### Abstract

A method for determining semiclassical eigenvalues and the canonical transformation relating "good" and harmonic action-angle variables for nonseparable molecular vibrations is developed. The method makes use of Fourier expansions of the harmonic action and good angle variables in terms of the harmonic angle variables (for fixed good actions). The coefficients in these expansions are determined by requiring that each expansion, when truncated at N terms, be exactly satisfied at N appropriately chosen times during the integration of a trajectory for the system of interest. Applications of this method are made to the determination of semi-classical eigenvalues for several model two mode systems which have been extensively studied using other semiclassical methods. Essentially exact agreement with these earlier calculations is obtained. We then study the dependence of cartesian coordinates and harmonic actions on good angle variables for two of the models. Weak correlation between motions in different modes is found, and this leads to a simple but reasonably accurate method for decoupling the two modes based on motional time scale separations.

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

Pages (from-to) | 239-251 |

Number of pages | 13 |

Journal | Chemical Physics |

Volume | 35 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - Dec 1 1978 |

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### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Spectroscopy
- Atomic and Molecular Physics, and Optics

### Cite this

*Chemical Physics*,

*35*(1-2), 239-251. https://doi.org/10.1016/0301-0104(78)85209-4

**A method for determining "good" action-angle variables and semiclassical eigenvalues in nonseparable systems.** / Schatz, George C; Moser, Mark D.

Research output: Contribution to journal › Article

*Chemical Physics*, vol. 35, no. 1-2, pp. 239-251. https://doi.org/10.1016/0301-0104(78)85209-4

}

TY - JOUR

T1 - A method for determining "good" action-angle variables and semiclassical eigenvalues in nonseparable systems

AU - Schatz, George C

AU - Moser, Mark D.

PY - 1978/12/1

Y1 - 1978/12/1

N2 - A method for determining semiclassical eigenvalues and the canonical transformation relating "good" and harmonic action-angle variables for nonseparable molecular vibrations is developed. The method makes use of Fourier expansions of the harmonic action and good angle variables in terms of the harmonic angle variables (for fixed good actions). The coefficients in these expansions are determined by requiring that each expansion, when truncated at N terms, be exactly satisfied at N appropriately chosen times during the integration of a trajectory for the system of interest. Applications of this method are made to the determination of semi-classical eigenvalues for several model two mode systems which have been extensively studied using other semiclassical methods. Essentially exact agreement with these earlier calculations is obtained. We then study the dependence of cartesian coordinates and harmonic actions on good angle variables for two of the models. Weak correlation between motions in different modes is found, and this leads to a simple but reasonably accurate method for decoupling the two modes based on motional time scale separations.

AB - A method for determining semiclassical eigenvalues and the canonical transformation relating "good" and harmonic action-angle variables for nonseparable molecular vibrations is developed. The method makes use of Fourier expansions of the harmonic action and good angle variables in terms of the harmonic angle variables (for fixed good actions). The coefficients in these expansions are determined by requiring that each expansion, when truncated at N terms, be exactly satisfied at N appropriately chosen times during the integration of a trajectory for the system of interest. Applications of this method are made to the determination of semi-classical eigenvalues for several model two mode systems which have been extensively studied using other semiclassical methods. Essentially exact agreement with these earlier calculations is obtained. We then study the dependence of cartesian coordinates and harmonic actions on good angle variables for two of the models. Weak correlation between motions in different modes is found, and this leads to a simple but reasonably accurate method for decoupling the two modes based on motional time scale separations.

UR - http://www.scopus.com/inward/record.url?scp=49349120886&partnerID=8YFLogxK

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U2 - 10.1016/0301-0104(78)85209-4

DO - 10.1016/0301-0104(78)85209-4

M3 - Article

VL - 35

SP - 239

EP - 251

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

IS - 1-2

ER -