Machine learning on frontier orbital energy of atomically precise gold nanoclusters

The highly promising application of atomically precise gold nanoclusters (Au NCs, protected by organic ligands such as thiolate, phosphate, etc.) in electrochemical and photochemical catalysis has highlighted the importance of accurately predicting their electronic states, which has been challenging because of the high experimental and computational cost. In this study, a machine learning model based on interpretable automated feature engineering was developed. Starting with the 99 data points of Au NCs, 227 candidate parameters were first screened by a bi-directional stepwise regression, associated with the Kolmogorov–Arnold network model, to improve the prediction performance. With this suite of codes and using only 79 data points as the training set and 4 key descriptors, the mean average error (MAE) of the HOMO, LUMO, and HOMO–LUMO gap of the testing set (20 data points) reaches 0.17, 0.27, and 0.16 eV, respectively. The model could also be used to generalize the oxidation potential (OP) of the target clusters, with an MAE of 0.20 V. In particular, four dominant physicochemical parameters for HOMO/LUMO/HOMO–LUMO gap/OP were identified. The number of cluster charges (NC) and average Au–Au coordination numbers (CNAu–Au) are consistently present in the four filtered features, indicating that these parameters are critical for determining the electronic structure of Au NCs. Overall, the present study demonstrates that a small set of key structural descriptors could enable a cost-efficient strategy to accurately predict the electronic structure of Au NCs.