ANHARMONIC POTENTIAL CONSTANTS FOR NITROGEN DIOXIDE
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Date
1975
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Ohio State University
Abstract
Data from recent infrared and resonance fluorescence analyses have been used to determine an equilibrium geometry and potential function through quartic terms for the ground electronic state of $NO_{2}$, using (a) the conventional perturbation expansion Hamiltonian, and (b) the non-rigid bender $Hamiltonian^{1}$ to fit virtual spin-free vibration-rotational term values. The latter Hamiltonian reproduces the term values of states with N $\leq$; 10, K $\leq$; 5,and $V_{2}$ $\leq$; 3 to within $0.02 cm^{-1}$. The fit to higher vibrational levels and the ability of the Hamiltonians to reproduce the spectra of Isotopically substituted molecules will be discussed. $$\begin{array}{l@{\hspace{30pt}}l} \multicolumn{1}{c}{r_e = 1.1946 {\AA}} &\multicolumn{1}{c}{\theta_e = 113.89^{\circ}} \\ f_{rr} = 10.9061 \mbox{ md/{\AA}} &f_{rrr} = - 90.9110 \mbox{ md/{\AA}}^2\\ f_{rr^{\prime}} = 1.9354 \mbox{ md{\AA}} &f_{rrr^{\prime}} = -3.2048\mbox{ md/{\AA}}^2\\ f_{r\theta} = 0.4819 \mbox{ md/rad} & f_{rr\theta} = 0.1439 \mbox{ md/{\AA} rad}\\ f_{\theta\theta} = 1.6101 \mbox{ md {\AA}/rad}^2 & f_{rr^{\prime} \theta} = -1.2355 \mbox{ md/{\AA} rad}\\ & f_{r\theta\theta} = -2.2691 \mbox{ md/rad}^2 \\ & f_{\theta\theta\theta} = -2.1170 \mbox{ md\AA/rad}^3 \end{array}$$ $$\begin{array}{l} f_{rrrr} = 526.3816 \mbox{ md/{\AA}}^3\\ f_{rrrr^{\prime}} = 5.4794\mbox{ md /{\AA}}^3\\ f_{rrr^{\prime} r [FIGURE]
Description
'} = - 17.6740 \mbox{ md/{\AA}}^3\\ f_{rr\theta\theta} = - 5.3020 \mbox{ md/{\AA}rad}^2\\ f_{rr'^\theta\theta} = 3.4230 \mbox{ md/{\AA}rad}^2\\ f_{\theta\theta\theta\theta} = 6.0220 \mbox{ md {\AA}/rad}^4 \end{array}$$ Using these constants, the file fit to N = 2, K = 2 term values is as follows: \centerline{F(N =2,K = 2} \centerline{\begin{tabular}{lll}\hline v$_2$ &obs. &calc. \\ \hline 0 &32.812 $cm^{-1}$ &32.814 $cm^{-1}$\\ 1 &783.938 &783.958\\ 2 &1534.238 &1534.232\\ 3 &2283.597 &2283.604\\ \hline\end{tabular}} The force constants are stated to the number of figures needed to reproduce the calculated therm values and do not reflect relative accuracy. $^1$A. R. Hoy and P. R. Bunker, J.Mol. Spectrosc.52, 439 (1974)s
Author Institution: Department of Chemistry, University of Western Ontario
Author Institution: Department of Chemistry, University of Western Ontario