Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory

Journal Article · Wed Dec 01 04:00:00 EST 1976 · J. Chem. Phys.; (United States)

DOI:https://doi.org/10.1063/1.432918· OSTI ID:7248119

Schatz, G C; Kuppermann, A

A method is presented for accurately solving the Schroedinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born--Oppenheimer potential energy surface. The Schroedinger equation is first expressed in body-fixed coordinates. The wavefunction is then expanded in a set of vibration--rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and integral cross sections are obtained. Simplifications arising from the use of parity symmetry to decouple the coupled-channel equations, the matching procedures and the asymptotic analysis are discussed in detail. Relations between certain important angular momentum operators in body-fixed coordinate systems are derived and the asymptotic solutions to the body-fixed Schroedinger equation are analyzed extensively. Application of this formalism to the three-dimensional H+H/sub 2/ reaction is considered including the use of arrangement channel permutation symmetry, even--odd rotational decoupling and postantisymmetrization. The range of applicability and limitations of the method are discussed. (AIP)

• Research Organization: Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125
• OSTI ID: 7248119
• Journal Information: J. Chem. Phys.; (United States), Journal Name: J. Chem. Phys.; (United States) Vol. 65:11; ISSN JCPSA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
640304 -- Atomic
Molecular & Chemical Physics-- Collision Phenomena
74 ATOMIC AND MOLECULAR PHYSICS
ATOM COLLISIONS
ATOM-MOLECULE COLLISIONS
CHEMICAL REACTION KINETICS
COLLISIONS
CRYOGENIC FLUIDS
DIFFERENTIAL EQUATIONS
ELEMENTS
EQUATIONS
FLUIDS
HYDROGEN
KINETICS
MOLECULE COLLISIONS
NONMETALS
REACTION KINETICS
SCHROEDINGER EQUATION
THREE-DIMENSIONAL CALCULATIONS
WAVE EQUATIONS