Daubechies Wavelets As a Basis Set for Density Functional

Electronic Structure Calculation Methods on Accelerators, Oak Ridge

BigDFT

Formalism

Wavelets Algorithms Daubechies wavelets as a basis set for density Poisson Solver Features functional pseudopotential calculation Applications

Publications Si clusters Boron clusters

Conclusion T. Deutsch, L. Genovese, D. Caliste

L_Sim – CEA Grenoble

February 7, 2012

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste A basis for nanosciences: The BigDFT project

STREP European project: BigDFT(2005-2008) Four partners, 15 contributors: CEA-INAC Grenoble (T. D.), U. Basel (S. Goedecker), U. Louvain-la-Neuve (X .Gonze), U. Kiel (R. Schneider)

BigDFT

Formalism Aim: To develop an ab-initio DFT code Wavelets based on Daubechies Wavelets Algorithms Poisson Solver and integrated in ABINIT (Gnu-GPL). Features

Applications BigDFT 1.0 −→ January 2008

Publications Si clusters Boron clusters Conclusion . . . Why have we done this? Test the potential advantages of a new formalism A lot of outcomes and interesting results A lot can be done starting from present know-how

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Outline

1 Formalism Wavelets Algorithms Poisson Solver BigDFT Features Formalism

Wavelets Algorithms 2 Applications Poisson Solver Features Publications Applications Si clusters Publications Si clusters Boron clusters Boron clusters Conclusion 3 Conclusion

Next talk: Performances (MPI+OpenMP+OpenCL)

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste A DFT code based on Daubechies wavelets

BigDFT: a PSP Kohn-Sham code A Daubechies wavelets basis has unique properties for DFT usage

Systematic, Orthogonal BigDFT Localised, Adaptive Formalism

Wavelets Algorithms Kohn-Sham operators are analytic Poisson Solver Daubechies Wavelets Features Short, Separable convolutions 1.5 Applications φ(x) Publications ˜c = a c ` ∑j j `−j 1 ψ(x) Si clusters

Boron clusters 0.5 Peculiar numerical properties Conclusion 0 Real space based, highly ﬂexible -0.5 -1 Big & inhomogeneous systems -1.5 -6 -4 -2 0 2 4 6 8 x

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste A brief description of wavelet theory

Two kind of basis functions A Multi-Resolution real space basis The functions can be classiﬁed following the resolution level they span. BigDFT

Formalism Scaling Functions Wavelets Algorithms The functions of low resolution level are a linear combination Poisson Solver Features of high-resolution functions Applications

Publications Si clusters = + Boron clusters m Conclusion φ(x) = ∑ hj φ(2x − j) j=−m

Centered on a resolution-dependent grid: φj = φ0(x − j).

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste A brief description of wavelet theory

Wavelets They contain the DoF needed to complete the information which is lacking due to the coarseness of the resolution.

= 1 + 1 BigDFT 2 2 m m Formalism (2x) = h˜ (x − j) + g˜ (x − j) Wavelets φ ∑ j φ ∑ j ψ Algorithms j=−m j=−m Poisson Solver Features Applications Increase the resolution without modifying grid space Publications Si clusters Boron clusters SF + W = same DoF of SF of higher resolution

Conclusion m ψ(x) = ∑ gj φ(2x − j) j=−m

All functions have compact support, centered on grid points.

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Wavelet properties: Adaptivity

Adaptivity Resolution can be reﬁned following the grid point.

The grid is divided in BigDFT Low (1 DoF) and High

Formalism (8 DoF) resolution points.

Wavelets Algorithms Points of different resolution Poisson Solver belong to the same grid. Features

Applications Empty regions must not be

Publications Si clusters “ﬁlled” with basis functions. Boron clusters

Conclusion

Localization property,real space description Optimal for big & inhomogeneous systems, highly ﬂexible

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Adaptivity of the mesh

Atomic positions (H2O), hgrid

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Adaptivity of the mesh

Fine grid (high resolution, frmult)

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Adaptivity of the mesh

Coarse grid (low resolution, crmult)

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste No integration error

Orthogonality, scaling relation Z 1 m dx φk (x)φj (x) = δkj φ(x) = √ ∑ hj φ(2x − j) 2 j=−m

BigDFT The hamiltonian-related quantities can be calculated up to

Formalism machine precision in the given basis. Wavelets Algorithms The accuracy is only limited by the basis set ( h14 ) Poisson Solver O grid Features

Applications Publications Exact evaluation of kinetic energy Si clusters Boron clusters Obtained by convolution with ﬁlters: Conclusion 2 f (x) = ∑c`φ`(x), ∇ f (x) = ∑˜c` φ`(x) , ` ` Z 2 ˜c` = ∑cj a`−j , a` ≡ φ0(x)∂x φ`(x) , j

