P. W. Anderson, More Is Different, Science, vol.177, issue.4047, pp.393-396, 1972.
DOI : 10.1126/science.177.4047.393

L. D. Landau, The Theory of a Fermi Liquid, Soviet Physics JETP, vol.3, pp.920-925, 1957.

R. M. Martin, L. Reining, and D. M. Ceperley, Interacting Electrons: Theory and Computational Approaches, 2016.
DOI : 10.1017/CBO9781139050807

M. Gatti, V. Olevano, L. Reining, and I. V. Tokatly, Transforming Nonlocality into a Frequency Dependence: A Shortcut to Spectroscopy, Physical Review Letters, vol.99, issue.5, p.57401, 2007.
DOI : 10.1088/0034-4885/70/3/R02

URL : https://hal.archives-ouvertes.fr/hal-00148137

W. Kohn and L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.119, issue.4A, pp.1133-1138, 1965.
DOI : 10.1103/PhysRev.119.1153

S. Y. Savrasov and G. Kotliar, Spectral density functionals for electronic structure calculations, Physical Review B, vol.301, issue.24, p.245101, 2004.
DOI : 10.1126/science.1087179

URL : http://arxiv.org/pdf/cond-mat/0106308

A. Georges and G. Kotliar, Hubbard model in infinite dimensions, Physical Review B, vol.33, issue.12, pp.6479-6483, 1992.
DOI : 10.1103/PhysRevB.33.7871

E. Runge and E. K. Gross, Density-Functional Theory for Time-Dependent Systems, Physical Review Letters, vol.140, issue.12, pp.997-1000, 1984.
DOI : 10.1103/PhysRev.140.A1133

L. J. Sham and M. Schlüter, Density-Functional Theory of the Energy Gap, Physical Review Letters, vol.14, issue.20, pp.1888-1891, 1983.
DOI : 10.1103/PhysRevA.14.36

J. Heyd, G. E. Scuseria, M. Ernzerhof, and . Erratum, Hybrid functionals based on a screened Coulomb potential, The Journal of Chemical Physics, vol.118, issue.18, p.219906, 2003.
DOI : 10.1063/1.477422

A. Einstein, ??ber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Annalen der Physik, vol.12, issue.6, pp.132-148, 1905.
DOI : 10.1002/andp.19053220607

URL : http://onlinelibrary.wiley.com/doi/10.1002/andp.19053220607/pdf

K. M. Siegbahn, Nobel Lecture: Electron Spectroscopy for Atoms, Molecules and Condensed Matter, 1981.
DOI : 10.1126/science.217.4555.111

J. S. Zhou, ARPES on valence aluminum

L. Venema, B. Verberck, I. Georgescu, G. Prando, E. Couderc et al., The quasiparticle zoo, Nature Physics, vol.10, issue.12, pp.1085-1089, 2016.
DOI : 10.1038/nmat2916

S. Hüfner, Photoelectron Spectroscopy, Principles and Applications, 2003.

C. N. Berglund and W. E. Spicer, Photoemission Studies of Copper and Silver: Theory, Physical Review, vol.81, issue.4A, pp.1030-1044, 1964.
DOI : 10.1103/PhysRev.81.612

A. Damascelli, Probing the Electronic Structure of Complex Systems by ARPES, Physica Scripta, vol.109, issue.T109, p.61, 2004.
DOI : 10.1238/Physica.Topical.109a00061

URL : http://arxiv.org/pdf/cond-mat/0307085

P. A. Dirac, The Quantum Theory of the Emission and Absorption of Radiation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.114, issue.767, pp.243-265, 1927.
DOI : 10.1098/rspa.1927.0039

E. Fermi, Nuclear Physics, 1950.

L. Hedin, approximation, Journal of Physics: Condensed Matter, vol.11, issue.42, p.489, 1999.
DOI : 10.1088/0953-8984/11/42/201

A. Damascelli, Z. Hussain, and Z. Shen, Angle-resolved photoemission studies of the cuprate superconductors, Reviews of Modern Physics, vol.86, issue.118, pp.473-541, 2003.
DOI : 10.1103/PhysRevLett.86.5578

URL : http://arxiv.org/pdf/cond-mat/0208504

G. Binnig and H. Rohrer, Scanning tunneling microscopy???from birth to adolescence, Reviews of Modern Physics, vol.43, issue.110, pp.615-625, 1987.
DOI : 10.1063/1.1685846

E. Ruska, The development of the electron microscope and of electron microscopy, Reviews of Modern Physics, vol.229, issue.3, pp.627-638, 1987.
DOI : 10.1126/science.4012326

