A Temperature Variation Method to Assist in Vibrational Analyses of Complex Molecular Spectra

A temperature variation method of determining the initial (lower) vibrational levels of the absorption bands of an electronic band system of a polyatomic molecule is presented. The determination is made from photometric measurements of the absorption at two temperatures not widely separated. Such absorption tube lengths are used that the absorption is everywhere much less than 100 percent in the bands to be studied. That variations in total absorption for a band may be measurable, the method is restricted to spectra in which the rotation lines are fairly broad compared with the intervals between them or else are very closely spaced. In such cases the rotational structure is blotted out on the photographic plate by the lack of resolution of the spectrograph and the exponential absorption law may be assumed in comparing absorption intensities at the two temperatures. A criterion is laid down for the applicability of the method in any instance. An equation is developed to give the heights (in ${\mathrm{cm}}^{-1\mathrm{}}$) of the excited vibrational levels of the normal electronic state involved in the various transitions, above that of some arbitrarily selected band of a group, as follows: ${log}_{10\frac{\rho b}{\rho a}}=-0.623\mathrm{}\left(\frac{1}{T_2}-\frac{1}{T_1}\right) {(G_b-G_a)}^{\prime \prime }.$ The determination of the heights ${(G_b-G_a)}^{\prime \prime }$ in ${\mathrm{cm}}^{-1\mathrm{}}$ comes from the two absolute temperatures and the ratio $\frac{\rho b}{\rho a}$ of the heights of the absorption peaks on the two micro-photometer traces.