Accelerated mapping of electronic density of states patterns of metallic nanoparticles via machine-learning

Within first-principles density functional theory (DFT) frameworks, it is challenging to predict the electronic structures of nanoparticles (NPs) accurately but fast. Herein, a machine-learning architecture is proposed 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). With the PCA, a mathematically high-dimensional DOS image can be converted 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 that are easily extracted 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 are considered. The PCA-CGCNN model predicts the R(2) value to be 0.85 or higher for Au pure NPs and 0.77 or higher for Au@Pt core@shell bimetallic NPs, respectively, in which the values are for the test sets. Although the PCA-CGCNN method showed a small loss of accuracy when compared with DFT calculations, the prediction time takes just ~ 160 s irrespective of the NP size in contrast to DFT method, for example, 13,000 times faster than the DFT method for Pt(147). 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).