Δ-Machine learning for quantum chemistry prediction of solution-phase molecular properties at the ground and excited states

Due to the limitation of solvent models, quantum chemistry calculation of solution-phase molecular properties often deviates from experimental measurements. Recently, Δ-machine learning (Δ-ML) was shown to be a promising approach to correcting errors in the quantum chemistry calculation of solvated molecules. However, this approach's applicability to different molecular properties and its performance in various cases are still unknown. In this work, we tested the performance of Δ-ML in correcting redox potential and absorption energy calculations using four types of input descriptors and various ML methods. We sought to understand the dependence of Δ-ML performance on the property to predict the quantum chemistry method, the data set distribution/size, the type of input feature, and the feature selection techniques. We found that Δ-ML can effectively correct the errors in redox potentials calculated using density functional theory (DFT) and absorption energies calculated by time-dependent DFT. For both properties, the Δ-ML-corrected results showed less sensitivity to the DFT functional choice than the raw results. The optimal input descriptor depends on the property, regardless of the specific ML method used. The solvent-solute descriptor (SS) is the best for redox potential, whereas the combined molecular fingerprint (cFP) is the best for absorption energy. A detailed analysis of the feature space and the physical foundation of different descriptors well explained these observations. Feature selection did not further improve the Δ-ML performance. Finally, we analyzed the limitation of our Δ-ML solvent effect approach in data sets with molecules of varying degrees of electronic structure errors.