Sobolev Spaces, Pure and Applied Mathematics, vol.65, issue.103, p.104, 1975. ,
A Posteriori Error Estimation in Finite Element Analysis, 37 in Pure and Applied Mathematics, p.172, 2000. ,
Existence of minimizers for Kohn???Sham models in quantum chemistry, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.26, issue.6, pp.2425-2455, 2009. ,
DOI : 10.1016/j.anihpc.2009.06.003
Multiresolution analysis of electronic structure: semicardinal and wavelet bases, Reviews of Modern Physics, vol.99, issue.1, pp.267-311, 1999. ,
DOI : 10.1016/S0038-1098(96)80049-4
Prolate-spheroidal orbitals for homonuclear and heteronuclear diatomic molecules. II. Shielding effects for the two-electron problem, Physical Review A, vol.41, issue.1, pp.61-70, 1974. ,
DOI : 10.1063/1.1726326
Eigenvalue problems, in Finite Element Methods of Handbook of Numerical Analysis, pp.64-787, 1991. ,
An h-adaptive finite element solver for the calculations of the electronic structures, Journal of Computational Physics, vol.231, issue.14, pp.4967-4979, 2012. ,
DOI : 10.1016/j.jcp.2012.04.002
Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique, Journal of Scientific Computing, vol.372, issue.12, pp.372-391, 2013. ,
DOI : 10.1016/j.physleta.2008.05.075
On the Representation of Operators in Bases of Compactly Supported Wavelets, SIAM Journal on Numerical Analysis, vol.29, issue.6, pp.1716-1740, 1992. ,
DOI : 10.1137/0729097
URL : https://hal.archives-ouvertes.fr/hal-01322928
Fast wavelet transforms and numerical algorithms I, Communications on Pure and Applied Mathematics, vol.1, issue.2, pp.141-183, 1991. ,
DOI : 10.1017/CBO9780511662294.012
A Multiresolution Approach to Regularization of Singular Operators and Fast Summation, SIAM Journal on Scientific Computing, vol.24, issue.1, pp.81-117, 2002. ,
DOI : 10.1137/S1064827500379227
\mathcal{O}(N) methods in electronic structure calculations, Reports on Progress in Physics, vol.75, issue.3, pp.36503-36544, 2012. ,
DOI : 10.1088/0034-4885/75/3/036503
Electronic Wave Functions. I. A General Method of Calculation for the Stationary States of Any Molecular System, Proc. R. Soc. Lond. A, pp.542-554, 1950. ,
DOI : 10.1098/rspa.1950.0036
Wavelets for electronic structure calculations, Journal of Mathematical Chemistry, vol.22, issue.2/4, pp.117-142, 1997. ,
DOI : 10.1023/A:1019171830287
Self-Consistent Field (SCF) algorithms, Encyclopedia of Applied and Computational Mathematics, pp.1310-1316, 2015. ,
Numerical Analysis of Nonlinear Eigenvalue Problems, Journal of Scientific Computing, vol.30, issue.1-3, pp.90-117, 2010. ,
DOI : 10.5802/aif.204
Numerical analysis of the planewave discretization of orbital-free and Kohn-Sham models, pp.46-341, 2012. ,
Computational quantum chemistry: A primer, in Special Volume: Computational Chemistry X of Handbook of Numerical Analysis, pp.3-270, 2003. ,
Can we outperform the DIIS approach for electronic structure calculations?, 2<82::AID-QUA3>3.0.CO;2-I. 31, pp.82-90, 2000. ,
On the convergence of SCF algorithms for the Hartree-Fock equations, pp.34-749, 2000. ,
Modèles à N corps. Notes du cours M2 : Méthodes variationnelles en physique quantique, Février, 2008. ,
Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations, The Journal of Chemical Physics, vol.128, issue.13, pp.134108-211, 2008. ,
DOI : 10.1103/PhysRevLett.94.233002
A bird's-eye view of density-functional theory, Braz, J. Phys, vol.36, pp.1318-1343, 2006. ,
