### Abstract

This paper presents a general theoretical formalism for describing quantum reactive scattering in four atom reactions of the type A + BCD→AB + CD based on the coupled channel distorted wave method (CCDW). In this formalism, we have derived expressions for the Schrödinger equation in body-fixed axis (bfa) coordinate systems associated with the A + BCD and AB + CD arrangement channels, and we have reduced the CCDW scattering matrix to a six dimensional internal coordinate quadrature in terms of the bfa wave functions. Explicit expressions for the nonreactive (coupled channel) centrifugal and potential coupling matrices are derived for both A + BCD and AB + CD using the bfa frame isomorphic Hamiltonian. The interconnection between A + BCD and AB + CD coordinate systems is explored in detail, and it is found that the resulting CCDW scattering matrix is similar in form to that derived earlier for atom-diatom collisions, with the main conceptual difference associated with use of an Eckart frame to define the vibrational wave functions for BCD. The relation between the Eckart and scattering frames is discussed in depth. Also, the imposition of parity decoupling in the CCDW calculation is developed for both the CC Hamiltonian matrices and the distorted wave overlap.

Original language | English |
---|---|

Pages (from-to) | 2038-2053 |

Number of pages | 16 |

Journal | Journal of Chemical Physics |

Volume | 85 |

Issue number | 4 |

Publication status | Published - 1986 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*85*(4), 2038-2053.

**Quantum reactive scattering for A + BCD→AB + CD reactions : Coupled channel distorted wave theory.** / Natanson, Grigory A.; Schatz, George C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 85, no. 4, pp. 2038-2053.

}

TY - JOUR

T1 - Quantum reactive scattering for A + BCD→AB + CD reactions

T2 - Coupled channel distorted wave theory

AU - Natanson, Grigory A.

AU - Schatz, George C

PY - 1986

Y1 - 1986

N2 - This paper presents a general theoretical formalism for describing quantum reactive scattering in four atom reactions of the type A + BCD→AB + CD based on the coupled channel distorted wave method (CCDW). In this formalism, we have derived expressions for the Schrödinger equation in body-fixed axis (bfa) coordinate systems associated with the A + BCD and AB + CD arrangement channels, and we have reduced the CCDW scattering matrix to a six dimensional internal coordinate quadrature in terms of the bfa wave functions. Explicit expressions for the nonreactive (coupled channel) centrifugal and potential coupling matrices are derived for both A + BCD and AB + CD using the bfa frame isomorphic Hamiltonian. The interconnection between A + BCD and AB + CD coordinate systems is explored in detail, and it is found that the resulting CCDW scattering matrix is similar in form to that derived earlier for atom-diatom collisions, with the main conceptual difference associated with use of an Eckart frame to define the vibrational wave functions for BCD. The relation between the Eckart and scattering frames is discussed in depth. Also, the imposition of parity decoupling in the CCDW calculation is developed for both the CC Hamiltonian matrices and the distorted wave overlap.

AB - This paper presents a general theoretical formalism for describing quantum reactive scattering in four atom reactions of the type A + BCD→AB + CD based on the coupled channel distorted wave method (CCDW). In this formalism, we have derived expressions for the Schrödinger equation in body-fixed axis (bfa) coordinate systems associated with the A + BCD and AB + CD arrangement channels, and we have reduced the CCDW scattering matrix to a six dimensional internal coordinate quadrature in terms of the bfa wave functions. Explicit expressions for the nonreactive (coupled channel) centrifugal and potential coupling matrices are derived for both A + BCD and AB + CD using the bfa frame isomorphic Hamiltonian. The interconnection between A + BCD and AB + CD coordinate systems is explored in detail, and it is found that the resulting CCDW scattering matrix is similar in form to that derived earlier for atom-diatom collisions, with the main conceptual difference associated with use of an Eckart frame to define the vibrational wave functions for BCD. The relation between the Eckart and scattering frames is discussed in depth. Also, the imposition of parity decoupling in the CCDW calculation is developed for both the CC Hamiltonian matrices and the distorted wave overlap.

UR - http://www.scopus.com/inward/record.url?scp=2442531541&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2442531541&partnerID=8YFLogxK

M3 - Article

VL - 85

SP - 2038

EP - 2053

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -