Predicting S ₁ TDDFT Energies from ZINDO Calculations Using Message-Passing ΔML with Electronically Informed Descriptors

We present a machine learning approach (ΔML) capable of enhancing the accuracy of semiempirical excited-state energy calculations to a level close to that of Time-Dependent Density Functional Theory (TDDFT). Using a data set of 7600 organic π-conjugated molecules calculated at the ZINDO and M06-2X/3-21G* TDDFT computational levels, we trained a set of models to learn the systematic errors of the low-level method and correct it toward higher-level accuracy values. The best performing model improved the correlation of ZINDO S₁ energy predictions from 0.77 to 0.96 on a 9500 molecule test set of TDDFT target energies. Our ΔML-ZINDO model presents a negligible additional cost (∼2 ms per molecule) to a standard ZINDO calculation (∼2 s per molecule), enabling the computational screening of large data sets of molecules. Critical to the performance of the model is the AttentiveFP Message-Passing Neural Network with added electronic information derived from ZINDO calculations such as particle-hole densities. We also investigate the utility of the Morgan fingerprint and a novel descriptor designed to capture the electronic structure of molecules: a molecular orbital-weighted radial distribution function. The ΔML framework is retrainable to other low- and high-level calculation pairs, achieving an improvement in correlation from 0.88 to 0.99 on a test set of 24,000 molecules from the QCDGE data set, when mapping ZINDO to ωB97X-D/6-31G* energies. We also adapt ΔML-ZINDO for S₁ oscillator strength prediction, improving ZINDO predictions from a correlation of 0.524 to 0.839 on our M06-2X/3-21G* target test set, thus enabling the identification of emissive molecules.