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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 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 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
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