A new parameter has been added to the compilation of atmospheric molecular spectroscopic data. This compilation contains fundamental parameters required for simulations of transmission and radiance calculations of molecular absorption properties due to rotational and vibration-rotation transitions. The new quantity is the weighted transition moment squared which is independent of both isotopic abundance and temperature. It fulfills a needed niche for upper atmospheric non-local thermodynamic equilibrium calculations in that it is directly proportional to the Einstein coefficients. In this paper, we review the development of this quantity as well as present relationships between the Einstein coefficients and oscillator strengths to the transition moment and other parameters on the compilation.