EAC-Net: Predicting Real-Space Charge Density via Equivariant Atomic Contributions.

Charge density is central to density functional theory (DFT), and deep learning charge density has emerged as a promising approach for accelerating electronic-structure calculations. Existing approaches mainly follow two paradigms: methods that predict coefficients of predefined atom-centered basis functions, which embed strong physical priors but restrict representational flexibility, and methods that directly predict values on real-space grids, which are highly expressive yet largely lack physical structure and efficiency. Here, we introduce the Equivariant Atomic Contribution Network (EAC-Net), which bridges these paradigms by decomposing the total charge density into symmetry-consistent, atom-centered contributions coupled to real space rather than directly predicting the full density on a grid or on a basis. This design enables both high accuracy and efficient training with errors typically below 1% across the periodic table and strong generalization to diverse chemical environments. Moreover, the embedded physical prior yields a natural and consistent atomic decomposition of the charge density, producing atomic charges that align with chemical intuition. Together, EAC-Net provides an accurate, efficient, and physically grounded framework for charge density prediction.