Vibrationally adiabatic zero-curvature approximation

We first consider the case where the reaction probabilities are computed for the adiabatic model with the reaction-path curvature neglected, the so-called vibrationally adiabatic zero-curvature approximation [36]. We approximate the quantum mechanical ground-state probabilities P (E) for the one-dimensional scattering problem by a uniform semiclassical expression [48], which for E < is given by... 

FIGURE 3. Reaction probability for collinear H+H2- H2+H on the Porter-Karplus potential energy surface. EQ denotes the exact quantum mechanical values, VAZC the results of the vibrationally adiabatic zero curvature approximation, and the points the results of the present SCP-IOS reaction path model. 

A direct test of the vibrationally adiabatic approximation for H + H2 has also been made (Bowman et al.. 1973). This test was done by projecting accurate wavefunctions on the vibrationally adiabatic functions for zero curvature, and measuring deviations of the resulting probability weight from unity. The symmetric stretch motion was found to be adiabatic to within 10 % for total energies between 0-51 and 0-72 eV, but adiabaticity was lost at lower and higher energies. 

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