Interpretable machine learning integrated with TD-DFT descriptors and SHAP analysis for predicting the maximum absorption wavelength of azo dyes

The maximum absorption wavelength (<i>λ</i> _max) represents a key property determining the application performance of azo dyes, and accurate prediction of <i>λ</i> _max is of paramount importance for accelerating the rational design of novel dye molecules. Existing prediction models exhibit significant limitations in terms of prediction accuracy and chemical interpretability. In this work, we propose an innovative prediction framework for <i>λ</i> _max of azo dyes by integrating Gaussian Process Regression (GPR) with key molecular descriptors derived from time-dependent density functional theory (TD-DFT) calculations. Results indicate that the coefficient of determination (<i>R</i> ²) for leave-one-out cross-validation (LOOCV) was 0.83, and that for the independent test set was 0.74. According to SHAP analysis, the S₀ → S₁ transition energy exhibits a negative correlation with <i>λ</i> _max (maximum absorption wavelength), while the concurrent elevation of HOMO and LUMO energies induces a red-shift in <i>λ</i> _max. Notably, the number of sulfur atoms in the <i>R</i> substituent shows a positive correlation with <i>λ</i> _max. Furthermore, a high-throughput screening strategy was employed to identify 21 azo molecules with relatively large <i>λ</i> _max values from 14 376 virtual samples. The predicted <i>λ</i> _max of these identified molecules is expected to undergo a red-shift relative to the baseline maximum <i>λ</i> _max of 650 nm in the original dataset. This study presents a straightforward approach for the discovery of azo dyes with extended <i>λ</i> _max, providing a practical reference for the targeted design of such functional materials.