Quantum rate theory

QUANTUM RATE THEORY V.l REAL TIME METHODS 

A different way, developed extensively by Schwartz and his coworkeis, - is to use approximate quantum propagators, based on expansions of the exponential operators. These approximations have been tested for a number of systems, including comparison with the numerically exact results of Ref 38 for the rate in a double well potential, with satisfying results. 

Progress has been recently made in constructing an iterative inverse Laplace transform method which is not exponentially sensitive to noise. This Short Time Inverse Laplace Transform (STILT) method is based on rewriting the Bromwich inversion formula as  

This approximate inversion formula is quite accurate for bell shaped or mono-tonically increasing functions f (E). It can be substantially improved by iteration. One Laplace transforms the function f i [E) and then applies STILT to the difference function f(P) - fi(P). The iterated inversion formula is exact for the class 

1 Centroid transition state theory. A third methodology, is to construct approximate theories for dynamical properties, which make use of only thermodynamic quantities. In analogy with classical TST, Gillan, Voth and coworkers have formulated and studied a quantum TST which is based on the centroid potential of mean force Wc (q)  

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Zhu J J and Cukier R I 1995 An imaginary energy method-based formulation of a quantum rate theory J. Chem. Phys. 102 4123... 

E. Poliak, Classical and quantum rate theory for condensed phases, in Theoretical Methods in Condensed Phase Chemistry, S. D. Schwartz (ed.), Kluwer Academic Publishers, Dordrecht, 2000, pp. 1-46. 

CLASSICAL AND QUANTUM RATE THEORY FOR CONDENSED PHASES... 

Classical and quantum rate theory for condensed phases 3... 

These include the Rayleigh quotient method" and variational transition state theory (VTST).46 9 xhg 0 called PGH turnover theory and its semiclassical analog/ which presents an explicit expression for the rate of reaction for almost arbitrary values of the friction function is reviewed in Section IV. Quantum rate theories are discussed in Section V and the review ends with a Discussion of some open questions and problems. 

The expressions presented above are restricted since we used the parabolic barrier transmission probabilities. Extension of the theory to temperatures below the crossover temperature may be foimd in Ref 136. More sophisticated quantum rate theories will be discussed in Section V. 

V. QUANTUM RATE THEORY V.l REAL TIME METHODS... 

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