Unconstrained and constrained minimization, localization, and the Grassmann manifold: Theory and application to electronic structure
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, Vol. 64, Issue 15; Other Information: DOI: 10.1103/PhysRevB.64.155203; Othernumber: PRBMDO000064000015155203000001; 105136PRB; PBD: 15 Oct 2001; ISSN 0163-1829
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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