Unconstrained and Constrained Minimization, Linear Scaling, and the Grassmann Manifold: Theory and Applications

Journal Article · 19 July 2000 · Physical Review B

OSTI ID:759995

RACZKOWSKI, DAVID ^[1]; FONG, C Y; SCHULTZ, PETER A; LIPPERT, ROSS A; STECHEL, E B

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1. Sandia National Laboratories

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 sub-space is a Grassmann conjugate gradient algorithm generalized from the algorithm of A. Edelman, T.A. Arias, and S. T. Smith, SIAM J. on Matrix Anal. Appl. 20, 303 (1998). The gradient takes into account the nonorthogonality of a local atom-centered basis, gaussian in their 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 1,458 atoms on a single processor are presented.

• Research Organization: Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
• Sponsoring Organization: US Department of Energy (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 759995
• Report Number(s): SAND2000-1909J
• Journal Information: Physical Review B, Journal Name: Physical Review B
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
ACCURACY
ALGORITHMS
CALCULATION METHODS
CONVERGENCE
ELECTRONIC STRUCTURE
SILICON CARBIDES