Doping Nanocrystals And The Role Of Quantum Confinement

Recent progress in developing algorithms for solving the electronic structure problem for nanostructures is illustrated. Key ingredients in this approach include pseudopotentials implemented on a real space grid and the use of density functional theory. This procedure allows one to predict electronic properties for many materials across the nano-regime, i.e., from atoms to nanocrystals of sufficient size to replicate bulk properties. We will illustrate this method for doping silicon nanocrystals with phosphorous.Institute for Computational Engineering and Sciences (ICES

Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration

Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first SCF iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problem. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before

Variational finite-difference representation of the kinetic energy operator

A potential disadvantage of real-space-grid electronic structure methods is the lack of a variational principle and the concomitant increase of total energy with grid refinement. We show that the origin of this feature is the systematic underestimation of the kinetic energy by the finite difference representation of the Laplacian operator. We present an alternative representation that provides a rigorous upper bound estimate of the true kinetic energy and we illustrate its properties with a harmonic oscillator potential. For a more realistic application, we study the convergence of the total energy of bulk silicon using a real-space-grid density-functional code and employing both the conventional and the alternative representations of the kinetic energy operator.Comment: 3 pages, 3 figures, 1 table. To appear in Phys. Rev. B. Contribution for the 10th anniversary of the eprint serve

Timesaving Double-Grid Method for Real-Space Electronic-Structure Calculations

We present a simple and efficient technique in ab initio electronic-structure calculation utilizing real-space double-grid with a high density of grid points in the vicinity of nuclei. This technique promises to greatly reduce the overhead for performing the integrals that involves non-local parts of pseudopotentials, with keeping a high degree of accuracy. Our procedure gives rise to no Pulay forces, unlike other real-space methods using adaptive coordinates. Moreover, we demonstrate the potential power of the method by calculating several properties of atoms and molecules.Comment: 4 pages, 5 figure

Electronic properties of silica nanowires

Thin nanowires of silicon oxide were studied by pseudopotential density functional electronic structure calculations using the generalized gradient approximation. Infinite linear and zigzag Si-O chains were investigated. A wire composed of three-dimensional periodically repeated Si4O8 units was also optimized, but this structure was found to be of limited stability. The geometry, electronic structure, and Hirshfeld charges of these silicon oxide nanowires were computed. The results show that the Si-O chain is metallic, whereas the zigzag chain and the Si4O8 nanowire are insulators

Large Scale Electronic Structure Calculations with Multigrid Acceleration

We have developed a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods permit efficient calculations on ill-conditioned systems with long length scales or high energy cutoffs. The technique has been applied to systems containing up to 100 atoms, including a highly elongated diamond cell, an isolated C$_{60}$ molecule, and a 32-atom cell of GaN with the Ga d-states in valence. The method is well suited for implementation on both vector and massively parallel architectures.Comment: 4 pages, 1 postscript figur

On the Origin of the -4.4 eV Band in CdTe(100)"

We calculate the bulk- (infinite system), (100)-bulk-projected- and (100)-Surface-projected Green's functions using the Surface Green's Function Matching method (SGFM) and an empirical tight-binding hamiltonian with tight-binding parameters (TBP) that describe well the bulk band structure of CdTe. In particular, we analyze the band (B--4) arising at --4.4 eV from the top of the valence band at $\Gamma$ according to the results of Niles and H\"ochst and at -4.6 eV according to Gawlik {\it et al.} both obtained by Angle-resolved photoelectron spectroscopy (ARPES). We give the first theoretical description of this band.Comment: 17 pages, Rev-TEX, CIEA-Phys. 02/9

Real space finite difference method for conductance calculations

We present a general method for calculating coherent electronic transport in quantum wires and tunnel junctions. It is based upon a real space high order finite difference representation of the single particle Hamiltonian and wave functions. Landauer's formula is used to express the conductance as a scattering problem. Dividing space into a scattering region and left and right ideal electrode regions, this problem is solved by wave function matching (WFM) in the boundary zones connecting these regions. The method is tested on a model tunnel junction and applied to sodium atomic wires. In particular, we show that using a high order finite difference approximation of the kinetic energy operator leads to a high accuracy at moderate computational costs.Comment: 13 pages, 10 figure

Evaluation of Exchange-Correlation Energy, Potential, and Stress

We describe a method for calculating the exchange and correlation (XC) contributions to the total energy, effective potential, and stress tensor in the generalized gradient approximation. We avoid using the analytical expressions for the functional derivatives of E_xc*rho, which depend on discontinuous second-order derivatives of the electron density rho. Instead, we first approximate E_xc by its integral in a real space grid, and then we evaluate its partial derivatives with respect to the density at the grid points. This ensures the exact consistency between the calculated total energy, potential, and stress, and it avoids the need of second-order derivatives. We show a few applications of the method, which requires only the value of the (spin) electron density in a grid (possibly nonuniform) and returns a conventional (local) XC potential.Comment: 7 pages, 3 figure

Atomic structure of dislocation kinks in silicon

We investigate the physics of the core reconstruction and associated structural excitations (reconstruction defects and kinks) of dislocations in silicon, using a linear-scaling density-matrix technique. The two predominant dislocations (the 90-degree and 30-degree partials) are examined, focusing for the 90-degree case on the single-period core reconstruction. In both cases, we observe strongly reconstructed bonds at the dislocation cores, as suggested in previous studies. As a consequence, relatively low formation energies and high migration barriers are generally associated with reconstructed (dangling-bond-free) kinks. Complexes formed of a kink plus a reconstruction defect are found to be strongly bound in the 30-degree partial, while the opposite is true in the case of 90-degree partial, where such complexes are found to be only marginally stable at zero temperature with very low dissociation barriers. For the 30-degree partial, our calculated formation energies and migration barriers of kinks are seen to compare favorably with experiment. Our results for the kink energies on the 90-degree partial are consistent with a recently proposed alternative double-period structure for the core of this dislocation.Comment: 12 pages, two-column style with 8 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#rn_di