Understanding and Employing (Non-)Linearities in Attenuated Total Reflection Spectroscopy

When Beer's law is interpreted through electromagnetic theory, it becomes clear that assuming a linear relationship between molar concentration and the imaginary part of the dielectric function is more accurate than using the absorption index function. A similar relationship holds true for attenuated total reflection (ATR) absorbance. When the negative logarithm of the reflectance is expanded into a series and truncated after the linear term, the approximation proves more accurate when based on the imaginary part of the dielectric function. Moreover, ATR correction schemes that utilize the low absorption approximation or the Bertie-Eysel formalism with this imaginary part, rather than the absorption index, tend to converge more quickly and provide more accurate results, particularly for stronger oscillators across an extended range of oscillator strength. Therefore, correction schemes for ATR spectra should prioritize the imaginary part of the dielectric function rather than the absorption index function when analyzing scalar and isotropic media.