7 The second overtone, 400-1000 K

We started with computing the spectra from 600 to 1000 K. We used the "ad hoc'' (unpublished) program written for this band and described by Borysow et al. (1997). Since no dipole information was available then, the simplest model has been assumed. Only the quadrupole induced terms were accounted for and the RRY intermolecular potential was used. The comparison of the CIA spectra using this model, with those using the full quantum mechanical approach (Borysow et al. 2001) showed that the "ad hoc'' and the most accurate spectra were surprisingly similar to each other. We therefore found it justifiable to use the previous model as a start, and only scale it in accordance with the more accurate results of Borysow et al. (2001), rather than performing a completely new and very time consuming full quantum mechanical computation.

We compared first the results of the old (1997) "ad hoc'' program with the far wing of the quantum mechanical results, in the spectral region where the second overtone is important (the maximum appears around 12 000 cm^-1). We noticed that the shape of the two spectra is quite similar, but the spectra we produced need to be rescaled by a common factor. It was not a surprise, because the spectra assumed only the 2023 and 0223 terms whereas there are more terms to account for.

After the rescaling there was still a difference in the slope of the very far wing. We adjusted the shape of the slope to match that of the quantum mechanical results. We found this to be the most reliable simple procedure.

Next, we addressed the data for 400 and 500 K. In principle, those data were available from the existing FORTRAN program (Borysow et al. 2000) which works up to 500 K. However, we found out that the width of the spectral lines does not match with that of the high temperature data. We therefore convoluted the spectra with a Gaussian weight function with a halfwidth equal to 40 cm^-1 and 50 cm^-1 at 400 and 500 K, respectively. Next, since the far wings were not suitable for use at very high wavenumbers, the slope of the far wings was adjusted accordingly, to match the spectra at higher temperatures.