A general multiplehyphen;perturbation theory is developed for the study of polyatomic vibrational potential functions. Using the quantitieslgr;iequiv; 1 minus; Riesol;Rias perturbation parameters for each pair of atoms atRinearRic, the polyatomic vibrational potential function is generated as a function of the several1 sol; Rin. By employing partial confocal elliptic coordinates, the Schrouml;dinger equation is transformed into a form in which the kinetic energy, electronicmdash;nuclear attractions, and nuclearmdash;nuclear repulsions are the perturbations. There results a new approach to the perturbation treatment of polyatomic vibrational force constants. Because of their simple forms the perturbations are much easier to handle this way than in the usualDgr; Riequiv; Riminus; Rieexpansions, where the perturbations involve first and second derivatives of the Hamiltonian. The formulation covers stretching as well as bending force constants. As a specific example, the application to triatomic molecules is discussed.
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