Contribution à l'analyse numérique de quelques problèmes en chimie quantique et mécanique, p.133, 2009. ,
Les ondelettes comme fonctions de base dans le calcul des structures électroniques, p.41, 2005. ,
Adaptive Finite Element Approximations for Kohn--Sham Models, Multiscale Modeling & Simulation, vol.12, issue.4, pp.1828-1869, 2014. ,
DOI : 10.1137/130916096
URL : http://arxiv.org/pdf/1302.6896
Numerical analysis of finite dimensional approximations of Kohn???Sham models, Advances in Computational Mathematics, vol.28, issue.2, pp.225-256, 2013. ,
DOI : 10.1002/mma.793
Finite element approximations of nonlinear eigenvalue problems in quantum physics, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.21-22, pp.1846-1865, 2011. ,
DOI : 10.1016/j.cma.2011.02.008
Calculations, Journal of the American Chemical Society, vol.132, issue.35, pp.12365-12377, 2010. ,
DOI : 10.1021/ja103365s
URL : https://hal.archives-ouvertes.fr/hal-01229899
Wavelets in electronic structure calculations, Physical Review Letters, vol.246, issue.12, pp.1808-1811, 1993. ,
DOI : 10.1098/rsta.1953.0014
An introduction to wavelets of Wavelet Analysis and its Applications, p.105, 1992. ,
A cardinal spline approach to wavelets, Proc. Amer, pp.785-793, 1991. ,
DOI : 10.1090/S0002-9939-1991-1077784-X
Ondelettes, analyses multir??solutions et filtres miroirs en quadrature, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.7, issue.5, pp.439-459, 1990. ,
DOI : 10.1016/S0294-1449(16)30286-4
A new technique to estimate the regularity of refinable functions, Revista Matem??tica Iberoamericana, vol.12, pp.527-591, 1996. ,
DOI : 10.4171/RMI/207
Biorthogonal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.485-560, 1992. ,
DOI : 10.1002/cpa.3160450502
Using the Refinement Equation for Evaluating Integrals of Wavelets, SIAM Journal on Numerical Analysis, vol.30, issue.2, pp.507-537, 1993. ,
DOI : 10.1137/0730024
Convergence and optimal complexity of adaptive finite element eigenvalue computations, Numerische Mathematik, vol.98, issue.3, pp.313-355, 2008. ,
DOI : 10.1007/s00211-008-0169-3
Orthonormal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.34, issue.7, pp.909-996, 1988. ,
DOI : 10.1007/978-3-642-61987-8
Two-Scale Difference Equations II. Local Regularity, Infinite Products of Matrices and Fractals, SIAM Journal on Mathematical Analysis, vol.23, issue.4, pp.1031-1079, 1992. ,
DOI : 10.1137/0523059
Calculation of Condensed Matter: Transparent Convergence through Semicardinal Multiresolution Analysis, Physical Review Letters, vol.13, issue.21, p.216402, 2003. ,
DOI : 10.1103/PhysRevB.13.5188
URL : http://arxiv.org/abs/cond-mat/0204411
Hemilabile Ligand Induced Selectivity:?? a DFT Study on Ethylene Trimerization Catalyzed by Titanium Complexes, Organometallics, vol.22, issue.17, pp.22-3404, 2003. ,
DOI : 10.1021/om030255w
Two-dimensional delta potential wells and condensed-matter physics, Rev. Mex. Fis, vol.51, pp.626-632, 2005. ,
Résolution numérique d'une équation de type Schrödinger 1-D non linéaire, 0211. ,
Calcul numérique du produit scalaire entre une gaussienne et la fonction d'échelle d'une ondelette, p.162, 2014. ,
analysis of a nonlinear Gross???Pitaevskii-type eigenvalue problem, IMA Journal of Numerical Analysis, vol.37, issue.1, pp.94-137, 2017. ,
DOI : 10.1093/imanum/drw001
URL : https://hal.archives-ouvertes.fr/hal-00903715
Multiresolution analysis for efficient, high precision all-electron density-functional calculations, Physical Review B, vol.3, issue.16, p.165106, 2002. ,
DOI : 10.1016/S1359-0286(98)80042-9
Rapid convergence of crystalline energy bands by use of a plane-wave-gaussian mixed basis set, International Journal of Quantum Chemistry, vol.179, issue.S5, pp.471-487, 1971. ,
DOI : 10.1103/PhysRevB.1.4692
Systematic approach to extended even-tempered orbital bases for atomic and molecular calculations, Theoretica Chimica Acta, vol.52, issue.3, pp.231-251, 1979. ,
DOI : 10.1007/BF00547681
Looking at atomic orbitals through fourier and wavelet transforms, International Journal of Quantum Chemistry, vol.25, issue.6, pp.619-636, 1993. ,
DOI : 10.1098/rspa.1935.0085
Iterative Process for Solving Hartree???Fock Equations by Means of a Wavelet Transform, Applied and Computational Harmonic Analysis, vol.1, issue.3, pp.232-241, 1994. ,
DOI : 10.1006/acha.1994.1010
Eigenvalue approximation by the finite element method, Advances in Mathematics, vol.10, issue.2, pp.300-316, 1973. ,
DOI : 10.1016/0001-8708(73)90113-8
URL : http://doi.org/10.1016/0001-8708(73)90113-8
Delta???Function Model. I. Electronic Energies of Hydrogen???Like Atoms and Diatomic Molecules, The Journal of Chemical Physics, vol.4, issue.6, pp.1150-76, 1956. ,
DOI : 10.1063/1.1742060
Bound States in Delta Function Potentials, Journal of Atomic, Molecular, and Optical Physics, vol.59, issue.12, pp.1-4, 2011. ,
DOI : 10.1119/1.16691
URL : http://doi.org/10.1155/2011/573179
Multipole-preserving quadratures for the discretization of functions in real-space electronic structure calculations, Phys. Chem. Chem. Phys., vol.97, issue.4, pp.31582-31591, 2015. ,
DOI : 10.1103/PhysRevLett.97.170201
Daubechies wavelets as a basis set for density functional pseudopotential calculations, The Journal of Chemical Physics, vol.129, issue.1, pp.14109-71, 2008. ,
DOI : 10.1137/1.9780898719604
URL : http://arxiv.org/pdf/0804.2583
Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures, The Journal of Chemical Physics, vol.131, issue.3, pp.34103-63, 1998. ,
DOI : 10.1016/0010-4655(93)90057-J
URL : http://edoc.unibas.ch/10299/1/1%252E3166140.pdf
Linear scaling electronic structure methods, Reviews of Modern Physics, vol.78, issue.4, pp.1085-1123, 1999. ,
DOI : 10.1103/PhysRevLett.78.479
Linear scaling solution of the Coulomb problem using wavelets, Solid State Commun, pp.665-669, 1998. ,
Frequency localization properties of the density matrix and its resulting hypersparsity in a wavelet representation, Physical Review B, vol.140, issue.11, pp.7270-7273, 1999. ,
DOI : 10.1006/jcph.1998.5885
Exact Gaussian expansions of Slater-type atomic orbitals, Journal of Computational Chemistry, vol.7, issue.10, pp.1007-1012, 2002. ,
DOI : 10.1093/comjnl/7.4.308
URL : https://hal.archives-ouvertes.fr/hal-00820886
ABINIT: First-principles approach to material and nanosystem properties, Computer Physics Communications, vol.180, issue.12, pp.180-2582, 2009. ,
DOI : 10.1016/j.cpc.2009.07.007
URL : https://digital.csic.es/bitstream/10261/95956/1/accesoRestringido.pdf
Multiresolution quantum chemistry: Basic theory and initial applications, The Journal of Chemical Physics, vol.121, issue.23, pp.11587-11598, 2004. ,
DOI : 10.1063/1.435280
Gaussian 70, quantum chemistry program exchange, program no, p.13, 1970. ,
Self???Consistent Molecular???Orbital Methods. I. Use of Gaussian Expansions of Slater???Type Atomic Orbitals, The Journal of Chemical Physics, vol.51, issue.6, pp.2657-2664, 1969. ,
