3,091 research outputs found
Low complexity method for large-scale self-consistent ab initio electronic-structure calculations without localization
A novel low complexity method to perform self-consistent electronic-structure
calculations using the Kohn-Sham formalism of density functional theory is
presented. Localization constraints are neither imposed nor required thereby
allowing direct comparison with conventional cubically scaling algorithms. The
method has, to date, the lowest complexity of any algorithm for an exact
calculation. A simple one-dimensional model system is used to thoroughly test
the numerical stability of the algorithm and results for a real physical system
are also given
Daubechies Wavelets for Linear Scaling Density Functional Theory
We demonstrate that Daubechies wavelets can be used to construct a minimal
set of optimized localized contracted basis functions in which the Kohn-Sham
orbitals can be represented with an arbitrarily high, controllable precision.
Ground state energies and the forces acting on the ions can be calculated in
this basis with the same accuracy as if they were calculated directly in a
Daubechies wavelets basis, provided that the amplitude of these contracted
basis functions is sufficiently small on the surface of the localization
region, which is guaranteed by the optimization procedure described in this
work. This approach reduces the computational costs of DFT calculations, and
can be combined with sparse matrix algebra to obtain linear scaling with
respect to the number of electrons in the system. Calculations on systems of
10,000 atoms or more thus become feasible in a systematic basis set with
moderate computational resources. Further computational savings can be achieved
by exploiting the similarity of the contracted basis functions for closely
related environments, e.g. in geometry optimizations or combined calculations
of neutral and charged systems
Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
We describe how to apply the recently developed pole expansion and selected
inversion (PEXSI) technique to Kohn-Sham density function theory (DFT)
electronic structure calculations that are based on atomic orbital
discretization. We give analytic expressions for evaluating the charge density,
the total energy, the Helmholtz free energy and the atomic forces (including
both the Hellman-Feynman force and the Pulay force) without using the
eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to
update the chemical potential without using Kohn-Sham eigenvalues. The
advantage of using PEXSI is that it has a much lower computational complexity
than that associated with the matrix diagonalization procedure. We demonstrate
the performance gain by comparing the timing of PEXSI with that of
diagonalization on insulating and metallic nanotubes. For these quasi-1D
systems, the complexity of PEXSI is linear with respect to the number of atoms.
This linear scaling can be observed in our computational experiments when the
number of atoms in a nanotube is larger than a few hundreds. Both the wall
clock time and the memory requirement of PEXSI is modest. This makes it even
possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a
sequential implementation of the selected inversion algorithm. We also perform
an accurate geometry optimization calculation on a truncated (8,0)
boron-nitride nanotube system containing 1024 atoms. Numerical results indicate
that the use of PEXSI does not lead to loss of accuracy required in a practical
DFT calculation
Accurate and efficient linear scaling DFT calculations with universal applicability
Density Functional Theory calculations traditionally suffer from an inherent
cubic scaling with respect to the size of the system, making big calculations
extremely expensive. This cubic scaling can be avoided by the use of so-called
linear scaling algorithms, which have been developed during the last few
decades. In this way it becomes possible to perform ab-initio calculations for
several tens of thousands of atoms or even more within a reasonable time frame.
However, even though the use of linear scaling algorithms is physically well
justified, their implementation often introduces some small errors.
Consequently most implementations offering such a linear complexity either
yield only a limited accuracy or, if one wants to go beyond this restriction,
require a tedious fine tuning of many parameters. In our linear scaling
approach within the BigDFT package, we were able to overcome this restriction.
Using an ansatz based on localized support functions expressed in an underlying
Daubechies wavelet basis -- which offers ideal properties for accurate linear
scaling calculations -- we obtain an amazingly high accuracy and a universal
applicability while still keeping the possibility of simulating large systems
with only a moderate demand of computing resources
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