Least-action tunneling

Section 2 also includes a brief review of the large-curvature and least-action tunneling approximations with emphasis on delineating the regions of the PES required for such calculations. 

Figure 6.19 Comparison between the rate constants of the reactions H+Hj and H+Dj, in units of mol dm sec , calculated by the scISM with Eckart-barrier tunnelling corrections and by the VTST with least-action tunnelling corrections (dotted lines) with the experimental rates.

State Theory and Least-Action Tunneling Calculations for the Reaction Rates of Atomic... 

Variational Transition State Theory With Least-Action Tunneling Calculations for the Kinetic Isotope Effects in the Atomic Chlorine + Molecular Hydrogen Reaction Tests of Extended-LEPS, Information-Theoretic, and Diatomics-in-Molecules Potential Energy Surfaces. 

Instead of this type of model, we suggest utilization of TST in the recently developed variational versions (Lauderdale and Truhlar 1985,1986 Truhlar et al. 1986 Truong et al. 1989b). These can be either microcanonical (E-,) or canonical (T) forms. These also include multidimensional tunneling via least-action techniques as well as surface atom motion via embedded cluster models. They do require a PES, but in our opinion, it is preferable to at least indicate a PES rather than make a multitude of assumptions about the dynamics. Because of the speed of the VTST methods, large computing facilities would not be necessary, and a well-documented program exists for these calculations, which should be available by the time of publication of this review (from QCPE at the University of Indiana). 

Garrett, B. C., Abusalbi, N., Kouri, D. J., Truhlar, D. G. (1983) Test of variational transition state theory and the least-action approximation for multidimensional tunneling probabilities against accurate quanta rate constants for a collinear reaction involving tunneling in an excited state, J. Chem. Phys. 83, 2252-2258. 

A least-action variational method for calculating multidimensional tunneling probabilities for chemical reactions, ]. Chem. Phys. 79, 4931-4938. 

H2, a harmonic model semiclassical adiabatic (SCAD) calculation for H + H2 and D + H2, a rotationally averaged lOS (RATOS) calculationl O for D + H2> ICVT calculations using a least action (LA) tunnelling... 

For intermediate reaction-path curvature, one may use either the SCSA or LC3 approximation, but even more accurate results are obtained by a least-action (LA) method.In the LA method, the tunneling paths are linear interpolations between the MEP and the LC3 paths. Thus this method does not require knowing the potential over a wider swath than is necessary for the LC3 method. 

Test of Variational Transition State Theory and the Least-Action Approximation for Multidimensional Tunneling Probabilities Against Accurate Quantal Rate Constants for a Collinear Reaction Involving Tunneling into an Excited State. 

The potential (6.37) corresponds with the previously discussed projection of the three-dimensional PES V(p,p2,p3) onto the proton coordinate plane (pi,p3), shown in Figure 6.20b. As pointed out by Miller [1983], the bifurcation of reaction path and resulting existence of more than one transition state is a rather common event. This implies that at least one transverse vibration, q in the case at hand, turns into a double-well potential. The instanton analysis of the PES (6.37) was carried out by Benderskii et al. [1991b], The existence of the onedimensional optimum trajectory with q = 0, corresponding to the concerted transfer, is evident. On the other hand, it is clear that in the classical regime, T > Tcl (Tc] is the crossover temperature for stepwise transfer), the transition should be stepwise and occur through one of the saddle points. Therefore, there may exist another characteristic temperature, Tc2, above which there exists two other two-dimensional tunneling paths with smaller action than that of the one-dimensional instanton. It is these trajectories that collapse to the saddle points at T = Tcl. The existence of the second crossover temperature Tc2 for two-proton transfer was noted by Dakhnovskii and Semenov [1989]. 

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