How is the radiative efficiency of a given gas (like a given CFC) analytically calculated?
Radiative efficiency is the radiative forcing per unit change in halocarbon mixing ratio.  Radiative Efficiency assumes that the Radiative Forcing is linear in mixing ratio—this is normally appropriate in the case of small perturbations in mixing ratio about current concentrations and is also appropriate for CFCs.  To calculate it requires a radiative transfer model, which includes both analytical and theoretical contributions.

The diagram shown in Hodnebrog et al.: "Global warming potentials and radiative efficiencies of halocarbons and related compounds: A comprehensive review" in Reviews of Geophysics
( http://dx.doi.org/10.1002/rog.20013 ) explains how radiative efficiency is calculated and is pasted below: