Factorized vs. Normalized Spectra: Comparative Spectrophotometric Approaches for Enhancing the Resolution of Zero-Order Absorption Spectra of Olanzapine and Fluoxetine in Mixtures

Simple, accurate and precise UV spectrophotometric methods were developed and validated for simultaneous determination of olanzapine (OLA) and fluoxetine (FLU) in both bulk powders and combined pharmaceutical formulations, without any prior separation steps. The methods employed advanced mathematical manipulation techniques using both the Constant Multiplication Method (CM) coupled with Spectrum Subtraction (SS) and the Factorized Zero Order Method (FZM) also coupled with SS. These approaches utilized normalized and factorized spectra, respectively, to resolve the overlapping spectral profiles of the two drugs. Unlike conventional methods in literature like derivative spectrophotometry, our approach enabled the extraction of each component in its original zero-order form, exhibiting spectral features identical to those of pure standards, which enhances accuracy and precision. A direct comparative evaluation of CM–SS and FZM–SS is presented, highlighting their respective analytical merits. The proposed methods demonstrated linearity over concentration ranges of 1.5–14 µg/mL, and 3.5–35 µg/mL for OLA and FLU, respectively. The proposed methods were successfully applied for the simultaneous determination of OLA and FLU in synthetic mixtures and in their combined dosage form with very good accuracy and precision. Furthermore, the environmental and practical merits of the methods were evaluated through the principles of Green Analytical Chemistry (GAC) and White Analytical Chemistry (WAC). The greenness assessment of the proposed spectrophotometric method was evaluated by the Analytical Greenness Metric (AGREE). The overall method performance, including validation efficiency, ecological impact, and practicality, was systematically evaluated using the RGB-based WAC approach.