Physical Significance of Descriptors to Predict the Band Center of High-Entropy Nanoalloys

The band center of d orbitals (d-band center) has been widely used as an effective descriptor for analyzing material properties. However, in high-entropy nanoalloys, the diverse atomic environments present challenges in systematically exploring all possible combinations. Due to computational resource limitations, generating a sufficient number of samples is infeasible. Consequently, the d-band center should be treated as a response variable in machine-learning models. We calculated the d-band center for individual atoms and applied supervised learning techniques to identify key factors influencing its behavior. While several factors were identified, their physical significance in predicting d-band centers remained unclear. To address this issue, we incorporated various interatomic distance terms as descriptors, along with element-based coordination numbers (ECN). The resulting model closely resembled the overlap integral of the Slater-type orbital, and the regression coefficients of the ECN exhibited sensitivity to the effective principal quantum number and nuclear charge. Understanding the physical significance of these descriptors is crucial for improving property predictions and facilitating data collection on novel materials.