Three-dimensional analytical infinite order sudden quantum theory for triatomic indirect photodissociation processes

Horacio Grinberg,Karl F Freed,Carl J Williams

doi:10.1063/1.474535

Abstract

Our previously developed analytical infinite order sudden (IOS) quantum theory of triatomic photodissociation is extended to describe indirect photodissociation processes through a real or virtual intermediate state. The theory uses the IOS approximation for the dynamics in the final dissociative channels and an Airy function approximation for the continuum states. These approximations enable us to evaluate the multi-dimensional non-separable transition amplitudes analytically (as one-dimensional quadratures), despite the different natural coordinates for the initial bound, the intermediate resonant, and the final dissociative states. The fragment internal energy distributions are described as a function of the initial and final quantum states and the photon excitation energy. The theory readily permits the evaluation of rotational distributions for high values of the total angular momentum J in the initial bound molecular state, a feature that would be very difficult with close-coupled methods. In paper II we apply the theory to describe the photofragment yield spectrum of NOCl in the region of the T1(13A″)←S0(11A′) transition.

Highlights

The enormous advancements with theories of the photodissociation dynamics and the explosion in computational power enable the treatment of full three-dimensional quantum calculations for light tri- and tetra-atomic system dynamics.[1]
We have extended our previously developed threedimensional analytical infinite order suddenIOSquantummechanical theory to study indirect and non-adiabatic photodissociation processes through a real or virtual unstable intermediate state
As an illustration of the general theory, the initial bound and intermediate states are described by harmonic potentials, while the dynamics in the final repul

Summary

INTRODUCTION

The enormous advancements with theories of the photodissociation dynamics and the explosion in computational power enable the treatment of full three-dimensional quantum calculations for light tri- and tetra-atomic system dynamics.[1]. Grinberg, Freed, and Williams: Triatomic photodissociation processes diate resonant state is long lived,[26] our previous theory[21] may be applied by just treating the process as a direct dissociation from the ‘‘bound’’ resonant state to the continuum, but the situation becomes more complicated when the intermediate states are short lived such that the intermediate states strongly overlap.[27,28] Both cases of weak final state interactions and of weak non-adiabatic interactions can basically be treated formally using the same mathematical tools[14,29] and the same two-potential description with the second order golden rule rate expression.[30,31].

THEORY

Initial and resonant state wave functions

Final state wave function

Evaluation of matrix elements

CONCLUSIONS