# ANHARMONIC POTENTIAL CONSTANTS FOR NITROGEN DIOXIDE

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 Title: ANHARMONIC POTENTIAL CONSTANTS FOR NITROGEN DIOXIDE Creators: Hardwick, J. L.; Brand, J. C. D. Issue Date: 1975 Publisher: 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 URI: http://hdl.handle.net/1811/9288 Other Identifiers: 1975-MG-11