## Abstract

The integral expressions of classical S matrix theory are tested against quantum mechanical results and classical path-forced quantum oscillator results for vibrational transition probabilities in collinear collisions of atoms with harmonic and Morse vibrators for the H+Br_{2} and He+HBr mass combinations. The interaction potential is assumed to be a repulsive exponential function. The energy range studied (in units of ℏ) is 2-10 for H+Br_{2} and 2-6 for He+HBr. The integral expressions are found to be accurate within a factor of two for almost all transition probabilities greater than 7×10^{-3} but to be very inaccurate for very small transition probabilities. Quasiclassical trajectory histogram methods are found to be accurate within a factor of two only for transition probabilities greater than 0.15. Neither the integral expressions of classical S matrix theory nor the quasiclassical trajectory histogram method are found to be as generally accurate as the classical path-forced quantum oscillator results.

Original language | English (US) |
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Pages (from-to) | 249-254 |

Number of pages | 6 |

Journal | Chemical Physics |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Nov 1 1976 |

### Bibliographical note

Funding Information:It has been shown that classical S matrix theory \[1\] can provide accurate values for vibrationaUy inelastic transition probabilities in atom-diatom collisions in nonreactive systems \[1-15\].T he uniform semiclassical approximations of classical S matrix theory are the most accurate but they involve searching for root trajectories which satisfy double-ended boundary conditions and in some cases they may require the evaluation of trajectories for complex values of the coordinates. In addition, in some cases the appropriate uniformization procedures do not exist. In contrast the integral expressions \[2,9,13-25\] of classical S matrix theory require no root searching or complex-valued trajectories (although sometimes the integral expressions cannot be applied because of a singularity in the pre-exponential factor in the semi- * Research supported in part by a grant from the National Science Foundation anit by a computer-time subsidy from the University of Minnesota Computing Center. * Present address: Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S1A1. * Alfred P. Sloan Foundation Research Fellow; Joint Insti-tute for Laboratory Astrophysics Visiting Fellow.

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