Three-dimensional analytic quantum theory for triatomic photodissociations. II. Angle dependent dissociative surfaces and rotational infinite order sudden approximation for bent triatomics

Abstract

We extend to triatomic molecules with bent initial bound states our analytical quantum theory of triatomic photodissociations. The theory uses basis functions for the initial bound state wave function that are product functions in the natural normal (or local) modes appropriate to that state and a continuum wave function that is a product function in the natural scattering coordinates appropriate to the dissociative surface. This choice of wave functions produces three-dimensional nonseparable transition amplitudes which are reduced to analytical forms by introduction of the infinite order sudden and Airy approximations for the continuum wave function and a quadrature formula for the integral over bending motions. The present theory also lifts some assumptions that had been introduced previously to simplify the theory for isotropic repulsive potentials. Thus, we use the exact nonlinear relation between the bound state bending angle and the scattering angle to remove the previous small angle approximation that is shown to lead to inaccuracies in some cases. We also study the ramifications of the fact that the bound state bending vibration is generally a linear combination of pure bend and both bond stretches in the transformation between normal modes and scattering coordinates. Inclusion of this bend–stretch coupling, ignored in our previous analytical work and in many theories of triatomic photodissociation that employ expansions of the bound state wave function in a basis set expressed in dissociative surface scattering coordinates, is shown to have profound influence on computed fragment rotational distributions. The bend–stretch couplings serve often to wash out the additional high frequency oscillations that appear in prior approximate treatments in which these couplings are ignored. This then leads to fragment rotational distributions that contain only those oscillations resulting from the map of the initial bound state bending vibration. Comparison is made with three-dimensional close coupled and DVR calculations for the photodissociation of HCN from the bent C̃1A′ state. Calculations are also presented for initial states of high rotational angular momenta.