773 research outputs found

### Density Functional Theory calculation on many-cores hybrid CPU-GPU architectures

The implementation of a full electronic structure calculation code on a
hybrid parallel architecture with Graphic Processing Units (GPU) is presented.
The code which is on the basis of our implementation is a GNU-GPL code based on
Daubechies wavelets. It shows very good performances, systematic convergence
properties and an excellent efficiency on parallel computers. Our GPU-based
acceleration fully preserves all these properties. In particular, the code is
able to run on many cores which may or may not have a GPU associated. It is
thus able to run on parallel and massive parallel hybrid environment, also with
a non-homogeneous ratio CPU/GPU. With double precision calculations, we may
achieve considerable speedup, between a factor of 20 for some operations and a
factor of 6 for the whole DFT code.Comment: 14 pages, 8 figure

### Efficient and accurate three dimensional Poisson solver for surface problems

We present a method that gives highly accurate electrostatic potentials for
systems where we have periodic boundary conditions in two spatial directions
but free boundary conditions in the third direction. These boundary conditions
are needed for all kind of surface problems. Our method has an O(N log N)
computational cost, where N is the number of grid points, with a very small
prefactor. This Poisson solver is primarily intended for real space methods
where the charge density and the potential are given on a uniform grid.Comment: 6 pages, 2 figure

### Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network

Based on an analysis of the short range chemical environment of each atom in
a system, standard machine learning based approaches to the construction of
interatomic potentials aim at determining directly the central quantity which
is the total energy. This prevents for instance an accurate description of the
energetics of systems where long range charge transfer is important as well as
of ionized systems. We propose therefore not to target directly with machine
learning methods the total energy but an intermediate physical quantity namely
the charge density, which then in turn allows to determine the total energy. By
allowing the electronic charge to distribute itself in an optimal way over the
system, we can describe not only neutral but also ionized systems with
unprecedented accuracy. We demonstrate the power of our approach for both
neutral and ionized NaCl clusters where charge redistribution plays a decisive
role for the energetics. We are able to obtain chemical accuracy, i.e. errors
of less than a milli Hartree per atom compared to the reference density
functional results. The introduction of physically motivated quantities which
are determined by the short range atomic environment via a neural network leads
also to an increased stability of the machine learning process and
transferability of the potential.Comment: 4 figure

### 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

### Particle-Particle, Particle-Scaling function (P3S) algorithm for electrostatic problems in free boundary conditions

An algorithm for fast calculation of the Coulombic forces and energies of
point particles with free boundary conditions is proposed. Its calculation time
scales as N log N for N particles. This novel method has lower crossover point
with the full O(N^2) direct summation than the Fast Multipole Method. The
forces obtained by our algorithm are analytical derivatives of the energy which
guarantees energy conservation during a molecular dynamics simulation. Our
algorithm is very simple. An MPI parallelised version of the code can be
downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic

### 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

### Accurate Complex Scaling of Three Dimensional Numerical Potentials

The complex scaling method, which consists in continuing spatial coordinates
into the complex plane, is a well-established method that allows to compute
resonant eigenfunctions of the time-independent Schroedinger operator. Whenever
it is desirable to apply the complex scaling to investigate resonances in
physical systems defined on numerical discrete grids, the most direct approach
relies on the application of a similarity transformation to the original,
unscaled Hamiltonian. We show that such an approach can be conveniently
implemented in the Daubechies wavelet basis set, featuring a very promising
level of generality, high accuracy, and no need for artificial convergence
parameters. Complex scaling of three dimensional numerical potentials can be
efficiently and accurately performed. By carrying out an illustrative resonant
state computation in the case of a one-dimensional model potential, we then
show that our wavelet-based approach may disclose new exciting opportunities in
the field of computational non-Hermitian quantum mechanics.Comment: 11 pages, 8 figure

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