### Abstract

Quantum scattering theories of chemical reaction usually require, at some stage, a transformation from the quantum states of reactants to those of the products. We show that it is useful to separate this transformation into angular momentum coefficients and translational-vibrational integrals. The angular momentum coefficients thus defined are general kinematic factors, depending only on the masses of the atoms and the product vibrational and translational distances, but not on the particular potential surface. Analytic formulas are derived for these angular momentum coefficients, both for reactions confined to a plane and for three-dimensional motion. Various selection rules, symmetry properties, orthogonality conditions, normalization rules, and recursion relations are derived from these formulas. An efficient and numerically stable method is derived for numerical evaluation of the angular momentum coefficients. Examples are given for several specific reactions and the trends with varying mass combinations are rationalized in terms of limiting cases. These results display the kinematic aspects of angular momentum transfer in chemical reactions. Comparison with classical trajectories, which include both dynamic and kinematic effects, shows the extent to which dynamic effects alter the distributions of rotational and orbital angular momenta from those given by the kinematic effects alone. Finally, the integral for the transformation of the vibrational and radial dependence of the scattering wavefunction is discussed qualitatively.

Original language | English (US) |
---|---|

Pages (from-to) | 2918-2938 |

Number of pages | 21 |

Journal | The Journal of Chemical Physics |

Volume | 64 |

Issue number | 7 |

DOIs | |

State | Published - Jan 1 1976 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*64*(7), 2918-2938. https://doi.org/10.1063/1.432553

**Quantum theory of angular momentum coupling in reactive collisions.** / Schulten, Klaus; Gordon, Roy G.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 64, no. 7, pp. 2918-2938. https://doi.org/10.1063/1.432553

}

TY - JOUR

T1 - Quantum theory of angular momentum coupling in reactive collisions

AU - Schulten, Klaus

AU - Gordon, Roy G.

PY - 1976/1/1

Y1 - 1976/1/1

N2 - Quantum scattering theories of chemical reaction usually require, at some stage, a transformation from the quantum states of reactants to those of the products. We show that it is useful to separate this transformation into angular momentum coefficients and translational-vibrational integrals. The angular momentum coefficients thus defined are general kinematic factors, depending only on the masses of the atoms and the product vibrational and translational distances, but not on the particular potential surface. Analytic formulas are derived for these angular momentum coefficients, both for reactions confined to a plane and for three-dimensional motion. Various selection rules, symmetry properties, orthogonality conditions, normalization rules, and recursion relations are derived from these formulas. An efficient and numerically stable method is derived for numerical evaluation of the angular momentum coefficients. Examples are given for several specific reactions and the trends with varying mass combinations are rationalized in terms of limiting cases. These results display the kinematic aspects of angular momentum transfer in chemical reactions. Comparison with classical trajectories, which include both dynamic and kinematic effects, shows the extent to which dynamic effects alter the distributions of rotational and orbital angular momenta from those given by the kinematic effects alone. Finally, the integral for the transformation of the vibrational and radial dependence of the scattering wavefunction is discussed qualitatively.

AB - Quantum scattering theories of chemical reaction usually require, at some stage, a transformation from the quantum states of reactants to those of the products. We show that it is useful to separate this transformation into angular momentum coefficients and translational-vibrational integrals. The angular momentum coefficients thus defined are general kinematic factors, depending only on the masses of the atoms and the product vibrational and translational distances, but not on the particular potential surface. Analytic formulas are derived for these angular momentum coefficients, both for reactions confined to a plane and for three-dimensional motion. Various selection rules, symmetry properties, orthogonality conditions, normalization rules, and recursion relations are derived from these formulas. An efficient and numerically stable method is derived for numerical evaluation of the angular momentum coefficients. Examples are given for several specific reactions and the trends with varying mass combinations are rationalized in terms of limiting cases. These results display the kinematic aspects of angular momentum transfer in chemical reactions. Comparison with classical trajectories, which include both dynamic and kinematic effects, shows the extent to which dynamic effects alter the distributions of rotational and orbital angular momenta from those given by the kinematic effects alone. Finally, the integral for the transformation of the vibrational and radial dependence of the scattering wavefunction is discussed qualitatively.

UR - http://www.scopus.com/inward/record.url?scp=0003573893&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0003573893&partnerID=8YFLogxK

U2 - 10.1063/1.432553

DO - 10.1063/1.432553

M3 - Article

AN - SCOPUS:0003573893

VL - 64

SP - 2918

EP - 2938

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

ER -