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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
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