Three-dimensional analytical quantum mechanical theory for triatomic photodissociation: Role of angle dependent dissociative surfaces on rotational and angular distributions in the rotational infinite order sudden limit

Abstract

An analytical quantum mechanical model is developed for calculating fragment energy distributions in photodissociation of linear triatomic molecules when the repulsive potential energy surface is anisotropic. The translational continuum function is taken to be given by the infinite order sudden approximation, but an equivalent adiabatic interpretation leads to a natural choice for the diatomic angular momentum j and for the retention of asymptotic rotational energy differences. Normal coordinates are used for the initial bound state before dissociation, while scattering coordinates are applied for wave functions on the dissociative surface. These natural choices lead to three-dimensional nonseparable bound–continuum transition amplitudes. The translational continuum wave function is further approximated using Airy functions, and additional approximations are introduced based on the presence of small amplitude vibrations in the initial bound state. The three-dimensional transition amplitudes are then analytically reduced to sums of one-dimensional quadratures. The theory has been applied to the photodissociation of several rovibronic states of N2O+(Ã 2∑+) (predissociation) and ICN(C̃ 1A′) (direct photodissociation), and the rotational distributions for J=0 are in good agreement with three-dimensional close-coupled calculations except when the potentials become highly anisotropic. Our photodissociation infinite order sudden approximation is tested against various versions of the rotational infinite order sudden approximation for N2O+ and are found to be in good agreement with previous results. The present theory readily permits calculations for J>0 and may be used for the calculation of rotational distributions for excited rotational and/or vibrational states. In the limit of isotropic potentials the remaining integrals are evaluated to provide analytical approximations for the transition amplitudes.