POTENTIAL FUNCTION FOR THE $\nu_{7}$ MODE OF $C_{3}O_{2}$ AND THE MOLECULAR CONSTANTS FOR THE $n\nu~_{7}^\ell$ AND THE $\nu_{4} + n\nu~_{7}^\ell$ STATES.
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Date
1976
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Ohio State University
Abstract
The model of a quasilinear molecule with a large amplitude bending $mode^{1}$ is used to analyze the recent infrared data on $C_{3}O_{2} \cdot ^{2,3}$ Exact rotation-vibration energy levels are computed for a molecule with only a single vibrational degree of freedom, namely the $\nu_{7}$ mode corresponding to the bending at the central carbon atom. The $C=C=O$ angle is constrained to be $180^\circ$. The model contains three adjustable parameters: the rotational constant $B_{0}$ in the linear configuration and two terms $V_{2}$ and $V_{4}$ in the potential function, which is written in the form $V(\alpha) = V_{2}sin^{2}\alpha, + V_{4}sin^{4}\alpha,$ where $2\alpha$ is the angular deviation from linearity. By fitting the rotational constants and the separation between the ground and $2\nu_{7}^{0}$ states, these parameters are determined to be $B_{0} = 0.073515 cm^{-1}, V_{2} = - 1664 cm^{-1},$ and $V_{4} = 22 687 cm^{-1}$. The model gives a good fit to the Raman data, and it gives a reasonable fit to the rotational and centrifugal distortion constants in all of the $n\nu_{7}^\ell$ states which have been analyzed. A similar analysis is applied to the $\nu_{7}$ potential in the $v_{4} = 1$ vibrational state. By fitting the rotational constants in the $\nu_{4}$ and $\nu_{4} + 2\nu_{7}^{0}$ states and the shift of the $\nu_{4} + 2\nu_{7}^{0} \leftarrow 2\nu_{7}^{0}$ ``hot"" band, the parameters were determined to be $B_{0} = 0.073296 cm^{-1}$, $V_{2} = - 2216 cm^{-1}$, and $V_{4} = 21 617 cm^{-1}$. Again the model gives a reasonable fit for the ``hot"" band shifts, rotational constants, and centrifugal distortion constants for all of the $\nu_{4} + n\nu~_{7}^{\ell}$ states analyzed. In the $\nu_{4} = 0$ state the $\nu_{7}$ potential has a minimum at $\alpha = 11.04^\circ$ with a $30.5 cm^{-1}$ barrier at the linear configuration, while in the $\nu_{4} = 1$ state the minimum is at $13.08^\circ$ with a $56.3 cm^{-1}$ barrier.
Description
$^{1}$ J. T. Hougen, P. R. Bunker, and J.W.C. Johns, J. Mol. Spectrosc. 34 136 (1970). $^{2}$ A. W. Mantz, P. Connes, G. Guelachvili, and C. Amiot, J. Mol. Spectcosc. 54, 43 (1975). $^{3}$ W. H. Weber, P. D. Maker, and C, W. Peters, J. Chem. Phys. 64, 2149 (1976).
Author Institution: Physics Department, Research Staff, Ford Motor Company; Department of Physics, University of Michigan
Author Institution: Physics Department, Research Staff, Ford Motor Company; Department of Physics, University of Michigan