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Separability in 3D

The 3-dim scaling basis is a tensor product decomposition of 1-dim Scaling Functions/ Wavelets.

e ,e ,e e φ x y z (x,y,z) = φex (x)φ y (y)φez (z) jx ,jy ,jz jx jy jz

BigDFT With (jx ,jy ,jz ) the node coordinates, (0) (1) Formalism φj and φj the SF and the W respectively. Wavelets Algorithms Poisson Solver Features Gaussians and wavelets Applications

Publications The separability of the basis allows us to save computational Si clusters Boron clusters time when performing scalar products with separable

Conclusion functions (e.g. gaussians): Initial wavefunctions (input guess) 1 Poisson solver (tensor decomposition of r ) Non-local pseudopotentials

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Wavelet families used in BigDFT code

Daubechies f (x) = ∑` c`φ`(x) Interpolating f (x) = ∑j fj ϕj (x) R Orthogonal c` = dx φ`(x)f (x) Dual to dirac deltas fj = f (j) LEAST ASYMMETRIC DAUBECHIES-16 1.5 INTERPOLATING (DESLAURIERS-DUBUC)-8 scaling function 1 wavelet scaling function wavelet 1

0.5 0.5 BigDFT

0 0 Formalism -0.5 Wavelets -0.5 Algorithms -1 Poisson Solver Features -1.5 -1 -6 -4 -2 0 2 4 6 -4 -2 0 2 4 Applications Used for wavefunctions, Used for charge density, Publications Si clusters scalar products function products Boron clusters

Conclusion “Magic Filter” method (A. Neelov, S. Goedecker) The passage between the two basis sets can be performed without losing accuracy.

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Operations performed

The SCF cycle Real Space Daub. Wavelets Orbital scheme: Hamiltonian Preconditioner BigDFT Coefﬁcient Scheme: Formalism Wavelets Overlap matrices Algorithms Poisson Solver Features Orthogonalisation

Applications Publications Comput. operations Si clusters Boron clusters Convolutions Conclusion BLAS routines FFT (Poisson Solver)

Why not GPUs?

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Kohn-Sham Equations: Computing Energies

Calculate different integrals

E[ρ] = K [ρ] + U[ρ]

BigDFT 2 Z 2 ~ ∗ 2 Formalism K [ρ] = − ∑ dr ψi ∇ ψi Wavelets 2 me i V Algorithms Poisson Solver Features Z Z 0 1 0 ρ(r)ρ(r ) Applications U[ρ] = dr Vext (r)ρ(r)+ dr dr 0 + Exc[ρ] Publications V 2 V |r − r | | {z } Si clusters | {z } exchange−correlation Boron clusters Hartree Conclusion We minimise with the variables ψi (r) and fi Z with the constraint dr ρ(r) = Nel . V

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste inv FWT + Magic Filter

occ 2 ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i

Poisson solver

V (r) = R G(.)ρ Vxc [ρ(r)] H VNL({ψi }) Veffective FWT 1 2 − 2 ∇ FWT Kinetic Term i ∂Etotal j δca = − ∗ + ∑Λij ca ∂ci (a) j Λij =< ψi |H|ψj > i Stop when δca small preconditioning Steepest Descent, new,i i i ca = ca + hstepδca DIIS

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Poisson solver

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste FWT 1 2 − 2 ∇ FWT Kinetic Term i ∂Etotal j δca = − ∗ + ∑Λij ca ∂ci (a) j Λij =< ψi |H|ψj > i Stop when δca small preconditioning Steepest Descent, new,i i i ca = ca + hstepδca DIIS

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Wavelets Algorithms Poisson solver Poisson Solver Features V (r) = R G(.)ρ Applications Vxc [ρ(r)] H VNL({ψi }) Veffective Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste FWT FWT i ∂Etotal j δca = − ∗ + ∑Λij ca ∂ci (a) j Λij =< ψi |H|ψj > i Stop when δca small preconditioning Steepest Descent, new,i i i ca = ca + hstepδca DIIS

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Wavelets Algorithms Poisson solver Poisson Solver Features V (r) = R G(.)ρ Applications Vxc [ρ(r)] H VNL({ψi }) Veffective Publications Si clusters Boron clusters − 1 ∇2 Kinetic Term Conclusion 2

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste i Stop when δca small preconditioning Steepest Descent, new,i i i ca = ca + hstepδca DIIS

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Wavelets Algorithms Poisson solver Poisson Solver Features V (r) = R G(.)ρ Applications Vxc [ρ(r)] H VNL({ψi }) Veffective Publications Si clusters FWT Boron clusters − 1 ∇2 Kinetic Term Conclusion 2 FWT i ∂Etotal j δca = − ∗ + ∑Λij ca ∂ci (a) j Λij =< ψi |H|ψj >

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste i Stop when δca small

Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Direct Minimisation: Flowchart

i ψi = ∑caφa Basis: adaptive mesh (0,...,Nφ) a Orthonormalized inv FWT + Magic Filter

occ 2 BigDFT ρ(r) = ∑ |ψi (r)| Fine non-adaptive mesh: < 8Nφ i Formalism

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Poisson Solver using Green function

What is still missing is a method that can solve Poisson’s equation with free boundary conditions for arbitrary charge densities. Z ρ(r0) V (r) = dr0 |r − r0| BigDFT 3 6 Formalism Real Mesh (100 ): 10 integral evaluations in each point!

Wavelets Algorithms INTERPOLATING (DESLAURIERS-DUBUC)-8 Poisson Solver 1 Features scaling function wavelet Applications Interpolating f (x) = ∑j fj ϕj (x) Publications 0.5 Si clusters Dual to dirac deltas fj = f (j) Boron clusters 0 Conclusion The expansion coefﬁcients are the point values on a grid. -0.5

-1 -4 -2 0 2 4

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Poisson Solver using interpolating scaling function

The Hartree potential is calculated in the interpolating scaling 1 function basis using a tensor decomposition of . r Poisson solver with interpolating scaling functions

BigDFT R ρ(~x) On an uniform grid it calculates: VH (~j) = d~x Formalism |~x −~j|

Wavelets Algorithms Very fast and accurate, optimal parallelization Poisson Solver Features Can be used independently from the DFT code Applications

Publications Integrated quantities (energies) are easy to extract Si clusters Boron clusters Non-adaptive, needs data uncompression

Conclusion Explicitly free boundary conditions No need to subtract supercell interactions → charged systems.

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Poisson Solver for surface boundary conditions

A Poisson solver for surface problems Based on a mixed reciprocal-direct space representation Z 0 0 Vpx ,py (z) = −4π dz G(|~p|;z − z )ρpx ,py (z) , BigDFT Can be applied both in real or reciprocal space codes Formalism No supercell or screening functions Wavelets Algorithms Poisson Solver More precise than other existing approaches Features Applications Example of the plane capacitor: Publications Si clusters Boron clusters Periodic Hockney Our approach

Conclusion

V V V

y y y

x x x

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Basis set features

BigDFT features in a nutshell Arbitrary absolute precision can be achieved Good convergence ratio for real-space approach (O(h14)) Optimal usage of the degrees of freedom (adaptivity) BigDFT Optimal speed for a systematic approach (less memory)

Formalism Hartree potential accurate for various boundary Wavelets Algorithms conditions Poisson Solver Features Free and Surfaces BC Poisson Solver

Applications (present also in CP2K, ABINIT, OCTOPUS)

Publications Si clusters Data repartition is suitable for optimal scalability Boron clusters Simple communications paradigm, multi-level parallelisation Conclusion possible (and implemented)

Improve and develop know-how Optimal for advanced DFT functionalities in HPC framework

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Optimal for isolated systems

Test case: cinchonidine molecule (44 atoms) 101 Plane waves

100 Wavelets Ec = 40 Ha

10-1

BigDFT Ec = 90 Ha 10-2 Formalism h = 0.4bohr Wavelets Ec = 125 Ha Algorithms 10-3 Poisson Solver Absolute energy precision (Ha) h Features = 0.3bohr -4 Applications 10 Publications 105 106 Si clusters Number of degrees of freedom Boron clusters Conclusion Allows a systematic approach for molecules Considerably faster than Plane Waves codes. 10 (5) times faster than ABINIT (CPMD) Charged systems can be treated explicitly with the same time

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Systematic basis set

Two parameters for tuning the basis The grid spacing hgrid The extension of the low resolution points crmult

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste BigDFT version 1.6.0: (ABINIT-related) capabilities http://inac.cea.fr/L_Sim/BigDFT Isolated, surfaces and 3D-periodic boundary conditions (k-points, symmetries) All XC functionals of the ABINIT package (libXC library)

BigDFT Hybrid functionals, Fock exchange operator

Formalism Direct Minimisation and Mixing routines (metals)

Wavelets Algorithms Local geometry optimizations (with constraints) Poisson Solver Features External electric ﬁelds (surfaces BC) Applications

Publications Born-Oppenheimer MD, ESTF-IO Si clusters Boron clusters Vibrations Conclusion Unoccupied states Empirical van der Waals interactions Saddle point searches (NEB, Granot & Bear) All these functionalities are GPU-compatible

