Instantons Quantum Mechanics

In this case the adjustable parameters of the PES (4.41) are V0 = 18.52 kcal/mol, V = 5.62 kcal/mol, C = 1.07, 11 = 0.91, and w0 = 1.50x 1014s 1 [Bosch et al., 1990], As in the case of malonaldehyde, the PES parameters place this system between the sudden and adiabatic regimes. The PES contour map and the instanton trajectory for this case are shown in Figure 6.11. Benderskii et al. [1993] have utilized the instanton analysis to obtain the prefactor Bt = 54 and the tunneling splitting 1.4 cm-1, which is in excellent agreement with the value 1.30 cm-1 obtained by Bosch et al. [1990] from a quantum mechanical calculation. 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

Due to the central role the reaction rate constant plays in physical chemistiy, many more or less accurate approximations for this quantity have been developed over time, starting from the Arrhenius equation [1] and transition state theory (TST) [2-4]. Among the most accurate of such approximations are so-called quantum transition state theories [5-18], which treat the rate constant quantum mechanically, but, similarly to the original classical TST, still rely on some sort of a transition state assumption. A recent such approximation that can also treat general many-dimensional systems is the quantum instanton (Ql) approximation of Miller et al. [17]. 

The instanton method is particularly congenial for the large-D limit, in that the zero-energy trajectory in imaginary time corresponds precisely to tunneling between minima in the effective potential with D oo. Despite the infinite effective mass, timneling still occurs because quantum fiuctuations persist in this limit. As usual with semiclassical methods, the dynamical aspects are evaluated by classical mechanics. However, the unusual and striking aspect of our... 

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