347 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
A Customized 3D GPU Poisson Solver for Free Boundary Conditions
A 3-dimensional GPU Poisson solver is developed for all possible combinations
of free and periodic boundary conditions (BCs) along the three directions. It
is benchmarked for various grid sizes and different BCs and a significant
performance gain is observed for problems including one or more free BCs. The
GPU Poisson solver is also benchmarked against two different CPU
implementations of the same method and a significant amount of acceleration of
the computation is observed with the GPU version.Comment: 10 pages, 5 figure
A wavelet-based Projector Augmented-Wave (PAW) method: reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set
We present a Projector Augmented-Wave~(PAW) method based on a wavelet basis
set. We implemented our wavelet-PAW method as a PAW library in the ABINIT
package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We
test our implementation in prototypical systems to illustrate the potential
usage of our code. By using the wavelet-PAW method, we can simulate charged and
special boundary condition systems with frozen-core all-electron precision.
Furthermore, our work paves the way to large-scale and potentially order-N
simulations within a PAW method
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
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