ASYMMETRIC-ROTATOR FOURTH VIBRATION-ROTATION INTERACTION CONSTANTS
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Date
1980
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Ohio State University
Abstract
The fourth-order constants $\rho$ of interest in the present work are the ones which specify the variation of the quadric centrifugal distortion constants with vibrational state for the terms of the vibration–rotational Hamiltonian which are of the form \[ \{\frac{1}{4}\tau_{\alpha\alpha\alpha\alpha} + \Sigma_{k} \rho^{k}_{\alpha\alpha\alpha\alpha} (v_{k} + \frac{1}{2})\} J^{4}_{\alpha},\quad \alpha = x, y, z, \] where the $\tau$’s are the well-known second-order equilibrium centrifugal distortion constants, k enumerated normal modes, and $J^{4}\alpha$ are angular momentum operators. We have determined algebraic expressions for the above type of $\rho$ constants in terms of fundamental molecular parameters on the basis of the Darling-Dennison model Hamiltonian and with the aid of recently described $modifications^{1}$ of the standard Amat-Nielsen contact transformation technique. These modifications results in a considerable reduction of the required algebraic effort although the details remain formidable. The details of our calculation will be out-lined and preliminary results will be shown. Calculation of the much more complicated $\rho$ constant associated with the angular momentum operators of the type $(J^{2}_{\alpha} J^{2}_{\beta} + J^{2}_{\beta} J^{2}_{\alpha}), \alpha \neq \beta$, has not been completed.
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$^{1}$ A. Niroomand-Rad and P. M. Parker, J. Mol. Spectrosc. 75, 454 (1979).
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