### 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+H_{2} 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 language | English |
---|---|

Pages (from-to) | 4596-4623 |

Number of pages | 28 |

Journal | Journal of Chemical Physics |

Volume | 65 |

Issue number | 11 |

Publication status | Published - 1976 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*65*(11), 4596-4623.

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

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 65, no. 11, pp. 4596-4623.

}

TY - JOUR

T1 - Quantum mechanical reactive scattering for planar atom plus diatom systems. I. Theory

AU - Kuppermann, Aron

AU - Schatz, George C

AU - Baer, M.

PY - 1976

Y1 - 1976

N2 - 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.

AB - 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.

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M3 - Article

VL - 65

SP - 4596

EP - 4623

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -