DEPENDENCE OF ASYMMETRIC--ROTATOR QUARTOIC CENTRIFUGAL DISTORTION CONSTANTS ON VIBRATIONAL STATE
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Date
1981
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Ohio State University
Abstract
``The fourth--order vibration-rotation interaction constants $\rho$ which specify the variation of the quartic centrifugal distortion constants with vibrational state appear in the vibration-rotation Hamiltonian in terms of the form $$ \{1/4\tau_{\alpha\alpha\alpha\alpha} +\sum\limits_{k} \rho^{(k)}_{\alpha\alpha\alpha\alpha}(v_{k}+1/2)\}\ \ {J}^{4}_{\alpha},\quad\quad\quad \alpha=x,y,z,\\ \leftline{and}\\$$ $$\{1/4\tau_{\alpha\alpha\beta\beta} +\sum\limits_{k} \rho^{(k)}_{\alpha\alpha\beta\beta}(v_{k}+1/2)\}\ \ ({J}^{2}_{\alpha} {J}^{2}_{\beta}+{J}^{2}_{\beta}{J}^{2}_{\alpha})\quad\quad\quad\alpha,\beta=x,y \ or \ y,z \ or \ z,x, $$ where the $\tau^{\prime} s$ are the well-know second order equilibrium centrifugal distortion constants, k enumerates normal modes, and $J_\alpha$ and $J_\beta$ are angular momentum operators, We have determined algebraic expressions for the complete set of the above $\rho$ constants in terms of fundamental molecular parameters on the basis of the Darling-Dennison model Hamiltonian and with the aid of a recently described $algorithm.^{1}$ the results can be readily specified to the $C_{2v}$ triatomic case which will be emphasized in our presentation. Modifications necessitated by accidental Coriolis resonance, especially between $\nu_{1}$ and $\nu_{3}$ in triatomics, remain to be studied. We hope to eventually be able to calculate $\rho$ constants for selected triatomic molecules and compare these to the corresponding empirical values.
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$^{1}$ A. Niroomand--Rad and P. M. Parker, J. Mol. Spectrosc. 85, 40 (1981)
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