We develop the basic formalism of a far-wing line shape theory that satisfies the detailed balance principle. For molecular systems of interest, e.g., CO2 –Ar at room temperature or higher, there are many individual vibration–rotational lines in a given band and many bands in the spectrum. In such cases, one must make additional approximations in order to carry out accurate calculations of the absorption coefficient using a reasonable amount of computer time. In the present paper, we discuss two such simplifications: the frequency detuning approximation of the line-coupling functions and the band-average approximation. We then apply the theory to a calculation of the far-wing absorption of the ν3 band of CO2 perturbed by Ar, successively including the effects of more lines in the calculations by increasing J max from 40 to 108. From the results of this work, we find that the frequency detuning approximation is good only for frequencies of interest far from the band center. In addition, we find that contrary to previous assertions of the adequacy of the first-order band-average approximation, the higher-order terms are significant. To a good approximation these can be incorporated by introducing a frequency shift in the first-order results so that extensive additional calculations are not required.
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