Augmented Lagrangian formulation of Orbital-Free Density Functional Theory
| Autor: | Deepa Phanish, Phanish Suryanarayana |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Mathematical optimization
Physics and Astronomy (miscellaneous) Discretization Orbital-free density functional theory FOS: Physical sciences 02 engineering and technology 01 natural sciences symbols.namesake Conjugate gradient method 0103 physical sciences 010306 general physics Mathematics Numerical Analysis Sequence Augmented Lagrangian method Applied Mathematics Computational Physics (physics.comp-ph) 021001 nanoscience & nanotechnology 16. Peace & justice Computer Science Applications Constraint (information theory) Computational Mathematics Modeling and Simulation Lagrange multiplier symbols Minification 0210 nano-technology Physics - Computational Physics |
| DOI: | 10.48550/arxiv.1405.6456 |
| Popis: | 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. Comment: 21 pages, 4 figures and 10 tables. Typos corrected |
| Databáze: | OpenAIRE |
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