Accelerated Mapping of Electronic Density of States Patterns of Metallic Nanoparticles via Machine-Learning

Within first-principles density functional theory (DFT) frameworks, accurate but fast prediction of electronic structures of nanoparticles (NPs) remains challenging. Herein, we propose a machine-learning architecture to rapidly but reasonably predict electronic density of states (DOS) patterns of metallic NPs via a combination of principal component analysis (PCA) and the crystal graph convolutional neural network (CGCNN). By applying PCA, one can convert a mathematically high-dimensional DOS image to a low-dimensional vector. The CGCNN plays a key role in reflecting the effects of local atomic structures on the DOS patterns of NPs with only a few of material features (e.g., melting temperature, the number of d electrons, and atomic radius) that are easily obtained from a periodic table. The PCA-CGCNN model is applicable for all pure and bimetallic NPs, in which a handful DOS training sets that are easily obtained with the typical DFT method, such as bulk, slab, and small-sized NPs, are considered. Although there is a small loss of accuracy with the PCA-CGCNN method compared to DFT calculations, the prediction speed is much faster than that of DFT methods and is not nearly as affected by the system sizes of NPs. Our approach not only can be immediately applied to predict electronic structures of actual nanometer scaled NPs to be experimentally synthesized, but also be used to explore correlations between atomic structures and other spectrum image data of the materials (e.g., X-ray diffraction, X-ray photoelectron spectroscopy, and Raman spectroscopy).