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

Journal Article · Mon Oct 15 04:00:00 EDT 2001 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.64.155203· OSTI ID:40277702

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

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.

• Research Organization: Sandia National Laboratory
• Sponsoring Organization: (US)
• DOE Contract Number: AC04-94AL85000
• OSTI ID: 40277702
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 15 Vol. 64; ISSN 0163-1829
• Publisher: The American Physical Society
• Country of Publication: United States
• Language: English

Related Subjects

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE WASTES FROM NUCLEAR FACILITIES
ACCURACY
ALGORITHMS
ATOMS
CONVERGENCE
ELECTRONIC STRUCTURE
FUNCTIONALS
IMPLEMENTATION
MINIMIZATION
SILICON CARBIDES