arXiv subjects

S. Goedecker

Publications and source records attributed to S. Goedecker.

12 recordsLinked to original sources

arXiv2015

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equation for neutral and ionic solutions, respectively. In the present work solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented to the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of a ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency, and allow for the treatment of different boundary conditions, as for example surface systems. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

cond-mat.mtrl-sci↗

arXiv2006

Questioning the existence of a unique ground state structure for Si clusters

Density functional and quantum Monte Carlo calculations challenge the existence of a unique ground state structure for certain Si clusters. For Si clusters with more than a dozen atoms the lowest ten isomers are close in energy and for some clusters entropic effects can change the energetic ordering of the configurations. Isotope pure configurations with rotational symmetry and symmetric configurations containing one additional isotope are disfavored by these effects. Comparisons with experiment are thus difficult since a mixture of configurations is to be expected at thermal equilibrium.

cond-mat.mtrl-sci↗

arXiv2006

An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis

An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wave function of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wave function.

physics.comp-ph↗

arXiv2003

Combining multigrid and wavelet ideas to construct more efficient multiscale algorithms for the solution of Poisson's equation

It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns out to be particularly fruitful. We propose a modified multigrid V cycle scheme that is not only much simpler, but also more efficient than the standard V cycle. Whereas in the traditional V cycle the residue is passed to the coarser grid levels, this new scheme does not require the calculation of a residue. Instead it works with copies of the charge density on the different grid levels that were obtained from the underlying charge density on the finest grid by wavelet transformations. This scheme is not limited to the pure wavelet setting, where it is faster than the preconditioned conjugate gradient method, but equally well applicable for finite difference discretizations.

physics.comp-ph↗

arXiv1999

Decay properties of the density matrix and Wannier functions for interacting systems

For non-interacting electrons the one-particle density matrix and the related Wannier functions characterize a material as insulating or metallic. Introducing many-body Wannier functions, we show that this characterization can be carried over to interacting systems. In particular, we find that an exponential decay of the density matrix characterizes not only band insulators but also Mott insulators. The properties of the many-body Wannier functions differ, however, from those of the Wannier functions of a non-interacting systems.

cond-mat↗

arXiv1998

Hyper-sparsity of the density matrix in a wavelet representation

O(N) methods are based on the decay properties of the density matrix in real space, an effect sometimes refered to as near-sightedness. We show, that in addition to this near-sightedness in real space there is also a near-sightedness in Fourier space. Using a basis set with good localization properties in both real and Fourier space such as wavelets, one can exploit both localization properties to obtain a density matrix which exhibits additional sparseness properties compared to the scenario where one has a basis set with real space localization only. We will call this additional sparsity hyper-sparsity. Taking advantage of this hyper-sparsity, it is possible to represent very large quantum mechanical systems in a highly compact way. This can be done both for insulating and metallic systems and for arbitrarily accurate basis sets. We expect that hyper-sparsity will pave the way for O(N) calculations of large systems requiring many basis functions per atom, such as Density Functional calculations.

cond-mat↗

arXiv1998

A natural orbital functional for the many-electron problem

The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the reduced first-order density matrix or equivalently the natural orbitals. In the former approach the unknown part of the functional contains both a kinetic and a potential contribution whereas in the latter approach it contains only a potential energy and consequently has simpler scaling properties. We present an approximate, simple and parameter-free functional of the natural orbitals, based solely on scaling arguments and the near satisfaction of a sum rule. Our tests on atoms show that it yields on average more accurate energies and charge densities than the Hartree Fock method, the local density approximation and the generalized gradient approximations.

physics.comp-ph↗

arXiv1998

The Decay Properties of the Finite Temperature Density Matrix in Metals

Using ordinary Fourier analysis, the asymptotic decay behavior of the density matrix F(r,r') is derived for the case of a metal at a finite electronic temperature. An oscillatory behavior which is damped exponentially with increasing distance between r and r' is found. The decay rate is not only determined by the electronic temperature, but also by the Fermi energy. The theoretical predictions are confirmed by numerical simulations.

cond-mat↗

arXiv1998

Relativistic separable dual-space Gaussian Pseudopotentials from H to Rn

We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole periodic table and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real space grid, it is highly accurate and due to its analytic form it can be specified by a very small number of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of molecular calculations.

cond-mat.soft↗

arXiv1997

Linear Scaling Solution of the Coulomb problem using wavelets

The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore highly desirable. Using wavelet based Multi Resolution Analysis we derive for the first time a method which has these properties. The power and accuracy of the method is illustrated by applying it to the calculation of of the electrostatic potential of a full three-dimensional all-electron Uranium dimer.

physics.comp-ph↗

arXiv1996

A critical assessment of the Self-Interaction Corrected Local Density Functional method and its algorithmic implementation

We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we first derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and show that previously given expressions do not correctly incorporate this constraint. In our atomic calculations the SIC-LDA yields total energies, ionization energies and charge densities that are superior to results obtained with the Local Density Approximation (LDA). However, for molecules SIC-LDA gives bond lengths and reaction energies that are inferior to those obtained from LDA. The nonlocal BLYP functional, which we include as a representative GGA functional, outperforms both LDA and SIC-LDA for all ground state properties we considered.

cond-mat↗

arXiv1995

Separable Dual Space Gaussian Pseudo-potentials

We present pseudo-potential coefficients for the first two rows of the periodic table. The pseudo potential is of a novel analytic form, that gives optimal efficiency in numerical calculations using plane waves as basis set. At most 7 coefficients are necessary to specify its analytic form. It is separable and has optimal decay properties in both real and Fourier space. Because of this property, the application of the nonlocal part of the pseudo-potential to a wave-function can be done in an efficient way on a grid in real space. Real space integration is much faster for large systems than ordinary multiplication in Fourier space since it shows only quadratic scaling with respect to the size of the system. We systematically verify the high accuracy of these pseudo-potentials by extensive atomic and molecular test calculations.

mtrl-th↗