Automatic Differentiation for Orbital-Free Density Functional Theory

TL;DR

This paper introduces PROFESS-AD, a differentiable programming tool that enhances orbital-free density functional theory simulations by enabling efficient, direct computation of derivatives, thus improving functional development and property evaluation.

Contribution

The paper presents PROFESS-AD, a novel automatic differentiation framework for OFDFT that simplifies derivative calculations and accelerates the development of new density functionals.

Findings

Enables direct evaluation of first and higher-order derivatives in OFDFT

Reduces complexity and improves efficiency over finite difference methods

Facilitates development and testing of new density functionals

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.