Classical phase space theory for product state distributions with application to the v–j vector correlation

Abstract

A classical phase space theory procedure for estimating product state distributions for ''barrierless'' dissociations is described. The distributions are determined in terms of an average over the available phase space on a fixed dividing surface of the function describing the distribution of interest. The use of a weighting function corresponding to the contribution of each randomly sampled phase space point to the number of available states, as in related state counting algorithms, provides an efficient route to the determination of any particular product state distribution or correlation. The coordinates employed in this sampling are the Euler angles, describing the orientation in space of each of the fragments and of the line of centers connecting the two fragments, and their conjugate momenta. Sample applications focus on the determination of the vector correlation between the angular momentum of one fragment and the relative velocity of the fragments for the dissociations of 2-chloro-2-nitrosopropane ͑CNP͒, NCCN, and CF 3 NO. Comparisons with the corresponding experimental measurements for the CNP and NCCN dissociations provide further evidence for the presence of important dynamical effects in these dissociations. The calculations for CF 3 NO are presented with the hope of motivating an experimental verification of the predicted strong v-j correlation for the CF 3 fragment in combination with the weak correlation for the NO fragment. Overall, these phase space theory results are found to provide a useful reference for the interpretation of experimental results.

Nonintuitive Asymmetry in the Three-Body Photodissociation of CH3COCN

“…In addition, the v‚j correlation should be negligible for the fragment with the larger rotational constant. 44 As a consequence, no correlation between v and j for the CN fragment is expected by statistical theory for this system. The measured CN v‚j correlations must, therefore, arise from dynamical factors in the dissociation.…”

Quantum phase space theory for the calculation of v-j vector correlations

“…The absolute state count and the rotational distributions will show more serious deviations due to the neglect of the centrifugal barrier. The The keyresult is that the observed vector cre1axion is about twice as large as the thermally averaged, statistical expectation, as noted by Klippenstein and Cline [4]. It seems very likely that this is a consequence of an additional constraint on the dissociation ofthe linear molecule, NCG4.…”

“…2, conventionally used in a phase space counting. Indeed, Klippenstein and Cline have resorted to a Monte Carlo calculation of classical phase space to address the identical question [4]. A helicity basis, as described by Jacob and Wick [6] lends itself to a direct quantum evaluation of the vj correlation, since the projections of fragment angular momenta on the recoil axis are good quantum numbers inthis basis.…”

“…Klippenstein and Cline have recently performed Monte Carlo evaluations of classical phase space integrals to estimate the statistical stateresolved vj correlations relevant to this system [4]. The full results of the helicitybased phase space calculations will be presented later [1O].…”

“…The ccmeciion betweenphase space theoryand vector correlations is less well known. Klippenstein and Cline [4] have recently used Monte Carlo methods to generate representative classical phase space ensembles from which vector correlations have been inspected. They present useful generalizations about the statistical expectations for photofragment vj correlations, based on the relative moments of inertia of two reaction products and on the total angular momentum.…”