DOI : 10.1016/0009-2614(68)80030-2
Certified Reduced Basis Methods for Parametrized Partial Differential Equations, SpringerBriefs in Mathematics, vol.169, p.170 ,
DOI : 10.1007/978-3-319-22470-1
URL : https://hal.archives-ouvertes.fr/hal-01223456
Electron Wavefunctions and Densities for Atoms, Annales Henri Poincar??, vol.2, issue.1, pp.77-100, 2001. ,
DOI : 10.1007/PL00001033
URL : http://arxiv.org/pdf/math/0005018
Local properties of Coulombic wave functions, Communications in Mathematical Physics, vol.7, issue.1, pp.185-215, 1994. ,
DOI : 10.1007/978-94-009-2323-2
Inhomogeneous Electron Gas, Physical Review, vol.80, issue.3B, pp.864-871, 1964. ,
DOI : 10.1088/0370-1328/80/5/307
Analysis of periodic Schr??dinger operators: Regularity and approximation of eigenfunctions, Journal of Mathematical Physics, vol.4, issue.8, p.83501, 2008. ,
DOI : 10.1016/S0168-2024(08)70178-4
Gaussian???Type Functions for Polyatomic Systems. I, The Journal of Chemical Physics, vol.42, issue.4, pp.1293-1302, 1965. ,
DOI : 10.1063/1.1725897
A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity, Signal Process Fundamental properties of Hamiltonian operators of Schrödinger type, Trans. Amer. Math. Soc, vol.70, pp.91-2699, 1951. ,
On the eigenfunctions of many-particle systems in quantum mechanics, Communications on Pure and Applied Mathematics, vol.6, issue.2, pp.151-177, 1957. ,
DOI : 10.1002/cpa.3160100201
Perturbation Theory for Linear Operators, p.23, 1980. ,
The convergence of the Rayleigh-Ritz method in quantum chemistry. I. The criteria of convergence, Theor. Chim. Acta, pp.44-53, 1977. ,
The convergence of the Rayleigh-Ritz method in quantum chemistry. II. Investigation of the convergence for special systems of Slater, Gauss and two-electron functions Sham, Self-consistent equations including exchange and correlation effects, Theor. Chim. Acta Phys. Rev, vol.140, pp.44-71, 1965. ,
total-energy calculations using a plane-wave basis set, Physical Review B, vol.2, issue.16, pp.11169-11186, 1996. ,
DOI : 10.1016/0927-0256(94)90105-8
The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces, Numerische Mathematik, vol.45, issue.4, pp.781-802, 2012. ,
DOI : 10.1051/m2an/2010103
Theory of the expansion of wave functions in a gaussian basis, International Journal of Quantum Chemistry, vol.199, issue.6, pp.447-463, 1994. ,
DOI : 10.1017/S0370164600017806
EXISTENCE AND CONVERGENCE RESULTS FOR THE GALERKIN APPROXIMATION OF AN ELECTRONIC DENSITY FUNCTIONAL, Mathematical Models and Methods in Applied Sciences, vol.8, issue.12, pp.2237-2265, 2010. ,
DOI : 10.1007/978-1-4612-4838-5
An energy-minimizing mesh for the Schr??dinger equation, Journal of Computational Physics, vol.83, issue.2, pp.361-3720021, 1989. ,
DOI : 10.1016/0021-9991(89)90124-1
Analysis of a modified Schr??dinger operator in 2D: Regularity, index, and FEM, Journal of Computational and Applied Mathematics, vol.224, issue.1, pp.320-338, 2009. ,
DOI : 10.1016/j.cam.2008.05.009
Thomas-fermi and related theories of atoms and molecules, Reviews of Modern Physics, vol.31, issue.4, pp.603-641, 1981. ,
DOI : 10.1143/JPSJ.31.882
Density functionals for coulomb systems, International Journal of Quantum Chemistry, vol.140, issue.3, pp.243-277, 1983. ,
DOI : 10.4153/CJM-1949-007-x
A hybrid Gaussian and plane wave density functional scheme, Molecular Physics, vol.48, issue.3, pp.477-488, 1997. ,
