Universal functions for estimating total vibration-rotation band absorptance—I. Linear molecules and spherical tops

We estimate total band absorptances and their derivatives for nonoverlapping lines of vibration-rotation bands for linear molecules and spherical tops. We use universal functions obtained by replacing the sums of line contributions by integrals over the rotational quantum numbers. An optical path is introduced for the total band. Only general information is utilized on vibrational transitions and line shapes. Power and asymptotic series have been obtained for Doppler and Lorentz line shapes. For a linear molecule and the Lorentz shape, approximate formulae have been derived for the universal functions.