### Abstract

Vibrational eigenvalues and eigenfunctions in the strongly coupled regime at intermediate and at high vibrational energy content are characterized in terms of distributions, both of observable and of wave function properties. In this regime, state-by-state description in terms of uncoupled modes is both difficult and too detailed; the distributions provide an adequate characterization of the vibrational behavior. We present results from numerical studies of realistic coupled-vibrational problems; the latter include local-mode Morse oscillators coupled by the Wilson interaction. The distributions studied are g(ω) (the distribution of nearest-neighbor energy spacings), G (ω) (the distribution of all energy spacings), π(χ) (the distribution of transition moments), and two different but related wave function expansion coefficient distributions. We find that in the strongly coupled regime, the parameters of the distributions depend only weakly on the Hamiltonian, and, moreover, that simple analytic forms can be found to represent the distributions over a wide range of systems and energies. We conclude that the distributional description of vibrational systems seems potentially very useful and that dynamical elucidation of the distributional parameters seems a desirable aim. Comments are made on the relation to mode mixing, and chaotic-like behavior.

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

Pages (from-to) | 5397-5404 |

Number of pages | 8 |

Journal | Journal of Chemical Physics |

Volume | 76 |

Issue number | 11 |

Publication status | Published - 1981 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*76*(11), 5397-5404.

**Distributions of energy spacings and wave function properties in vibrationally excited states of polyatomic molecules. I. Numerical experiments on coupled Morse oscillators.** / Buch, V.; Gerber, R. B.; Ratner, Mark A.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 76, no. 11, pp. 5397-5404.

}

TY - JOUR

T1 - Distributions of energy spacings and wave function properties in vibrationally excited states of polyatomic molecules. I. Numerical experiments on coupled Morse oscillators

AU - Buch, V.

AU - Gerber, R. B.

AU - Ratner, Mark A

PY - 1981

Y1 - 1981

N2 - Vibrational eigenvalues and eigenfunctions in the strongly coupled regime at intermediate and at high vibrational energy content are characterized in terms of distributions, both of observable and of wave function properties. In this regime, state-by-state description in terms of uncoupled modes is both difficult and too detailed; the distributions provide an adequate characterization of the vibrational behavior. We present results from numerical studies of realistic coupled-vibrational problems; the latter include local-mode Morse oscillators coupled by the Wilson interaction. The distributions studied are g(ω) (the distribution of nearest-neighbor energy spacings), G (ω) (the distribution of all energy spacings), π(χ) (the distribution of transition moments), and two different but related wave function expansion coefficient distributions. We find that in the strongly coupled regime, the parameters of the distributions depend only weakly on the Hamiltonian, and, moreover, that simple analytic forms can be found to represent the distributions over a wide range of systems and energies. We conclude that the distributional description of vibrational systems seems potentially very useful and that dynamical elucidation of the distributional parameters seems a desirable aim. Comments are made on the relation to mode mixing, and chaotic-like behavior.

AB - Vibrational eigenvalues and eigenfunctions in the strongly coupled regime at intermediate and at high vibrational energy content are characterized in terms of distributions, both of observable and of wave function properties. In this regime, state-by-state description in terms of uncoupled modes is both difficult and too detailed; the distributions provide an adequate characterization of the vibrational behavior. We present results from numerical studies of realistic coupled-vibrational problems; the latter include local-mode Morse oscillators coupled by the Wilson interaction. The distributions studied are g(ω) (the distribution of nearest-neighbor energy spacings), G (ω) (the distribution of all energy spacings), π(χ) (the distribution of transition moments), and two different but related wave function expansion coefficient distributions. We find that in the strongly coupled regime, the parameters of the distributions depend only weakly on the Hamiltonian, and, moreover, that simple analytic forms can be found to represent the distributions over a wide range of systems and energies. We conclude that the distributional description of vibrational systems seems potentially very useful and that dynamical elucidation of the distributional parameters seems a desirable aim. Comments are made on the relation to mode mixing, and chaotic-like behavior.

UR - http://www.scopus.com/inward/record.url?scp=36749109527&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749109527&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36749109527

VL - 76

SP - 5397

EP - 5404

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -