### 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.

Original language | English (US) |
---|---|

Article number | 155203 |

Pages (from-to) | 1552031-15520310 |

Number of pages | 13968280 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 64 |

Issue number | 15 |

State | Published - Oct 15 2001 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*64*(15), 1552031-15520310. [155203].

**Unconstrained and constrained minimization, localization, and the Grassmann manifold : Theory and application to electronic structure.** / Raczkowski, D.; Fong, C. Y.; Schultz, P. A.; Lippert, R. A.; Stechel, Ellen.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 64, no. 15, 155203, pp. 1552031-15520310.

}

TY - JOUR

T1 - Unconstrained and constrained minimization, localization, and the Grassmann manifold

T2 - Theory and application to electronic structure

AU - Raczkowski, D.

AU - Fong, C. Y.

AU - Schultz, P. A.

AU - Lippert, R. A.

AU - Stechel, Ellen

PY - 2001/10/15

Y1 - 2001/10/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0141479340&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141479340&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0141479340

VL - 64

SP - 1552031

EP - 15520310

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

M1 - 155203

ER -