Differentiable Optimization in Plane-Wave Density Functional Theory for Solid States

Plane-wave density functional theory is a computational quantum mechanical modeling method used to investigate the electronic structure of solids. It employs plane-waves as the basis set for representing electronic wave functions and leverages density functional theory to compute the electronic structure properties of many-body systems. Traditionally, the Self-Consistent Field (SCF) method is predominantly adopted for optimization in current DFT computations. However, this method encounters notable convergence and computational challenges, and its iterative nature obstructs the incorporation of emergent deep learning enhancements. To address these challenges, we introduce a fully differentiable optimization method tailored to resolve the intrinsic challenges associated with the optimization of plane-wave density functional methods. This methodology includes a direct total energy minimization approach for solving Kohn-Sham equations in periodic crystalline systems, which is coherent with deep learning infrastructures. The efficacy of our approach is illustrated through its two applications in solid-state physics: electron band structure prediction and geometry optimization. Our enhancements potentially pave the way for various gradient-based applications within deep learning paradigms in solid-state physics, extending the boundaries of material innovation and design. We illustrate the utility and diverse applications of our method on real crystal structures and compare its effectiveness with several established SCF-based packages, demonstrating its accuracy and robust convergence property.