J. Stroscio and D. M. Eigler, Atomic and Molecular Manipulation with the Scanning Tunneling Microscope, Science, vol.254, issue.5036, pp.1319-1326, 1991.
DOI : 10.1126/science.254.5036.1319

C. Hellenthal, R. Heimbuch, K. Sotthewes, E. S. Kooij, and H. J. Zandvliet, Determining the local density of states in the constant current STM mode, Physical Review B, vol.88, issue.3, p.35425, 2013.
DOI : 10.3762/bjnano.2.64

J. Tersoff and D. R. Hamann, Theory and Application for the Scanning Tunneling Microscope, Physical Review Letters, vol.46, issue.25, pp.1998-2001, 1983.
DOI : 10.1103/PhysRevLett.46.1227

J. R. Schrieffer, D. J. Scalapino, and J. W. Wilkins, Effective Tunneling Density of States in Superconductors, Physical Review Letters, vol.251, issue.8, pp.336-339, 1963.
DOI : 10.1098/rsta.1958.0010

M. M. Ervasti, F. Schulz, P. Liljeroth, and A. Harju, Single- and many-particle description of scanning tunneling spectroscopy, Journal of Electron Spectroscopy and Related Phenomena, vol.219, pp.63-71, 2017.
DOI : 10.1016/j.elspec.2016.11.004

URL : http://arxiv.org/pdf/1607.00240

P. A. Dirac, The Fundamental Equations of Quantum Mechanics, Proc. R. Soc. Lond. A, pp.642-653, 1925.
DOI : 10.1098/rspa.1925.0150

E. Schrödinger, An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review, vol.38, issue.6, pp.1049-1070, 1926.
DOI : 10.1007/BF01399113

M. Born and R. Oppenheimer, Zur Quantentheorie der Molekeln, Annalen der Physik, vol.24, issue.20, pp.457-484, 1927.
DOI : 10.1002/andp.19273892002

N. I. Gidopoulos and E. K. Gross, Electronic non-adiabatic states: towards a density functional theory beyond the Born-Oppenheimer approximation, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.45, issue.2011, p.20130059, 2014.
DOI : 10.1103/PhysRevA.14.36

S. Pisana, M. Lazzeri, C. Casiraghi, K. S. Novoselov, A. K. Geim et al., Breakdown of the adiabatic Born???Oppenheimer approximation in graphene, Nature Materials, vol.75, issue.3, pp.198-201, 2007.
DOI : 10.1038/nmat1846

URL : https://hal.archives-ouvertes.fr/hal-00135075

F. Sottile, Response functions of semiconductors and insulators: from the Bethe-Salpeter equation to time-dependent density functional theory, 2003.
URL : https://hal.archives-ouvertes.fr/tel-00007531

J. E. Jones, On the Determination of Molecular Fields. II. From the Equation of State of a Gas, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.106, issue.738, p.463, 1924.
DOI : 10.1098/rspa.1924.0082

P. M. Morse, Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels, Physical Review, vol.3, issue.1, pp.57-64, 1929.
DOI : 10.1007/BF01327754

P. A. Dirac, Quantum Mechanics of Many-Electron Systems, Containing Papers of a Mathematical and Physical Character, 1929.
DOI : 10.1098/rspa.1929.0094

URL : http://rspa.royalsocietypublishing.org/content/royprsa/123/792/714.full.pdf

W. Kohn, Nobel Lecture: Electronic structure of matter???wave functions and density functionals, Reviews of Modern Physics, vol.34, issue.5, pp.1253-1266, 1999.
DOI : 10.1039/tf9383400678

J. H. Van-vleck, Nonorthogonality and Ferromagnetism, Physical Review, vol.123, issue.3, pp.232-240, 1936.
DOI : 10.1098/rspa.1929.0094

M. Schlosshauer, J. Kofler, and A. Zeilinger, A snapshot of foundational attitudes toward quantum mechanics, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, vol.44, issue.3, pp.222-230, 2013.
DOI : 10.1016/j.shpsb.2013.04.004

R. O. Jones and O. Gunnarsson, The density functional formalism, its applications and prospects, Reviews of Modern Physics, vol.76, issue.77, pp.689-746, 1989.
DOI : 10.1016/0304-8853(88)90307-1

G. F. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid, 2005.
DOI : 10.1017/CBO9780511619915

P. A. Dirac, Note on Exchange Phenomena in the Thomas Atom, Mathematical Proceedings of the Cambridge Philosophical Society, vol.26, issue.03, pp.376-385, 1930.
DOI : 10.1017/S0305004100016108

URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6C5FF7297CD96F49A8B8E9E3EA50E412/S0305004100016108a.pdf/div-class-title-note-on-exchange-phenomena-in-the-thomas-atom-div.pdf

R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, 1989.
DOI : 10.1007/978-94-009-9027-2_2

R. M. Martin, Electronic Structure: Basic Theory and Applications, 2004.
DOI : 10.1017/CBO9780511805769

M. Levy, Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem, Proceedings of the National Academy of Sciences, vol.76, issue.12, pp.6062-6065, 1979.
DOI : 10.1073/pnas.76.12.6062

P. Hohenberg and W. Kohn, Inhomogeneous Electron Gas, Physical Review, vol.80, issue.3B, pp.864-871, 1964.
DOI : 10.1088/0370-1328/80/5/307

T. L. Gilbert, Hohenberg-Kohn theorem for nonlocal external potentials, Physical Review B, vol.60, issue.6, pp.2111-2120, 1975.
DOI : 10.1063/1.1680827

A. M. Müller, Explicit approximate relation between reduced two- and one-particle density matrices, Physics Letters A, vol.105, issue.9, pp.446-452, 1984.
DOI : 10.1016/0375-9601(84)91034-X

S. Sharma, J. K. Dewhurst, S. Shallcross, and E. K. Gross, Spectral Density and Metal-Insulator Phase Transition in Mott Insulators within Reduced Density Matrix Functional Theory, Physical Review Letters, vol.110, issue.11, p.116403, 2013.
DOI : 10.1016/0022-4596(75)90340-0

URL : http://arxiv.org/pdf/1206.1712

S. , D. Sabatino, J. A. Berger, L. Reining, and P. Romaniello, Photoemission spectra from reduced density matrices: The band gap in strongly correlated systems, Phys. Rev. B, vol.94, p.155141, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01418336

E. K. Gross, J. F. Dobson, and M. Petersilka, Density functional theory of timedependent phenomena, 1996.

V. M. Galitskii and A. B. , Application of Quantum Field Theory Methods to the Many Body Problem, Sov. Phys. JETP, vol.34, p.96, 1958.

W. Tarantino, P. Romaniello, J. A. Berger, L. Reining, and H. Lehmann, Self-consistent Dyson equation and self-energy functionals: An analysis and illustration on the example of the Hubbard atom, Über Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder, pp.45124-342, 1954.
DOI : 10.1088/0953-8984/13/43/304

URL : https://hal.archives-ouvertes.fr/hal-01583906

B. Farid, Towards ab initio calculation of electron energies in semiconductors, 1989.

B. Farid, Ground and Low-Lying Excited States of Interacting Electron Systems: A Survey and Some Critical Analyses, Electron Correlation in the Solid State, pp.103-261, 2011.
DOI : 10.1142/9781860944079_0003

J. M. Luttinger, Analytic Properties of Single-Particle Propagators for Many-Fermion Systems, Physical Review, vol.293, issue.4, pp.942-949, 1961.
DOI : 10.1098/rspa.1957.0037

G. Onida, L. Reining, and A. Rubio, Electronic excitations: density-functional versus many-body Green???s-function approaches, Reviews of Modern Physics, vol.41, issue.118, pp.601-659, 2002.
DOI : 10.1002/pssb.19700410103

URL : https://digital.csic.es/bitstream/10261/98472/1/Electronic%20excitations.pdf

L. Hedin, New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem, Physical Review, vol.121, issue.3A, pp.796-823, 1965.
DOI : 10.1103/PhysRev.121.950

URL : http://lup.lub.lu.se/search/ws/files/5381803/8835242.pdf

F. Aryasetiawan and O. Gunnarsson, method, Reports on Progress in Physics, vol.61, issue.3, p.237, 1998.
DOI : 10.1088/0034-4885/61/3/002

E. Jensen and E. W. Plummer, Experimental Band Structure of Na, Physical Review Letters, vol.115, issue.18, pp.1912-1915, 1985.
DOI : 10.1088/0022-3719/17/1/021

E. G. Dalla-torre, D. Benjamin, Y. He, D. Dentelski, and E. Demler, Friedel oscillations as a probe of fermionic quasiparticles, Physical Review B, vol.4, issue.20, p.205117, 2016.
DOI : 10.1103/PhysRevB.83.081106

