### Abstract

We formulate a general method for calculating energy eigenvalues and eigenfunctions in a simultaneous analysis of nearly degenerate vibrational-rotational bands of spherical top molecules. The basis functions are products of rigid rotor and N-dimensional harmonic oscillator eigenfunctions. General explicit expressions are derived for the matrix elements of vibrational operators in the basis of N-dimensional harmonic oscillator eigenfunctions. Using these general expressions, the matrix elements of vibrational operators in the basis of five-dimensional harmonic oscillator eigenfunctions applicable, for example, in the analysis of the nearly degenerate ν_{2} and ν_{4} fundamental vibrational-rotational bands of tetrahedral XY _{4} molecules like CH_{4}, are calculated explicitly.

Original language | English (US) |
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Pages (from-to) | 3908-3912 |

Number of pages | 5 |

Journal | The Journal of chemical physics |

Volume | 76 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 1982 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry