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

Joint de grains dans le silicium et suite du nombre d'argent

International audienceA scheme is proposed to solve the structure of incommensurate interfaces, starting from high-resolution images of electron microscopy, supplemented by adapted simulation techniques and complemented by theoretical tools. Direct silicon bonding is a way to produce artificial interfaces, in particular incommensurate ones. We focus on a technology-driven tilt grain boundary in silicon. While the Fibonacci sequence, linked to the golden ratio, is a prototype of the quasicrystalline structures, a silver-ratio sequence allows us to analyze this incommensurate interface. The four-fold coordination of the Si atoms is kept at the interface.Une procédure est proposée pour résoudre la structure d'interfaces incommensurables, en partant d'images de microscopie électronique de haute résolution, en complétant avec des techniques de simulation adaptées et en parachevant avec des outils théoriques. Le collage de plaques de silicium est une manière de créer des interfaces artificielles, en particulier de type incommensurable. Nous nous concentrons sur un joint de grains de flexion dans le silicium, joint ayant un intérêt technologique. Alors que la suite de Fibonacci, liée au nombre d'or, est un prototype des structures quasi-cristallines, la suite du nombre d'argent nous permet d'analyser cette interface incommensurable. La tétravalence des atomes de silicium est conservée à l'interface

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 Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library

We present CheSS, the “Chebyshev Sparse Solvers” library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and efficient expansion in terms of Chebyshev polynomials and presently features the calculation of the density matrix, the calculation of matrix powers for arbitrary powers, and the extraction of eigenvalues in a selected interval. CheSS is able to exploit the sparsity of the matrices and scales linearly with respect to the number of nonzero entries, making it well-suited for large-scale calculations. The approach is particularly adapted for setups leading to small spectral widths of the involved matrices and outperforms alternative methods in this regime. By coupling CheSS to the DFT code BigDFT, we show that such a favorable setup is indeed possible in practice. In addition, the approach based on Chebyshev polynomials can be massively parallelized, and CheSS exhibits excellent scaling up to thousands of cores even for relatively small matrix sizes.We gratefully acknowledge the support of the MaX (SM) and POP (MW) projects, which have received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 676598 and 676553, respectively. This work was also supported by the Energy oriented Centre of Excellence (EoCoE), grant agreement number 676629, funded within the Horizon2020 framework of the European Union, as well as by the Next-Generation Supercomputer project (the K computer project) and the FLAGSHIP2020 within the priority study5 (Development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We (LG, DC, WD, TN) gratefully acknowledge the joint CEA-RIKEN collaboration action.Peer ReviewedPostprint (author's final draft

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

Daubechies wavelets as a basis set for density functional pseudopotential calculations

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances and an excellent efficiency for parallel calculations.Comment: 15 pages, 11 figure

The crystal structure of cold compressed graphite

Through a systematic structural search we found an allotrope of carbon with Cmmm symmetry which we predict to be more stable than graphite for pressures above 10 GPa. This material, which we refer to as Z-carbon, is formed by pure sp3 bonds and is the only carbon allotrope which provides an excellent match to unexplained features in experimental X-ray diffraction and Raman spectra of graphite under pressure. The transition from graphite to Z-carbon can occur through simple sliding and buckling of graphene sheets. Our calculations predict that Z-carbon is a transparent wide band gap semiconductor with a hardness comparable to diamond.Comment: 4 pages, 5 figure

ABINIT: Overview and focus on selected capabilities

Paper published as part of the special topic on Electronic Structure SoftwareABINIT is probably the first electronic-structure package to have been released under an open-source license about 20 years ago. It implements density functional theory, density-functional perturbation theory (DFPT), many-body perturbation theory (GW approximation and Bethe–Salpeter equation), and more specific or advanced formalisms, such as dynamical mean-field theory (DMFT) and the “temperaturedependent effective potential” approach for anharmonic effects. Relying on planewaves for the representation of wavefunctions, density, and other space-dependent quantities, with pseudopotentials or projector-augmented waves (PAWs), it is well suited for the study of periodic materials, although nanostructures and molecules can be treated with the supercell technique. The present article starts with a brief description of the project, a summary of the theories upon which ABINIT relies, and a list of the associated capabilities. It then focuses on selected capabilities that might not be present in the majority of electronic structure packages either among planewave codes or, in general, treatment of strongly correlated materials using DMFT; materials under finite electric fields; properties at nuclei (electric field gradient, Mössbauer shifts, and orbital magnetization); positron annihilation; Raman intensities and electro-optic effect; and DFPT calculations of response to strain perturbation (elastic constants and piezoelectricity), spatial dispersion (flexoelectricity), electronic mobility, temperature dependence of the gap, and spin-magnetic-field perturbation. The ABINIT DFPT implementation is very general, including systems with van der Waals interaction or with noncollinear magnetism. Community projects are also described: generation of pseudopotential and PAW datasets, high-throughput calculations (databases of phonon band structure, second-harmonic generation, and GW computations of bandgaps), and the library LIBPAW. ABINIT has strong links with many other software projects that are briefly mentioned.This work (A.H.R.) was supported by the DMREF-NSF Grant No. 1434897, National Science Foundation OAC-1740111, and U.S. Department of Energy DE-SC0016176 and DE-SC0019491 projects. N.A.P. and M.J.V. gratefully acknowledge funding from the Belgian Fonds National de la Recherche Scientifique (FNRS) under Grant No. PDR T.1077.15-1/7. M.J.V. also acknowledges a sabbatical “OUT” grant at ICN2 Barcelona as well as ULiège and the Communauté Française de Belgique (Grant No. ARC AIMED G.A. 15/19-09). X.G. and M.J.V. acknowledge funding from the FNRS under Grant No. T.0103.19-ALPS. X.G. and G.-M. R. acknowledge support from the Communauté française de Belgique through the SURFASCOPE Project (No. ARC 19/24-057). X.G. acknowledges the hospitality of the CEA DAM-DIF during the year 2017. G.H. acknowledges support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under Contract No. DE-AC02-05-CH11231 (Materials Project Program No. KC23MP). The Belgian authors acknowledge computational resources from supercomputing facilities of the University of Liège, the Consortium des Equipements de Calcul Intensif (Grant No. FRS-FNRS G.A. 2.5020.11), and Zenobe/CENAERO funded by the Walloon Region under Grant No. G.A. 1117545. M.C. and O.G. acknowledge support from the Fonds de Recherche du Québec Nature et Technologie (FRQ-NT), Canada, and the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grant No. RGPIN-2016-06666. The implementation of the libpaw library (M.T., T.R., and D.C.) was supported by the ANR NEWCASTLE project (Grant No. ANR-2010-COSI-005-01) of the French National Research Agency. M.R. and M.S. acknowledge funding from Ministerio de Economia, Industria y Competitividad (MINECO-Spain) (Grants Nos. MAT2016-77100-C2-2-P and SEV-2015-0496) and Generalitat de Catalunya (Grant No. 2017 SGR1506). This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation program (Grant Agreement No. 724529). P.G. acknowledges support from FNRS Belgium through PDR (Grant No. HiT4FiT), ULiège and the Communauté française de Belgique through the ARC project AIMED, the EU and FNRS through M.ERA.NET project SIOX, and the European Funds for Regional Developments (FEDER) and the Walloon Region in the framework of the operational program “Wallonie-2020.EU” through the project Multifunctional thin films/LoCoTED. The Flatiron Institute is a division of the Simons Foundation. A large part of the data presented in this paper is available directly from the Abinit Web page www.abinit.org. Any other data not appearing in this web page can be provided by the corresponding author upon reasonable request.Peer reviewe

Simulations multi-échelles de la diffusion des défauts dans les semi-conducteurs Si et SiGe

This work is a numerical study of point defect diffusion in semi-conductors such as Si and SiGe. As macroscopic gradients of concentrations are the result of atomic moves, a multi-scale approach can be used.Ab initio calculations are highly useful when investigating atomic interactions, and, when linked with geometric minimization algorithms they give access to stable and transition states. The macroscopic movement can then be simulated using kinetic Monte Carlo calculations.We detail, in this work, the geometry and the energetic cost of most stable points defects of Si and SiGe. This includes vacancies, dumbbell [110] interstitials, hexagonal interstitals and four-folded coordinated defects. We study their movements and use this information in thermodynamical simulations to show that several regimes exist for the diffusion, depending on the interactions between mediators. In the case of the vacancy assisted diffusion, the differences observed in diffusivity are explained by the existence of the di-vacancies and their dissociation mechanisms.This study shows that the coupling between atomistic and macroscopic simulations is required to explain diffusion mechanisms.Le sujet abordé dans ce manuscrit traite de l'étude des défauts ponctuels et de leur rôle dans la diffusion au sein des semi-conducteurs Si et SiGe suivant une approche numérique. Le fait que les changements de concentrations observés dans un cristal à son échelle soient induits par des mouvements à l'échelle atomique, a conduit à une approche multi-échelle.Le calcul ab initio est un outil adapté à l'exploration des phénomènes inter-atomiques. Couplées à des algorithmes de minimisation des configurations, cet outil donne accès aux états stables et aux états de transition des phénomènes diffusifs. Le mouvement macroscopique est ensuite reproduit par l'utilisation de simulations de Monte Carlo cinétique.Nous détaillons, dans le présent travail, les coûts énergétiques et les géométries des principaux défauts répertoriés dans Si et SiGe. Il en ressort que la lacune, l'interstitiel dissocié, l'interstitiel hexagonal et le défaut tétra-coordonné sont tous les quatre des défauts de moindre énergie dans ces systèmes. L'étude des mouvements possibles et leurs utilisations dans des simulations de physique thermodynamique, permet de montrer l'existence de plusieurs régimes de diffusion, selon que les médiateurs du mouvement agissent seuls ou de façon coordonnée. Nous donnons l'exemple de la diffusion lacunaire, dont les variations observées s'expliquent par la présence plus ou moins importante de bi-lacunes et par les phénomènes de dissociation en jeu.Par cette étude, nous mettons en avant la nécessité de combiner, dans le cas de la diffusion, une analyse de l'échelle atomique avec des simulations à des échelles plus macroscopiques