Reactive states, finite-resolution density

F is the full width at half maximum, and E, and Ef are the lowest and highest energies in the convolution. The finite-resolution density of reactive states pJ(E F) is then defined by... 

The finite-resolution density of reactive states introduced in Sec. II is especially useful for analyzing the halogen-hydrogen halide reactions because, as stated above, the features due to quantized transition states are partially obscured in these systems by a number of narrow resonances associated with other regions of the potential energy surfaces. Therefore the accurate cumulative reaction probabilities N°(E) were convoluted with a Gaussian function of variable width F to obtain finite-resolution cumulative reaction probabilities N°(E F). Analysis of dN°(E F)/dE reveals the influence of quantized transition states underlying the narrower dynamical features of N°(E). 

Figure 9 Original and finite-resolution densities of reactive states for the Cl + HC1 reaction with 7 = 0. (a)N"(E). (b) p°( ). (c) ( 0.027 eV). (d) p"(E 0.027 eV). The value of AT( F) is indicated at each minimum in p°( F). (Reprinted with permission from Ref. 11, copyright 1992, American Chemical Society.)...

The Cl + HC1 quantized transition states have also been studied by Cohen et al. (159), using semiclassical transition state theory based on second-order perturbation theory for cubic force constants and first-order perturbation theory for quartic ones. Their treatment yielded 0), = 339 cm-1 and to2 = 508 cm"1. The former is considerably lower than the values extracted from finite-resolution quantal densities of reactive states and from vibrationally adiabatic analysis, 2010 and 1920 cm 1 respectively (11), but the bend frequency to2 is in good agreement with the previous (11) values, 497 and 691 cm-1 from quantum scattering and vibrationally adiabatic analyses respectively. The discrepancy in the stretching frequency is a consequence of Cohen et al. using second-order perturbation theory in the vicinity of the saddle point rather than the variational transition state. As discussed elsewhere (88), second-order perturbation theory is inadequate to capture large deviations in position of the variational transition state from the saddle point. 

---