N. F. Mott, The Basis of the Electron Theory of Metals, with Special Reference to the Transition Metals, Proceedings of the Physical Society. Section A, p.416, 1949.
DOI : 10.1088/0370-1298/62/7/303

N. F. Mott, Metal-Insulator Transition, Reviews of Modern Physics, vol.17, issue.4, pp.677-683, 1968.
DOI : 10.1103/PhysRevLett.17.1286

URL : https://hal.archives-ouvertes.fr/jpa-00209009

A. Georges, Strongly Correlated Electron Materials: Dynamical Mean-Field Theory and Electronic Structure, AIP Conference Proceedings, pp.3-74, 2004.
DOI : 10.1063/1.1800733

URL : https://hal.archives-ouvertes.fr/hal-00001233

M. C. Gutzwiller, Effect of Correlation on the Ferromagnetism of Transition Metals, Physical Review Letters, vol.25, issue.5, pp.159-162, 1963.
DOI : 10.1103/RevModPhys.25.199

J. Kanamori, Electron Correlation and Ferromagnetism of Transition Metals, Progress of Theoretical Physics, pp.275-289, 1963.
DOI : 10.1143/PTP.30.275

URL : https://academic.oup.com/ptp/article-pdf/30/3/275/5278869/30-3-275.pdf

J. Hubbard, Electron Correlations in Narrow Energy Bands, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.276, issue.1365, pp.238-257, 1963.
DOI : 10.1098/rspa.1963.0204

D. Vollhardt, Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials, AIP Conference Proceedings, vol.1297, issue.1, pp.339-403, 2010.
DOI : 10.1063/1.3518901

URL : http://arxiv.org/pdf/1004.5069.pdf

M. Prokof-'ev, G. E. Qin, H. Scuseria, B. V. Shi, L. F. Svistunov et al., Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms, Phys. Rev. X, vol.5, p.41041, 2015.

H. Bethe, Zur Theorie der Metalle, Zeitschrift f???r Physik, vol.71, issue.3-4, pp.205-226, 1931.
DOI : 10.1007/BF01341708

M. Gatti, Correlation effects in valence?electron spectroscopy of transition?metal oxydes: many?body perturbation theory and alternative approaches, 2007.

J. P. Perdew, R. G. Parr, M. Levy, and J. L. Balduz, Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy, Physical Review Letters, vol.50, issue.23, pp.1691-1694, 1982.
DOI : 10.1063/1.1671628

J. P. Perdew and M. Levy, Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities, Physical Review Letters, vol.25, issue.20, pp.1884-1887, 1983.
DOI : 10.1103/PhysRevB.25.2867

L. J. Sham, Exchange and correlation in density-functional theory, Physical Review B, vol.51, issue.2, pp.3876-3882, 1985.
DOI : 10.1103/PhysRevLett.51.1884

M. E. Casida, Generalization of the optimized-effective-potential model to include electron correlation: A variational derivation of the Sham-Schl??ter equation for the exact exchange-correlation potential, Physical Review A, vol.50, issue.3, pp.2005-2013, 1995.
DOI : 10.1103/PhysRevA.50.4707

R. T. Sharp and G. K. Horton, A Variational Approach to the Unipotential Many-Electron Problem, Physical Review, vol.141, issue.2, pp.317-317, 1953.
DOI : 10.1098/rspa.1933.0118

J. D. Talman and W. F. Shadwick, Optimized effective atomic central potential, Physical Review A, vol.9, issue.1, pp.36-40, 1976.
DOI : 10.1103/PhysRevA.9.1885

P. Rinke, A. Qteish, J. Neugebauer, and M. Scheffler, Exciting prospects for solids: Exact-exchange based functionals meet quasiparticle energy calculations, physica status solidi (b), vol.70, issue.5, pp.929-945, 2008.
DOI : 10.1103/PhysRevA.45.101

URL : http://onlinelibrary.wiley.com/doi/10.1002/pssb.200743380/pdf

A. Ferretti, I. Dabo, M. Cococcioni, and N. Marzari, Bridging density-functional and many-body perturbation theory: Orbital-density dependence in electronic-structure functionals, Physical Review B, vol.119, issue.19, p.195134, 2014.
DOI : 10.1103/PhysRevB.84.155127

W. Metzner and D. Vollhardt, Dimensions, Physical Review Letters, vol.61, issue.3, pp.324-327, 1989.
DOI : 10.1103/PhysRevLett.61.2582

M. Jarrell, Hubbard model in infinite dimensions: A quantum Monte Carlo study, Physical Review Letters, vol.41, issue.1, pp.168-171, 1992.
DOI : 10.1103/PhysRevB.41.2380