DOI : 10.1103/PhysRevB.48.14646
Gaussian and wavelet bases in electronic structure calculations, pp.71-212, 2011. ,
P finite element approximation for full-potential electronic structure calculations, Chin, Ann. Math., Ser. B, vol.35, pp.1-24, 2014. ,
DOI : 10.1007/978-3-642-41401-5_14
Numerical Analysis of Eigenproblems for Electronic Structure Calculations, Encyclopedia of Applied and Computational Mathematics, pp.1042-1047, 2015. ,
DOI : 10.1007/978-3-540-70529-1_258
A Priori and A Posteriori Error Analysis in Chemistry, Encyclopedia of Applied and Computational Mathematics, pp.5-10 ,
DOI : 10.1007/978-3-540-70529-1_255
Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations, Multiresolution approximation and wavelet orthonormal bases of, pp.739-770, 1989. ,
DOI : 10.1126/science.271.5245.51
URL : https://hal.archives-ouvertes.fr/hal-00798321
A wavelet tour of signal processing: The sparse way, pp.51-52, 2008. ,
Interpolating Wavelets in Kohn-Sham Electronic Structure Calculations, Computational Science ? ICCS 2001: International Conference Proceedings, 2001. ,
DOI : 10.1007/3-540-45545-0_63
Algorithm 929, ACM Transactions on Mathematical Software, vol.39, issue.4, pp.27-61, 2013. ,
DOI : 10.1145/2491491.2491497
Daubechies wavelets for linear scaling density functional theory, The Journal of Chemical Physics, vol.140, issue.20, 2014. ,
DOI : 10.1103/PhysRevB.82.035431
URL : https://hal.archives-ouvertes.fr/hal-01334186
Orthonormal Wavelet Bases Adapted for Partial Differential Equations with Boundary Conditions, SIAM Journal on Mathematical Analysis, vol.29, issue.4, pp.1040-1065, 1998. ,
DOI : 10.1137/S0036141095295127
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.56.4210
Higher-order adaptive finite-element methods for Kohn???Sham density functional theory, Journal of Computational Physics, vol.253, pp.308-343, 2013. ,
DOI : 10.1016/j.jcp.2013.06.042
URL : http://arxiv.org/abs/1207.0167
Volume data and wavelet transforms, IEEE Computer Graphics and Applications, vol.13, issue.4, pp.50-56, 1993. ,
DOI : 10.1109/38.219451
A wavelet-based adaptive method for determining eigenstates of electronic systems, Theoretical Chemistry Accounts, vol.38, issue.3-6, pp.471-479, 2010. ,
DOI : 10.1016/S0377-0427(00)00511-2
An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis, Journal of Computational Physics, vol.217, issue.2, pp.312-339, 2006. ,
DOI : 10.1016/j.jcp.2006.01.003
Multiresolution density-matrix approach to electronic structure calculations, Physical Review B, vol.340, issue.15, p.155120, 2002. ,
DOI : 10.1016/S0009-2614(01)00409-2
Density Functional Theory of Atoms and Molecules, of International Series of Monographs on Chemistry, p.13, 1989. ,
DOI : 10.1007/978-94-009-9027-2_2
Periodical wavelet analysis, a tool for inhomogeneous field investigations: Theory and algorithms, Rech. Aérosp, pp.53-67, 1989. ,
Bases mixtes ondelettes?gaussiennes pour le calcul des structures électroniques, tech. report, IFP Energies nouvelles, p.141, 2013. ,
Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bound methods, J. Fluids Engrg, vol.124, issue.167, pp.70-80, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00798326
Reduced Basis Methods for Partial Differential Equations: An Introduction, pp.2015-2032 ,
DOI : 10.1007/978-3-319-15431-2
Inner product computations using periodized Daubechies wavelets, 19<3557::AID-NME227>3.0.CO;2-A. 69, pp.3557-35781097, 1998. ,
DOI : 10.1137/0724066
