GTAttn-XC: Physically constrained attention for nonlocal density functionals

Abstract

Machine-learning-based nonlocal density functional approximations have demonstrated substantial potential in advancing the applicability of electronic density functional theory. However, most existing approaches rely on handcrafted local or nonlocal descriptors, which limits their scalability in modeling long-range electronic responses. In this work, we propose a novel exchange–correlation functional approximation model—GTAttn-XC, which introduces a learnable attention mechanism to enable unsupervised modeling of long-range electronic responses. By coupling a multiscale real-space grid graph representation with attention operators, the proposed method achieves a unified description of local accuracy and nonlocal interactions, while avoiding the computational overhead associated with explicit high-order correlation terms. Evaluations on multiple benchmark datasets, including MGCDB84, demonstrate that the model consistently delivers high accuracy across a range of tasks, such as weak interactions, reaction energies, barrier heights, and thermochemical energies. These results establish a new technical pathway toward high-accuracy nonlocal exchange–correlation approximations.