### Abstract

Effective Hamiltonian theory has previously been applied in a quantum mechanical framework, where the computational savings resulted from the reduced number of coupled equations. The present paper shows how effective Hamiltonian theory can be combined with classical S-matrix theory. In this case the computational difficulty is reduced by lowering the number of degrees of freedom that must be semiclassically "quantized" via root-searching techniques. It is shown, for example, that a full classical S-matrix calculation for collisions of two rigid diatoms would require root searches in a four-dimensional space while an effective potential calculation would need only two-dimensional root searches. This can represent a substantial decrease in computational effort. A modified effective potential and the centrifugal decoupling method are formulated for application to classical S-matrix theory. Also included is a description of the rotational coordinates and momenta needed for the semiclassical treatment of an arbitrary, nonreactive bimolecular collision.

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

Pages (from-to) | 4821-4831 |

Number of pages | 11 |

Journal | The Journal of chemical physics |

Volume | 64 |

Issue number | 12 |

DOIs | |

State | Published - Jan 1 1976 |

### All Science Journal Classification (ASJC) codes

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

## Fingerprint Dive into the research topics of 'Effective Hamiltonian methods for the semiclassical treatment of molecular collisions'. Together they form a unique fingerprint.

## Cite this

*The Journal of chemical physics*,

*64*(12), 4821-4831. https://doi.org/10.1063/1.432137