URL : https://hal.archives-ouvertes.fr/hal-01323007
Periodized Daubechies wavelets, tech. report, p.69, 1996. ,
DOI : 10.2172/211651
URL : https://digital.library.unt.edu/ark:/67531/metadc669960/m2/1/high_res_d/211651.pdf
Operator methods in quantum mechanics, North-Holland, p.23, 1981. ,
The calculation of exchange forces: General results and specific models, The Journal of Chemical Physics, vol.36, issue.4, pp.2841-2854, 1993. ,
DOI : 10.1063/1.1724312
General relativity and quantum mechanics: Towards a generalization of the Lambert W function, AAECC, pp.17-41, 2006. ,
Gaussian???Transform Method for Molecular Integrals. I. Formulation for Energy Integrals, The Journal of Chemical Physics, vol.49, issue.2, pp.398-414, 1964. ,
DOI : 10.1017/S0370164600026262
How many electrons can a nucleus bind?, Annals of Physics, vol.157, issue.2, pp.307-3200003, 1984. ,
DOI : 10.1016/0003-4916(84)90062-9
Atomic Shielding Constants, Physical Review, vol.35, issue.1, pp.57-64, 1930. ,
DOI : 10.1103/PhysRev.35.509
Wave Functions in a Periodic Potential, Physical Review, vol.51, issue.10, pp.846-851, 1937. ,
DOI : 10.1103/PhysRev.51.129
Quadrature Formulae and Asymptotic Error Expansions for Wavelet Approximations of Smooth Functions, SIAM Journal on Numerical Analysis, vol.31, issue.4, pp.31-1240, 1994. ,
DOI : 10.1137/0731065
Modern quantum chemistry: An introduction to advanced electronic structure theory, p.37, 1982. ,
Une analyse de l'erreur de quadrature du produit scalaire gaussienne-fonction d'échelle. Note de travail, p.162, 2014. ,
Shift-orthogonal wavelet bases using splines, IEEE Signal Processing Letters, vol.3, issue.3, pp.85-88, 1996. ,
DOI : 10.1109/97.481163
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.19.1564
Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach, Computer Physics Communications, vol.167, issue.2, pp.103-128, 2005. ,
DOI : 10.1016/j.cpc.2004.12.014
A review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, Advances in numerical mathematics, p.172, 1996. ,
Periodic wavelets from scratch, J. Comput. Anal. Appli, vol.1, pp.25-41, 1999. ,
Multiresolution quantum chemistry in multiwavelet bases: Analytic derivatives for Hartree???Fock and density functional theory, The Journal of Chemical Physics, vol.121, issue.7, pp.2866-2876, 2004. ,
DOI : 10.1080/00268970210133206
Multiresolution quantum chemistry in multiwavelet bases: Hartree???Fock exchange, The Journal of Chemical Physics, vol.98, issue.14, p.6680, 2004. ,
DOI : 10.1063/1.457068
On the regularity of the electronic Schr???dinger equation in Hilbert spaces of mixed derivatives, Numerische Mathematik, vol.4, issue.4, pp.731-759, 2004. ,
DOI : 10.1007/s00211-003-0498-1
Finite element method for solving Kohn???Sham equations based on self-adaptive tetrahedral mesh, Physics Letters A, vol.372, issue.30, pp.5071-5076, 2008. ,
DOI : 10.1016/j.physleta.2008.05.075
Discussion of the spectrum of Schrödinger operators for systems of many particles, Trudy Mosk, Mat. Obs, vol.9, pp.81-120, 1960. ,
An analysis of finite-dimensional approximations for the ground state solution of Bose???Einstein condensates, Nonlinearity, vol.17, issue.2, pp.541-550010, 2004. ,
DOI : 10.1088/0951-7715/17/2/010
Finite dimensional approximations for the electronic ground state solution of a molecular system, Mathematical Methods in the Applied Sciences, vol.26, issue.4, pp.429-447, 2007. ,
DOI : 10.1007/978-1-4612-0603-3