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Linear scaling algorithms: Progress and promise

Description: The goal of this laboratory-directed research and development (LDRD) project was to develop a new and efficient electronic structure algorithm that would scale linearly with system size. Since the start of the program this field has received much attention in the literature as well as in terms of focused symposia and at least one dedicated international workshop. The major success of this program is the development of a unique algorithm for minimization of the density functional energy which replaces the diagonalization of the Kohn-Sham hamiltonian with block diagonalization into explicit occupied and partially occupied (in metals) subspaces and an implicit unoccupied subspace. The progress reported here represents an important step toward the simultaneous goals of linear scaling, controlled accuracy, efficiency and transferability. The method is specifically designed to deal with localized, non-orthogonal basis sets to maximize transferability and state by state iteration to minimize any charge-sloshing instabilities and accelerate convergence. The computational demands of the algorithm do scale as the particle number, permitting applications to problems involving many inequivalent atoms. Our targeted goal is at least 10,000 inequivalent atoms on a teraflop computer. This report describes our algorithm, some proof-of-principle examples and a state of the field at the conclusion of this LDRD.
Date: August 1, 1996
Creator: Stechel, E.B.
Partner: UNT Libraries Government Documents Department

Charge Accumulation at a Threading Edge Dislocation in GaN

Description: We have performed Monte Carlo calculations to determine the charge accumulation on threading edge dislocations in GaN as a function of the dislocation density and background dopant density. Four possible core structures have been examined, each of which produces defect levels in the gap and may therefore act as electron or hole traps. Our results indicate that charge accumulation, and the resulting electrostatic interactions, can change the relative stabilities of the different core structures. Structures having Ga and N vacancies at the dislocation core are predicted to be stable under nitrogen-rich and gallium-rich growth conditions, respectively. Due to dopant depletion at high dislocation density and the multitude of charge states, the line charge exhibits complex crossover behavior as the dopant and dislocation densities vary.
Date: January 20, 1999
Creator: Leung, K.; Stechel, E.B. & Wright, A.F.
Partner: UNT Libraries Government Documents Department

Auger spectroscopy and electronically-stimulated surface processes

Description: Electronic excitations in adsorbate layers stimulate desorption and dissociation of adsorbed molecules as well as chemical reactions between adsorbates. The highest-probability stimulated processes produce neutral desorbates and determine how surface composition is altered by electron or photon radiation. A basic understanding has emerged, due largely to laser resonance-enhanced multi-photon ionization (REMPI) experiments, which provide quantum-state resolution of the gas-phase products. Auger phenomena enter this understanding in several ways. For example, CVV Auger spectroscopy determines the screened hole-hole interaction, U, in adsorbates, which in turn provides insight into the degree of charge-transfer screening from the substrate. In those systems where screening charge is used in excitation Auger decay, screening directly determines the lifetime, which in turn can exponentially affect the yield. Reductions in screening, e.g. induced by coadsorption of electro-negative species, thus can result in giant yield enhancements. As separate issues, a finite U may prevent the fast resonant decay and thus increase the yield from two-hole excitations, as has been suggested for NO{sub 2} dissociation on Pt (111), or may assist in the localization (self-trapping) of two-hole excitations in dense adsorbate layers, as apparently is the case for NO desorption from the same surface. The latter causes the yields from one- and two-hole excitations to differ in their coverage dependence. Finally, CVV Auger spectroscopy, of course, measures the energies of two-hole excitations, which can be correlated with observed stimulated thresholds. 27 refs., 15 figs.
Date: January 1, 1991
Creator: Jennison, D. R.; Burns, A. R. & Stechel, E. B.
Partner: UNT Libraries Government Documents Department

The electronic transport mechanism in amorphous tetrahedrally-coordinated carbon films

Description: The electronic transport mechanism in tetrahedrally coordinated amorphous carbon was investigated using measurements of stress relaxation, thermal evolution of electrical conductivity, and temperature dependent conductivity measurements. Stress relaxation measurements were used to determine the change in 3-fold coordinated carbon concentration, and the electrical conductivity was correlated to this change. It was found that the conductivity was exponentially proportional to the change in 3-fold concentration, indicating a tunneling or hopping transport mechanism. It was also found that the activation energy for transport decreased with increasing anneal temperature. The decrease in activation energy was responsible for the observed increase in electrical conductivity. A model is described wherein the transport in this material is described by thermally activated conduction along 3-fold linkages or chains with variable range and variable orientation hopping. Thermal annealing leads to chain ripening and a reduction in the activation energy for transport.
Date: February 1, 1998
Creator: Sullivan, J.P.; Friedmann, T.A.; Dunn, R.G.; Stechel, E.B. & Schultz, P.A.
Partner: UNT Libraries Government Documents Department

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

Description: 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.
Date: July 19, 2000
Partner: UNT Libraries Government Documents Department