Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory

Aron Kuppermann, George C Schatz, M. Baer

Research output: Contribution to journalArticle

62 Citations (Scopus)

Abstract

A method is presented for accurately solving the Schrödinger equation for the reactive collision of an atom with a diatomic molecule on a space-fixed plane. The procedure consists primarily of two steps. First, the Schrödinger equation in each of the three arrangement channel regions is transformed into a set of coupled differential equations and numerically integrated in each of these regions to generate primitive solutions. The rotational part of the vibration-rotation basis functions involved is not changed from its asymptotic form during this propagation, but the vibrational eigenfunctions as well as the integration variable are changed periodically so as to follow the vibrational motions in a nearly adiabatic manner. In the second step, the primitive solutions generated in each of the three arrangement channels are smoothly matched to each other on a set of appropriately chosen matching surfaces. The resulting solutions are then linearly combined to satisfy the proper asymptotic boundary conditions, and the scattering matrix, scattering amplitudes, and cross sections are determined. Application of this procedure to the special case of the H+H2 reaction is discussed in detail including simplifications arising from the additional symmetries involved, and the inclusion of effects resulting from indistinguishability of identical particles.

Original languageEnglish
Pages (from-to)4596-4623
Number of pages28
JournalJournal of Chemical Physics
Volume65
Issue number11
Publication statusPublished - 1976

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algae
Scattering
Atoms
scattering
atoms
S matrix theory
diatomic molecules
simplification
Eigenvalues and eigenfunctions
scattering amplitude
eigenvectors
Differential equations
differential equations
Boundary conditions
inclusions
boundary conditions
vibration
Molecules
collisions
propagation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory. / Kuppermann, Aron; Schatz, George C; Baer, M.

In: Journal of Chemical Physics, Vol. 65, No. 11, 1976, p. 4596-4623.

Research output: Contribution to journalArticle

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