Compact Table for the Publication of Infrared Spectra That are Quantitative on Both Intensity and Wavenumber Axes

Abstract

A Compact Table format is presented for the publication of infrared spectra that are quantitative on both intensity and wavenumber axes. The format is illustrated with a molar absorption coefficient spectrum, E_m(ν˜) vs. ν˜, and with infrared real and imaginary refractive index spectra, n(ν˜) vs. ν˜ and k(ν˜) vs. ν˜, respectively. The algorithm consists of two steps: first, the number of spectral points is reduced by using larger wavenumber spacings than appear in the original spectrum; second, the resulting spectral points are presented in a compressed table format. The Compact Table is about one tenth the size required for the original spectrum to be presented in a conventional XY table. The essential criterion for increasing the wavenumber spacing is that it must be possible to recover the original spectrum by interpolation to an accuracy better than that of the original spectrum. Nearly all the recovered imaginary refractive index and molar absorption coefficient values are within 1% of the original values, and for each quantity the average of the magnitudes of the accuracies of recovery is 0.2%. The real refractive index spectrum is most accurately recovered by Kramers-Kronig transformation of the recovered imaginary refractive index spectrum. Nearly all the recovered real refractive index values are within 0.02% of the original values, and the average of the magnitudes of the accuracies of recovery is 0.005%. The real and imaginary infrared dielectric constant spectra, ɛ′(ν˜) vs. ν˜ and ɛ″(ν˜) vs. ν˜, can be calculated from the recovered data with an accuracy in ɛ′ that is about one half of that of the real refractive index and an accuracy in ɛ″ that is approximately that of the imaginary refractive index. The detailed method is outlined and is applied to infrared intensities of chlorobenzene. Computer programs are presented for the construction of the Compact Table and for the recovery of the full spectrum from the tabulated information.