### Abstract

The energy spacing distribution and the transition moment distribution of highly excited vibrational states are studied by numerical solution for a model of coupled Morse oscillators with typical molecular parameters. The results show the following: (a) The transition moment distribution differs considerably from the statistical (gaussian) Porter Model, even in the regime of strong coupling. Agreement of the numerical results with the statistical model improves for states that increasingly approach the dissociation limit (6) A much improved statistical model for the transition moment distribution can be constructed, using certain empirical statistical properties of the wave-functions involved, (c) For states differing substantially in energy, the relevant transition moment distribution exhibits ah energy gap dependence. (d) The energy spacing distribution for states in a small range of energies obeys the Brody form g(w)αw^{β} exp [-αw^{1+β}]. β increases systematically with the energy of the states, with the distribution increasingly approaching the Wigner model. A significant difference between the two distributions persists even near dissociation.

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

Pages (from-to) | 1129-1140 |

Number of pages | 12 |

Journal | Molecular Physics |

Volume | 46 |

Issue number | 5 |

DOIs | |

Publication status | Published - Aug 10 1982 |

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### ASJC Scopus subject areas

- Biophysics
- Molecular Biology
- Physical and Theoretical Chemistry
- Condensed Matter Physics

### Cite this

*Molecular Physics*,

*46*(5), 1129-1140. https://doi.org/10.1080/00268978200101851

**Properties of vibrationally excited polyatomic molecules and their energy variation : Transition moment and energy spacing distributions.** / Buch, V.; Ratner, Mark A; Gerber, R. B.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 46, no. 5, pp. 1129-1140. https://doi.org/10.1080/00268978200101851

}

TY - JOUR

T1 - Properties of vibrationally excited polyatomic molecules and their energy variation

T2 - Transition moment and energy spacing distributions

AU - Buch, V.

AU - Ratner, Mark A

AU - Gerber, R. B.

PY - 1982/8/10

Y1 - 1982/8/10

N2 - The energy spacing distribution and the transition moment distribution of highly excited vibrational states are studied by numerical solution for a model of coupled Morse oscillators with typical molecular parameters. The results show the following: (a) The transition moment distribution differs considerably from the statistical (gaussian) Porter Model, even in the regime of strong coupling. Agreement of the numerical results with the statistical model improves for states that increasingly approach the dissociation limit (6) A much improved statistical model for the transition moment distribution can be constructed, using certain empirical statistical properties of the wave-functions involved, (c) For states differing substantially in energy, the relevant transition moment distribution exhibits ah energy gap dependence. (d) The energy spacing distribution for states in a small range of energies obeys the Brody form g(w)αwβ exp [-αw1+β]. β increases systematically with the energy of the states, with the distribution increasingly approaching the Wigner model. A significant difference between the two distributions persists even near dissociation.

AB - The energy spacing distribution and the transition moment distribution of highly excited vibrational states are studied by numerical solution for a model of coupled Morse oscillators with typical molecular parameters. The results show the following: (a) The transition moment distribution differs considerably from the statistical (gaussian) Porter Model, even in the regime of strong coupling. Agreement of the numerical results with the statistical model improves for states that increasingly approach the dissociation limit (6) A much improved statistical model for the transition moment distribution can be constructed, using certain empirical statistical properties of the wave-functions involved, (c) For states differing substantially in energy, the relevant transition moment distribution exhibits ah energy gap dependence. (d) The energy spacing distribution for states in a small range of energies obeys the Brody form g(w)αwβ exp [-αw1+β]. β increases systematically with the energy of the states, with the distribution increasingly approaching the Wigner model. A significant difference between the two distributions persists even near dissociation.

UR - http://www.scopus.com/inward/record.url?scp=84913408414&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84913408414&partnerID=8YFLogxK

U2 - 10.1080/00268978200101851

DO - 10.1080/00268978200101851

M3 - Article

AN - SCOPUS:84913408414

VL - 46

SP - 1129

EP - 1140

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 5

ER -