The Beta Bands of Nitric Oxide. I. Measurements and Quantum Analysis

Band structure and wave-number data for band lines. Using an active nitrogen source, the $\ensuremath{\beta}$ bands of NO included in the region of 2300 to 5300A have been photographed in the second order of a 21-ft. Rowland concave grating. Each complete band consists of two sub-bands with a $P$ and an $R$ branch of the ordinary type and also a very weak $Q$ branch. The latter is relatively more intense in the lower frequency sub-band. Here there are four missing lines in the otherwise continuous $P\ensuremath{-}R$ series, while there are two in the higher frequency sub-band. The lines of the latter are narrow doublets superficially resembling those of the violet CN bands. The six branches for each of eighteen bands have been measured, and wave-numbers are tabulated for 20 to 30 lines in the $P$ and $R$ branches, and for the few visible members of the $Q$ branches. The bands measured include nine of the strong ${n}^{\ensuremath{'}}=0$ progression (${n}^{\ensuremath{'}\ensuremath{'}}=4 \mathrm{to} 12$), three of ${n}^{\ensuremath{'}}=1({n}^{\ensuremath{'}\ensuremath{'}}=6, 11, 13)$, four of ${n}^{\ensuremath{'}}=2({n}^{\ensuremath{'}\ensuremath{'}}=9, 13, 14, 15)$, and two of ${n}^{\ensuremath{'}}=3({n}^{\ensuremath{'}\ensuremath{'}}=8, 16)$.Isolation and representation of spectral terms. Combinations involving the $P$ and $R$ branches are found to hold, and show the existence of four different sets of rotational terms, two (one for each sub-band) in the initial electronic state and similarly two in the final state. For low values of $j$ the rotational terms in all four cases are representable by $F(j)=B({j}^{2}\ensuremath{-}{\ensuremath{\sigma}}^{2})$. From a consideration of the missing lines, the observed transitions are classified as $^{2}P_{1}\ensuremath{\rightarrow}^{2}P_{1}$. with ${\ensuremath{\sigma}}^{\ensuremath{'}}={\ensuremath{\sigma}}^{\ensuremath{'}\ensuremath{'}}=\frac{1}{2}$, for the higher frequency system, and $^{2}P_{2}\ensuremath{\rightarrow}^{2}P_{2}$, ${\ensuremath{\sigma}}^{\ensuremath{'}}={\ensuremath{\sigma}}^{\ensuremath{'}\ensuremath{'}}=\frac{3}{2}$, for the lower frequency system. A table is given of the weighted mean values of ${\ensuremath{\Delta}}_{2}F$ in the observed vibrational states of the initial and final electronic levels, and another of the empirical coefficients in analytical expressions for ${\ensuremath{\Delta}}_{2}F(j)$ and $F(j)$. Certain anomalies in the form of the latter in particular the appreciable difference in $B$ for the components of a doublet, are shown to be a necessary consequence of Hund's theory of molecular electronic states as applied quantitatively to doublet states by E. C. Kemble. These effects are found to be larger in the initial state, thus showing, according to the theory, that the doublet separation must be smaller here than in the final state. Equations for the band origins are obtained (Eqs. 8 of the text) which permit a representation of the vibrational energy levels; in these, cubic and biquadratic terms are both definitely required, and when they are included the observed values are reproduced with a mean error of 0.03 ${\mathrm{cm}}^{\ensuremath{-}1}$.Constants of the nitric oxide molecule. The moment of inertia ${I}_{0}$ and the internuclear distance ${r}_{0}$ for the vibrationless molecules are evaluated as ${{I}_{0}}^{\ensuremath{'}}=(24.80\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}$ gr ${\mathrm{cm}}^{2}$, ${{I}_{0}}^{\ensuremath{'}\ensuremath{'}}=(16.30\ifmmode\pm\else\textpm\fi{}0.02)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40}$, ${{r}_{0}}^{\ensuremath{'}}=1.418\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$ cm, ${{r}_{0}}^{\ensuremath{'}\ensuremath{'}}=1.150\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}$. $B$, the coefficient of ${j}^{2}$ in $F(j)$, is represented within experimental error by the linear relation $B={B}_{0}\ensuremath{-}\ensuremath{\alpha}n$, where for the $^{2}P_{1}$ bands ${{B}_{0}}^{\ensuremath{'}}=1.0704$, ${{B}_{0}}^{\ensuremath{'}\ensuremath{'}}=1.6754$, ${\ensuremath{\alpha}}^{\ensuremath{'}}=0.01162$, ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}=0.01783$, and for the $^{2}P_{2}$ bands ${{B}_{0}}^{\ensuremath{'}}=1.1678$, ${{B}_{0}}^{\ensuremath{'}\ensuremath{'}}=1.7239$, ${\ensuremath{\alpha}}^{\ensuremath{'}}=0.01892$, ${\ensuremath{\alpha}}^{\ensuremath{'}\ensuremath{'}}=0.01866$. The $\ensuremath{\beta}$ bands exhibit a longer series of ${n}^{\ensuremath{'}\ensuremath{'}}$ values than any system yet investigated in respect to the variation of $B$ with $n$. Equations are given which permit a quantitative representation of the frequencies of all observed lines (Eqs. (2), (8), and (6) in conjunction with Table IV). From the equations for band-origins, the following quantities are obtained for the vibration frequency ${\ensuremath{\omega}}_{0}$ for infinitesimal amplitudes, $^{2}P_{1}$ bands, ${{\ensuremath{\omega}}_{0}}^{\ensuremath{'}}=1029.43$ ${\mathrm{cm}}^{\ensuremath{-}1}$, ${{\ensuremath{\omega}}_{0}}^{\ensuremath{'}\ensuremath{'}}=1892.12$, ${x}^{\ensuremath{'}}{{\ensuremath{\omega}}_{0}}^{\ensuremath{'}}=7.460$, ${x}^{\ensuremath{'}\ensuremath{'}}{{\ensuremath{\omega}}_{0}}^{\ensuremath{'}\ensuremath{'}}=14.424$; $^{2}P_{2}$ bands ${{\ensuremath{\omega}}_{0}}^{\ensuremath{'}}=1030.88$, ${{\ensuremath{\omega}}_{0}}^{\ensuremath{'}\ensuremath{'}}=1891.98$, ${x}^{\ensuremath{'}}{{\ensuremath{\omega}}_{0}}^{\ensuremath{'}}=7.455$, ${x}^{\ensuremath{'}\ensuremath{'}}{{\ensuremath{\omega}}_{0}}^{\ensuremath{'}\ensuremath{'}}=14.454$. The change of ${\ensuremath{\omega}}_{0}$ (and also of ${r}_{0}$ and ${I}_{0}$) during the emission is exceptionally great. Since the final state of the NO $\ensuremath{\beta}$ bands is the normal state of nitric oxide, the above values of ${{I}_{0}}^{\ensuremath{'}\ensuremath{'}}$, ${{r}_{0}}^{\ensuremath{'}\ensuremath{'}}$, ${{\ensuremath{\omega}}_{0}}^{\ensuremath{'}\ensuremath{'}}$, etc., apply to this state. An integration of the vibration frequency curve for the final state to the point of dissociation is carried out to determine the heat of dissociation.Electronic states and relation to other bands. The doublet separation (for the rotationless molecule) in the initial $^{2}P$ state is 32.9 ${\mathrm{cm}}^{\ensuremath{-}1}$, if that in the final $^{2}P$ state is taken as 124.4 in accordance with Frl. Guillery's data on the $\ensuremath{\gamma}$("third positive nitrogen") bands of NO. Only the difference between these (91.54 ${\mathrm{cm}}^{\ensuremath{-}1}$) can be accurately found from the $\ensuremath{\beta}$ bands. (See Fig. 1). The $\ensuremath{\gamma}$ bands have the final doublet level in common with the $\ensuremath{\beta}$ bands; hence all constants derived for the final state of the $\ensuremath{\beta}$ bands apply equally well to that of the $\ensuremath{\gamma}$ bands. The ultra-violet ${\mathrm{O}}_{2}^{+}$ bands and certain SiN bands, whose structure is like that of the $\mathrm{NO}\ensuremath{\beta}$ bands, are probably also $^{2}P\ensuremath{\rightarrow}^{2}P$ transitions.