Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

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The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ2TVIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C3 molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191-207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C3. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.

Original languageEnglish
Pages (from-to)24-61
Number of pages38
JournalJournal of Molecular Spectroscopy
Issue number1
Publication statusPublished - Mar 1988


ASJC Scopus subject areas

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

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