Predicting S1 TDDFT energies from ZINDO calculations using Message-Passing Delta-ML with electronically-informed descriptors

We present a machine learning approach capable of enhancing the accuracy of semiempirical excited state energies calculation (ZINDO in this case) with respect to reference time-dependent DFT (TDDFT) calculations. Using a dataset of 10,000 organic pi-conjugated molecules calculated at the ZINDO and M06-2X/3-21G* TDDFT computational levels, we trained a model to learn the systematic errors of the low-level method and correct it towards higher-level accuracy values. The best performing model improved the correlation of ZINDO data from 0.75 to 0.95 on a test set of S1 TDDFT target energies, which is consistent with the correlation between TDDFT and experiment. Our model presents a negligible additional computational cost to ZINDO (0.02 ms per molecule), enabling the computational screening of large datasets of molecules using Delta-ML corrected ZINDO calculations. 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 from the transition density matrix. We also investigate the utility of the Morgan fingerprint and a newly introduced descriptor for the electronic structure of molecules based on the radial distribution function weighted by Molecular Orbital coefficients. The possible applications of this approach in virtual screening projects are discussed.