Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure
Abstract
An unconstrained minimization algorithm for electronic structure calculations using density functional for systems with a gap is developed to solve for nonorthogonal Wannier-like orbitals in the spirit of E. B. Stechel, A. R. Williams, and P. J. Feibelman [Phys. Rev. B 49, 10 008 (1994)]. The search for the occupied subspace is a Grassmann conjugate gradient algorithm generalized from the algorithm of A. Edelman, T. A. Arias, and S. T. Smith [SIAM J. Matrix Anal. Appl. 20, 303 (1998)]. The gradient takes into account the nonorthogonality of a local atom-centered basis, Gaussian in our implementation. With a localization constraint on the Wannier-like orbitals, well-constructed sparse matrix multiplies lead to O(N) scaling of the computationally intensive parts of the algorithm. Using silicon carbide as a test system, the accuracy, convergence, and implementation of this algorithm as a quantitative alternative to diagonalization are investigated. Results up to 1458 atoms on a single processor are presented.
- Authors:
- Publication Date:
- Research Org.:
- Sandia National Laboratory
- Sponsoring Org.:
- (US)
- OSTI Identifier:
- 40277702
- DOE Contract Number:
- AC04-94AL85000
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 64; Journal Issue: 15; Other Information: DOI: 10.1103/PhysRevB.64.155203; Othernumber: PRBMDO000064000015155203000001; 105136PRB; PBD: 15 Oct 2001; Journal ID: ISSN 0163-1829
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 12 MANAGEMENT OF RADIOACTIVE WASTES, AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES; ACCURACY; ALGORITHMS; ATOMS; CONVERGENCE; ELECTRONIC STRUCTURE; FUNCTIONALS; IMPLEMENTATION; MINIMIZATION; SILICON CARBIDES
Citation Formats
Raczkowski, David, Fong, C Y, Schultz, Peter A, Lippert, R A, and Stechel, E B. Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure. United States: N. p., 2001.
Web. doi:10.1103/PhysRevB.64.155203.
Raczkowski, David, Fong, C Y, Schultz, Peter A, Lippert, R A, & Stechel, E B. Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure. United States. https://doi.org/10.1103/PhysRevB.64.155203
Raczkowski, David, Fong, C Y, Schultz, Peter A, Lippert, R A, and Stechel, E B. 2001.
"Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure". United States. https://doi.org/10.1103/PhysRevB.64.155203.
@article{osti_40277702,
title = {Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure},
author = {Raczkowski, David and Fong, C Y and Schultz, Peter A and Lippert, R A and Stechel, E B},
abstractNote = {An unconstrained minimization algorithm for electronic structure calculations using density functional for systems with a gap is developed to solve for nonorthogonal Wannier-like orbitals in the spirit of E. B. Stechel, A. R. Williams, and P. J. Feibelman [Phys. Rev. B 49, 10 008 (1994)]. The search for the occupied subspace is a Grassmann conjugate gradient algorithm generalized from the algorithm of A. Edelman, T. A. Arias, and S. T. Smith [SIAM J. Matrix Anal. Appl. 20, 303 (1998)]. The gradient takes into account the nonorthogonality of a local atom-centered basis, Gaussian in our implementation. With a localization constraint on the Wannier-like orbitals, well-constructed sparse matrix multiplies lead to O(N) scaling of the computationally intensive parts of the algorithm. Using silicon carbide as a test system, the accuracy, convergence, and implementation of this algorithm as a quantitative alternative to diagonalization are investigated. Results up to 1458 atoms on a single processor are presented.},
doi = {10.1103/PhysRevB.64.155203},
url = {https://www.osti.gov/biblio/40277702},
journal = {Physical Review B},
issn = {0163-1829},
number = 15,
volume = 64,
place = {United States},
year = {Mon Oct 15 00:00:00 EDT 2001},
month = {Mon Oct 15 00:00:00 EDT 2001}
}