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste The vessel: Ambitions from BigDFT experience

Reliable formalism Systematic convergence properties Explicit environments, analytic operator expressions

BigDFT State-of-the-art computational technology Formalism

Wavelets Data locality optimal for operator applications Algorithms Poisson Solver Massive parallel environments Features

Applications Material accelerators (GPU)

Publications Si clusters Boron clusters New physics can be approached Conclusion Enhanced functionalities can be applied relatively easily Beyond the DFT approximations Order N method (in progress)

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Production version (robustness)

1 Energy Landscape of Fullerene Materials: A Comparison of Boron to Boron Nitride an Carbon, PRL 106, 2011 2 Low-energy boron fullerenes: Role of disorder and potential synthesis pathways, PRB 83, 2011 3 Optimized energy landscape exploration using the ab initio based activation-relaxation technique, JCP 135, 2011 BigDFT 4 The effect of ionization on the global minima of small and medium sized silicon and magnesium clusters, JCP 134, 2011 Formalism Wavelets 5 Energy landscape of silicon systems and its description by force ﬁelds, tight Algorithms binding schemes, density functional methods, and quantum Monte Carlo Poisson Solver Features methods, PRB 81, 2010 6 Applications First-principles prediction of stable SiC cage structures and their synthesis Publications pathways, PRB 82, 2010 Si clusters 7 Boron clusters Metallofullerenes as fuel cell electrocatalysts: A theoretical investigation of adsorbates on C59Pt, PCCP 12, 2010 Conclusion 8 Structural metastability of endohedral silicon fullerenes, PRB 81, 2010 9 Adsorption of small NaCl clusters on surfaces of silicon nanostructures, Nanotechnology 20, 2009 10 Ab initio calculation of the binding energy of impurities in semiconductors: Application to Si nanowires, PRB 81, 2010

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Metal doped silicon clusters

Are fullerene like Si20 cages ground state conﬁgurations?

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Collaboration with the group of S. Goedecker, Basel University

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Ground state structures of metal doped Si clusters

Never a fullerene conﬁguration!

Ba Ca Cr Cu K Na

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features Applications Pb Rb Sr Ti V Zr Publications Si clusters Boron clusters

Conclusion

Phys. Rev. B 82 201405(R) 2010

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Is it possible to have Boron fullerenes?

Boron sheet (Ismail-Beigi) B80 (G. Szwacki)

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Lower energy B80 cage structures

20:0 14:6 B 80 B 80

A (0.00) D (-0.22)

BigDFT

Formalism

Wavelets Algorithms Poisson Solver 14:6 10:10 B 80 Features B 80

Applications B (-0.82) E (-0.22)

Publications Si clusters Boron clusters

Conclusion

12:8 8:12 B B 80 80 C (0.22) F (-0.35)

Phys. Rev. B 83, 081403(R) 2011

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Lowest energy B80 cluster

Not a cage!

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Phys. Rev. Lett. 106, 225502 (2011)

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste The conﬁgurational energy spectrum of B80 and C60

BigDFT

Formalism

Wavelets Algorithms Poisson Solver Features

Applications

Publications Si clusters Boron clusters

Conclusion

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Conclusions

BigDFT code: a modern approach for nanosciences Flexible, reliable formalism (wavelet properties) Easily ﬁt with massively parallel architecture Open a path toward the diffusion of Hybrid architectures BigDFT

Formalism Development in progress Wavelets Algorithms Poisson Solver Wire boundary conditions and non-orthorhombic system Features (full and robust DFT code) Applications Publications PAW pseudopotentials (smoother pseudopotentials) Si clusters Boron clusters Order N methods (localization regions): large system, Conclusion QM/QM scheme for embedding systems

BigDFT tutorial on Wednesday Hands-on, Basic runs, Scalability, GPUs

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste Acknowledgments

CEA Grenoble – L_Sim L. Genovese, D. Caliste, B. Videau, P. Pochet, M. Ospici, I. Duchemin, P. Boulanger, E. Machado-Charry, S. Krishnan, F. Cinquini

BigDFT Basel University – Group of Stefan Goedecker Formalism Wavelets S. A. Ghazemi, A. Willand, M. Amsler, S. Mohr, A. Sadeghi, Algorithms Poisson Solver N. Dugan, H. Tran Features

Applications

Publications And other groups Si clusters Boron clusters Montreal University: Conclusion L. Béland, N. Mousseau European Synchrotron Radiation Facility: Y. Kvashnin, A. Mirone, A. Cerioni ABINIT community (BigDFT inside, strong reusing)

Laboratoire de Simulation Atomistique http://inac.cea.fr/L_Sim T. Deutsch, L. Genovese, D. Caliste