Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure

David Raczkowski, C. Y. Fong, Peter A. Schultz, R. A. Lippert, E. B. Stechel

Research output: Contribution to journalArticle

11 Citations (Scopus)


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 languageEnglish
Article number155203
Pages (from-to)1552031-15520310
Number of pages13968280
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number15
Publication statusPublished - Oct 15 2001


ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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