### Abstract

The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

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

Article number | 052704 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 73 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*73*(5), [052704]. https://doi.org/10.1103/PhysRevA.73.052704

**Mass effects and internal space geometry in triatomic reaction dynamics.** / Yanao, Tomohiro; Koon, Wang S.; Marsden, Jerrold E.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 73, no. 5, 052704. https://doi.org/10.1103/PhysRevA.73.052704

}

TY - JOUR

T1 - Mass effects and internal space geometry in triatomic reaction dynamics

AU - Yanao, Tomohiro

AU - Koon, Wang S.

AU - Marsden, Jerrold E.

PY - 2006

Y1 - 2006

N2 - The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

AB - The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

UR - http://www.scopus.com/inward/record.url?scp=33646495533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646495533&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.73.052704

DO - 10.1103/PhysRevA.73.052704

M3 - Article

AN - SCOPUS:33646495533

VL - 73

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 5

M1 - 052704

ER -