Reducing Non-Linearity in Spectral Evaluation via a Modified Lorentz–Lorenz Relation

Abstract

Quantitative infrared spectroscopy of liquids often assumes linear Beer–Lambert behavior, although local-field interactions and dipole–dipole coupling introduce intrinsic nonlinearities. We investigate whether a modified Lorentz–Lorenz relation, motivated by electromagnetic theory, can reduce these deviations and restore approximate linearity in binary mixtures. Using benzene–toluene and benzene–cyclohexane as model systems, we evaluate linearity through RMSE metrics, hybrid 2D-correlation analysis, asynchronous residual sums of squares, and complex-valued classical least squares (CLS) regression. While correlation-based measures provide qualitative insights, they fail to reliably identify optimal linearization parameters. In contrast, CLS in the Lorentz–Lorenz–transformed domain, particularly with systematic-error correction, yields clear minima and substantially improves prediction accuracy, reducing mean absolute errors by more than a factor of three relative to the Beer–Lambert domain. These results demonstrate that the modified Lorentz–Lorenz transformation provides a physics-informed chemometric domain in which spectral mixing becomes more linear. The approach suggests extending inverse least square regression, principal component regression, and partial least squares regression into this domain to further enhance quantitative mixture analysis.

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