BigDFT

BigDFT implements density functional theory (DFT) by solving the Kohn–Sham equations describing the electrons in a material, expanded in a Daubechies wavelet basis set and using a self-consistent direct minimization or Davidson diagonalisation methods to determine the energy minimum. Computational efficiency is achieved through the use of fast short convolutions

and pseudopotentials to describe core electrons. In addition to total energy, forces and stresses are also calculated so that geometry optimizations and ab initio molecular dynamics may be carried out.

The Daubechies wavelet basis sets are an orthogonal systematic basis set as plane wave basis set but has the great advantage to allow adapted mesh with different levels of resolutions (see multi-resolution analysis). Interpolating scaling functions are used also to solve the Poisson's equation{{cite journal | last1=Genovese | first1=Luigi | last2=Deutsch | first2=Thierry | last3=Neelov | first3=Alexey | last4=Goedecker | first4=Stefan | last5=Beylkin | first5=Gregory | title=Efficient solution of Poisson's equation with free boundary conditions | journal=The Journal of Chemical Physics | publisher=AIP Publishing | volume=125 | issue=7 | date=2006-08-21 | issn=0021-9606 | doi=10.1063/1.2335442 | pmid=16942320 | page=074105|arxiv=cond-mat/0605371| bibcode=2006JChPh.125g4105G | s2cid=13918003 }}{{cite journal | last1=Genovese | first1=Luigi | last2=Deutsch | first2=Thierry | last3=Goedecker | first3=Stefan | title=Efficient and accurate three-dimensional Poisson solver for surface problems | journal=The Journal of Chemical Physics | publisher=AIP Publishing | volume=127 | issue=5 | date=2007-08-07 | issn=0021-9606 | doi=10.1063/1.2754685 | pmid=17688354 | arxiv=cond-mat/0703677 | bibcode=2007JChPh.127e4704G | page=054704| s2cid=13526036 }} with different boundary conditions as isolated or surface systems.

BigDFT was among the first massively parallel density functional theory codes which benefited from graphics processing units (GPU){{cite journal|url=http://inac.cea.fr/L_Sim/Publications/2009/Genovese-Ospici-GPU-2009.pdf|title=Density Functional Theory calculation on many-cores hybrid CPU-GPU architectures in hybrid architecture|author=L. Genovese, M. Ospici, T. Deutsch, J.-F. Méhaut, A. Neelov, S. Goedecker|arxiv=0904.1543|journal=Journal of Chemical Physics|volume=131 034103|issue=3|pages=034103| year=2009|doi=10.1063/1.3166140|pmid=19624177}} using CUDA and then OpenCL languages.

Because the Daubechies wavelets have a compact support, the Hamiltonian application can be done locally{{cite journal | last1=Mohr | first1=Stephan | last2=Ratcliff | first2=Laura E. | last3=Boulanger | first3=Paul | last4=Genovese | first4=Luigi | last5=Caliste | first5=Damien | last6=Deutsch | first6=Thierry | last7=Goedecker | first7=Stefan | title=Daubechies wavelets for linear scaling density functional theory | journal=The Journal of Chemical Physics | publisher=AIP Publishing | volume=140 | issue=20 | date=2014-05-28 | issn=0021-9606 | doi=10.1063/1.4871876 | pmid=24880269 | arxiv=1401.7441 | bibcode=2014JChPh.140t4110M | page=204110| s2cid=4619389 }} which permits to have a linear scaling in function of the number of atoms instead of a cubic scaling for traditional DFT software.

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