Exploring the limits of cryospectroscopy: Least-squares based approaches for analyzing the self-association of HCl

• Polynomials are least-squares fitted to the experimental data to study the self-association in cryosolutions.
• The appropriate polynomial degree is chosen using the AIC and BIC information criteria.
• As a prototype of self-association, HCl is used for validation.
• The methodology should allow other self-associating systems to be analyzed with higher accuracy than before.

To rationalize the concentration dependent behavior observed for a large spectral data set of HCl recorded in liquid argon, least-squares based numerical methods are developed and validated. In these methods, for each wavenumber a polynomial is used to mimic the relation between monomer concentrations and measured absorbances. Least-squares fitting of higher degree polynomials tends to overfit and thus leads to compensation effects where a contribution due to one species is compensated for by a negative contribution of another. The compensation effects are corrected for by carefully analyzing, using AIC and BIC information criteria, the differences observed between consecutive fittings when the degree of the polynomial model is systematically increased, and by introducing constraints prohibiting negative absorbances to occur for the monomer or for one of the oligomers. The method developed should allow other, more complicated self-associating systems to be analyzed with a much higher accuracy than before.

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