Isotope effects on Franck-Condon factors: Intensity distribution in the rotational structure of the O₂ Schumann-Runge and the H₂ and D₂ Lyman band systems

The distribution of intensity between rotational lines in a vibrational band for electronic transitions of diatomic molecules is considered by assuming that: (a) the transition probability to each vibration-rotation level is determined by the Franck-Condon factor and by the line strength, which is that of a symmetric top as represented by the Hönl-London factor. The variation of the electronic transition moment with inter-nuclear distance is taken into account by using the r-centroid approximation, (b) the distribution of rotational levels in the initial state is given by the Boltzmann factor and by the statistical weight due to the nuclear spin, (c) the line shape is Lorentzian. A computer-plot of the predicted intensity distribution for the (5, 0) band of the Schumann-Runge system of ¹⁶O₂ and of ¹⁸O₂ was found to agree well with the measured absorption spectra of normal and isotopic oxygen gas. The method has been applied to prediction of the hitherto unknown absorption of the (0, 0) to (2, 0) bands of the Lyman system of H₂. The Franck-Condon factors for both the O₂ Schumann-Runge and the H₂ Lyman system were found to vary considerably with rotational quantum number.