Analysis of nearly degenerate bands of spherical top molecules: Matrix elements of the vibrational-rotational Hamiltonian

Daniel B. Litvin, Kenneth Fox

Research output: Contribution to journalArticle

3 Scopus citations

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 ν2 and ν4 fundamental vibrational-rotational bands of tetrahedral XY 4 molecules like CH4, are calculated explicitly.

Original languageEnglish (US)
Pages (from-to)3908-3912
Number of pages5
JournalThe Journal of chemical physics
Volume76
Issue number8
DOIs
StatePublished - Jan 1 1982

All Science Journal Classification (ASJC) codes

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

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