Augmented Lagrangian formulation of Orbital-Free Density Functional Theory

TL;DR

This paper introduces an Augmented Lagrangian approach for orbital-free DFT calculations, enabling efficient unconstrained optimization, and demonstrates its effectiveness and accuracy through parallel implementation and large-scale system simulations.

Contribution

It develops a novel Augmented Lagrangian formulation for OF-DFT, improving computational efficiency and robustness over existing methods, with a focus on real-space implementation and large system validation.

Findings

Augmented Lagrangian method outperforms penalty and Lagrange multiplier methods.

Higher-order finite-differences are computationally efficient for OF-DFT.

Validated accuracy against plane-wave methods for large systems.

Abstract

We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic orbital-free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas-Fermi-von Weizscaker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation is both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.