198 research outputs found
Multipole-Preserving Quadratures for Discretization of Functions in Real-Space Electronic Structure Calculations
Discretizing an analytic function on a uniform real-space grid is often done
via a straightforward collocation method. This is ubiquitous in all areas of
computational physics and quantum chemistry. An example in Density Functional
Theory (DFT) is given by the external potential or the pseudo-potential
describing the interaction between ions and electrons. The accuracy of the
collocation method used is therefore very important for the reliability of
subsequent treatments like self-consistent field solutions of the electronic
structure problems. By construction, the collocation method introduces
numerical artifacts typical of real-space treatments, like the so-called
egg-box error, that may spoil the numerical stability of the description when
the real-space grid is too coarse. As the external potential is an input of the
problem, even a highly precise computational treatment cannot cope this
inconvenience. We present in this paper a new quadrature scheme that is able to
exactly preserve the moments of a given analytic function even for large grid
spacings, while reconciling with the traditional collocation method when the
grid spacing is small enough. In the context of real-space electronic structure
calculations, we show that this method improves considerably the stability of
the results for large grid spacings, opening the path towards reliable
low-accuracy DFT calculations with reduced number of degrees of freedom.Comment: 20 pages, 7 figure
Exact solution of the many-body problem with a complexity
In this article, we define a new mathematical object, called a pair
of anti-commutation matrices (ACMP) based on the
anti-commutation relation
applied to the scalar product between the many-body wavefunctions. This ACMP
explicitly separates the different levels of correlation. The one-body
correlations are defined by a ACMP and the two-body
ones by a set of ACMPs where is the number
of states. We show that we can have a compact and exact parametrization with
parameters of the two-body reduced density matrix (\TRDM) of any pure or
mixed -body state to determine the ground state energy with a
complexity
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
Fragment Approach to Constrained Density Functional Theory Calculations using Daubechies Wavelets
In a recent paper we presented a linear scaling Kohn-Sham density functional
theory (DFT) code based on Daubechies wavelets, where a minimal set of
localized support functions is optimized in situ and therefore adapted to the
chemical properties of the molecular system. Thanks to the systematically
controllable accuracy of the underlying basis set, this approach is able to
provide an optimal contracted basis for a given system: accuracies for ground
state energies and atomic forces are of the same quality as an uncontracted,
cubic scaling approach. This basis set offers, by construction, a natural
subset where the density matrix of the system can be projected. In this paper
we demonstrate the flexibility of this minimal basis formalism in providing a
basis set that can be reused as-is, i.e. without reoptimization, for
charge-constrained DFT calculations within a fragment approach. Support
functions, represented in the underlying wavelet grid, of the template
fragments are roto-translated with high numerical precision to the required
positions and used as projectors for the charge weight function. We demonstrate
the interest of this approach to express highly precise and efficient
calculations for preparing diabatic states and for the computational setup of
systems in complex environments
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
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
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
Structural Metastability of Endohedral Silicon Fullerenes
Endohedrally doped Si20 fullerenes appear as appealing building blocks for
nanoscale materials. We investigate their structural stability with an unbiased
and systematic global geometry optimization method within density-functional
theory. For a wide range of metal doping atoms, it was sufficient to explore
the Born Oppenheimer surface for only a moderate number of local minima to find
structures that clearly differ from the initial endohedral cages, but are
considerably more favorable in terms of energy. Previously proposed structures
are thus all metastable.Comment: 4 pages, 1 figur
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