### 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 |
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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 |

DOIs | |

Publication status | Published - Oct 15 2001 |

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### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

### Cite this

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

*64*(15), 1552031-15520310. [155203]. https://doi.org/10.1103/PhysRevB.64.155203