## Abstract

Three kinds of semiclassical theory are tested against quantum mechanical results for vibrational transition probabilities and average vibrational energy transfers in collinear collisions of atoms with harmonic and Morse vibrators for the He-H_{2} mass combination. The interaction potential is assumed to be a repulsive exponential function with an exponential parameter which is realistic for He-H_{2} collisions. The energy range studied is total energies of 2-8 in units of h{stroke}ω_{e}. The uniform semiclassical approximations of classical S matrix theory are tested only for classically allowed transitions, i.e., for transition probabilities greater than about 0.2. They are accurate quantitatively for both harmonic and Morse vibrators. The integral expressions of classical S matrix theory are found to be quantitatively accurate for classically allowed and weakly classically forbidden transitions, i.e., for transition probabilities greater than about 0.01-0.05, and to be unreliable for strongly classically forbidden transitions. Quasiclassical trajectory methods yield qualitatively accurate results only for classically allowed transitions but the phase-averaged energy transfer in quasiclassical collisions may be accurate even when classically forbidden transition probabilities are important for the calculation of the average energy transfer. Forced quantum oscillator methods using a classical path whose initial velocity is the average of the initial and final velocities corresponding to the transition of interest are accurate for transition probabilities as small as 4 × 10^{-8} for harmonic vibrators but do not seem to accurately account for the effect of anharmonicity.

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

Pages (from-to) | 243-273 |

Number of pages | 31 |

Journal | Chemical Physics |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1975 |

### Bibliographical note

Funding Information:+ This work was supported in part by the National Science Foundation under grant no. GP-28684. * National Defense Education Act Predoctoral Fellow, 19714. * Alfred P. Sloan Research Fellow. 1973 - present. l * For reviews, including extensive literature coverage through 1967 and mid-1968. respectively. see refs. [ 1.21. More recent work may be found in the review by Seaest [3] and in refs. (4-133). Additional special techniques have been developed to study the hard-sphere interaction model [IlZ. 122,134-1391.