Automatic Differentiation for Orbital-Free Density Functional Theory

Abstract: Differentiable programming has facilitated numerous methodological advances in scientific computing. Physics engines supporting automatic differentiation have simpler code, accelerating the development process and reducing the maintenance burden. Furthermore, fully-differentiable simulation tools enable direct evaluation of challenging derivatives - including those directly related to properties measurable by experiment - that are conventionally computed with finite difference methods. Here, we investigate automatic differentiation in the context of orbital-free density functional theory (OFDFT) simulations of materials, introducing PROFESS-AD. Its automatic evaluation of properties derived from first derivatives, including functional potentials, forces, and stresses, facilitates the development and testing of new density functionals, while its direct evaluation of properties requiring higher-order derivatives, such as bulk moduli, elastic constants, and force constants, offers more concise implementations compared to conventional finite difference methods. For these reasons, PROFESS-AD serves as an excellent prototyping tool and provides new opportunities for OFDFT.