Adiabatic bend theory

The centrifugal sudden-adiabatic bend theory we jnst reviewed represents approximations to the partial wave vibrational state-to-state cumulative reaction probability Because that quan-... 

It is possible to incorporate a sudden correlation within the present adiabatic bend theory and to achieve the objective of extending that theory to describe rotational state-to-state processes. A requirement of any such extension is that the cumulative probability obtained from it agree with one from the adiaba-... 

These ideas and many obvious modifications of them for extending the adiabatic bend theory to obtain rotational state-to-state reaction probabilites are, we believe, a promising new area of research in the quantum theory of reactive scattering. 

As a consequence of the two above points, there is presently no satisfactory theory able to incorporate the specific relaxation of the fast mode and of the bending modes in a model working beyond both the adiabatic and exchange approximations. 

As noted in Section III.C.2, the adiabatic method allows one to separate "slow" rotational motion from "fast" vibrational motion. The evaluation of vibrational distributions that has been described is based on this feature of adiabatic theory. In many cases one can also similarly ignore "slow" bending motion. However, advances in experimental methods have led to measurements of rotational distributions of photofragments (see Okabe and Jackson, this volume) and thus the evaluation of these distributions has become a timely and interesting problem. 

We have not yet implemented the fully adiabatic theory represented by Equation 5. That theory bears some resemblance to the bending-corrected rotating linear model (BCRLM)(16-18). In this model a partial wave hamiltonian is given by... 

With all of the v, and v2 assignments made, some interesting trends in the fitted parameters kt and W7 appear. From Table 2, we see that the significant deviations of kt from unity are generally found for the highly bend excited transition state levels. Therefore, most of the breakdown of transition state theory appears to be associated with only those few levels. In addition, we see in Table 2 that W7 becomes larger as v2 is increased from 0 to 2 for a given value of v,. This is consistent with the discussion below Eq. (13) since the vibrationally adiabatic potentials become narrower as v2 increases (8,16). This same trend in W7 is even more apparent in the results discussed below for H + H2, 7=1, where both even and odd values of v2 are allowed. 

Many but not all of the quantized transition states observed in the densities of state-selected reaction probability are observed as peaks in the total density of reactive states. Some highly bend excited states (e.g., [0 12°], and [0 14°]) are observed as peaks only in the state-selected dynamics. If the closely spaced features in the stretch-excited manifolds for p(i are indicative of supernumerary transition states more closely spaced in energy than the variational transition states (which adiabatic transition state theory also suggests), then only some of the supernumerary transition states, in particular S[20°], 5[22°], 5[24°], 5[30°], 5[32°], 5[34°], and 5[36°], are observed in the total density, i.e., only some are of the first kind. The other supernumerary transition states identified in the state-selected dynamics are of the second kind. 

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. 

A hierarchy of reduced dimensionality exact quantum theories of reactive scattering is presented for the vibrational state-to-state cumulative reaction probability and vibrational state-to-state thermal rate constant. The central approximation in these theories is the adiabatic treatment of the bending motion of the reactive species in the strong interaction region of configuration space. Applications of the theories are made to the reactions MU+H2, 0( P)+H2, D2 and HD... 

The figure also shows that the CS results of Schatz, which do not assume an adiabatic or a sudden approach, are compatible with the SCAD theory. In fact, the quantal cross section seems to be primarily dominated by the probability to cross the vibrational bend adiabatic barrier. This is an encouraging result since it indicates that TST, when properly applied, may be just as accurate in 3D as in ID. 

Nesbitt, Child and Clarys applied the theory, with this modification, to the (10°0), (12o0) and (110) bands of Ar HF, using the I type doubling of the (110) bands to deperturb the (12 0) band, and thereby obtained the diatomic like potential curves in Fig.3. An adiabatic inversion procedure was then adopted, in the sense that the three potential curves were interpreted as bending vibrational eigenvalues (parametrically dependent on R) of a three term potential surface. 

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