(84a) Machine Learning with Weighted-Soap to Efficiently Predict Electron Densities

We address the computational complexity limitations of density functional theory (DFT) in predicting electron densities for materials chemistry applications. We have developed a deep learning formalism, the Deep-learning Charge Density Prediction (DeepCDP) method, which can be used to generate 3D charge density maps using only atomic positions as input data. Our method is trained on DFT electron densities for small systems and can predict densities for arbitrarily large systems. We used weighted-Smooth Overlap of Atomic Orbitals (w-SOAP) descriptors to fingerprint atomic environments and map this information onto their electron densities on a grid-point basis. Our DeepCDP formalism was tested for both molecular and periodic systems, achieving electron density prediction accuracies in excess of 99% for large system sizes (>900 atoms) using models trained on small systems (≤10 atoms). DeepCDP also achieves similar accuracies for both charged and uncharged systems, making it possible to address phenomena like proton diffusion on large sheets of functionalized graphene over time scales sufficient to estimate proton diffusion barriers with DFT accuracy. Additionally, the ability of DeepCDP's to exploit the locality of the electron-electron interactions allows us to bypass the memory inefficiencies of common DFT implementation schemes, resulting in rapid and accurate electron density predictions for arbitrarily large systems. This development has significant implications for materials chemistry research and paves the way for further advancements in computational chemistry.