### 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

### Cite this

**The semiclassical self-consistent-field (SC-SCF) approach to energy levels of coupled vibrational modes. II. The semiclassical state-interaction procedure.** / Ratner, Mark A; Buch, V.; Gerber, R. B.

Research output: Contribution to journal › Article

*Chemical Physics*, vol. 53, no. 3, pp. 345-356. https://doi.org/10.1016/0301-0104(80)85123-8

}

TY - JOUR

T1 - The semiclassical self-consistent-field (SC-SCF) approach to energy levels of coupled vibrational modes. II. The semiclassical state-interaction procedure

AU - Ratner, Mark A

AU - Buch, V.

AU - Gerber, R. B.

PY - 1980/12/1

Y1 - 1980/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039788739&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039788739&partnerID=8YFLogxK

U2 - 10.1016/0301-0104(80)85123-8

DO - 10.1016/0301-0104(80)85123-8

M3 - Article

AN - SCOPUS:0039788739

VL - 53

SP - 345

EP - 356

JO - Chemical Physics

JF - Chemical Physics

SN - 0301-0104

IS - 3

ER -