Augmented Lagrangian formulation of orbital-free density functional theory

JOURNAL OF COMPUTATIONAL PHYSICS

卷:275

Article

Suryanarayana, Phanish¹  Phanish, Deepa¹ 

[1] Georgia Inst Technol, Coll Engn, Atlanta, GA 30332 USA

关键词: Augmented Lagrangian;    Lagrange multiplier;    Penalty;    Higher-order finite-differences;    Real-space;    Non-periodic;   

DOI  :  10.1016/j.jcp.2014.07.006

来源: Elsevier

【 摘 要 】

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 Weizsacker (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 are 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. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free