### Abstract

A method for obtaining energy levels of coupled vibrational modes is described, that utilizes a state-interaction approach combined with semiclassical approximations. The method starts with a semiclassical self-consistent-field calculation of the coupled problem, and uses the eigenstates of the resulting Hartree-like separable SCF vibrational hamiltonian to define a basis set of Hartree products in which the full vibrational hamiltonian is represented and diagonalized. Matrix elements of any interaction potential between single-mode states are approximated semiclassically as the Fourier component of the interaction at the frequency corresponding to the SCF eigenvalue difference. A Fourier-component expression can also be given for the overlap between non-orthogonal single mode states. Thus no wavefunctions ever need to be defined. Application to a sample two-mode problem shows that the method is highly accurate. Further possible applications, in particular to intramolecular rate calculations are noted.

Original language | English |
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Pages (from-to) | 345-356 |

Number of pages | 12 |

Journal | Chemical Physics |

Volume | 53 |

Issue number | 3 |

DOIs | |

Publication status | Published - Dec 1 1980 |

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### ASJC Scopus subject areas

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