derived a suitable expression for the transition amplitude, we now return to the time correlation function. Substituting (35) in the path integral expression for the propagator, (17), and using the latter and its analog for the backward evolution in (12) we obtain... 

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