M. Ostilli, Cayley Trees and Bethe Lattices: A concise analysis for mathematicians and physicists, Physica A: Statistical Mechanics and its Applications, vol.391, issue.12, pp.3417-3423, 2012.
DOI : 10.1016/j.physa.2012.01.038

URL : http://arxiv.org/pdf/1109.6725

W. Metzner and D. Vollhardt, Dimensions, Physical Review Letters, vol.61, issue.3, pp.324-327, 1989.
DOI : 10.1103/PhysRevLett.61.2582

M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt, Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory, Physical Review B, vol.49, issue.23, p.235119, 2005.
DOI : 10.1103/PhysRevB.58.2635

URL : http://arxiv.org/pdf/cond-mat/0409730

E. Economou, Green's Functions in Quantum Physics, Series in Solid-State Sciences, 2006.

R. Bulla, Zero Temperature Metal-Insulator Transition in the Infinite-Dimensional Hubbard Model, Physical Review Letters, vol.47, issue.1, pp.136-139, 1999.
DOI : 10.1103/PhysRevB.47.3553

URL : http://arxiv.org/pdf/cond-mat/9902290

D. J. Carrascal, J. Ferrer, J. C. Smith, and K. Burke, The Hubbard dimer: a density functional case study of a many-body problem, Journal of Physics: Condensed Matter, vol.27, issue.39, p.393001, 2015.
DOI : 10.1088/0953-8984/27/39/393001

P. Romaniello, F. Bechstedt, and L. Reining, approximation: Combining correlation channels, Physical Review B, vol.134, issue.15, p.155131, 2012.
DOI : 10.1103/PhysRevB.62.3006

URL : https://hal.archives-ouvertes.fr/hal-00690287

E. Wigner, On the Interaction of Electrons in Metals, Physical Review, vol.145, issue.11, pp.1002-1011, 1934.
DOI : 10.1098/rspa.1934.0089

M. Gell-mann and K. A. Brueckner, Correlation Energy of an Electron Gas at High Density, Physical Review, vol.92, issue.2, pp.364-368, 1957.
DOI : 10.1103/PhysRev.92.609

P. A. Dirac, Note on Exchange Phenomena in the Thomas Atom, Mathematical Proceedings of the Cambridge Philosophical Society, vol.26, issue.03, pp.376-385, 1930.
DOI : 10.1017/S0305004100016108

URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/6C5FF7297CD96F49A8B8E9E3EA50E412/S0305004100016108a.pdf/div-class-title-note-on-exchange-phenomena-in-the-thomas-atom-div.pdf

J. C. Slater, A Simplification of the Hartree-Fock Method, Physical Review, vol.57, issue.3, pp.385-390, 1951.
DOI : 10.1007/BF01340281

R. M. Dreizler and E. K. Gross, Density Functional Theory, 1990.
DOI : 10.1007/978-3-642-86105-5

D. M. Ceperley and B. J. Alder, Ground State of the Electron Gas by a Stochastic Method, Physical Review Letters, vol.34, issue.7, pp.566-569, 1980.
DOI : 10.1039/tf9383400678

J. Heyd, G. E. Scuseria, and M. Ernzerhof, Hybrid functionals based on a screened Coulomb potential, The Journal of Chemical Physics, vol.118, issue.18, pp.8207-8215, 2003.
DOI : 10.1063/1.477422

T. M. Henderson, J. Paier, and G. E. Scuseria, Accurate treatment of solids with the HSE screened hybrid, physica status solidi (b), vol.109, issue.18, pp.767-774, 2011.
DOI : 10.1002/qua.22049

K. Hummer, J. Harl, and G. Kresse, Heyd-Scuseria-Ernzerhof hybrid functional for calculating the lattice dynamics of semiconductors, Physical Review B, vol.80, issue.11, p.115205, 2009.
DOI : 10.1103/PhysRevB.50.13347

A. Sharan, Z. Gui, and A. Janotti, Hybrid-Functional Calculations of the Copper Impurity in Silicon, Physical Review Applied, vol.16, issue.2, p.24023, 2017.
DOI : 10.1103/PhysRevB.25.7688

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Physical Review Letters, vol.80, issue.18, pp.3865-3868, 1996.
DOI : 10.1063/1.446965

A. D. Becke, Density???functional thermochemistry. III. The role of exact exchange, The Journal of Chemical Physics, vol.98, issue.7, pp.5648-5652, 1993.
DOI : 10.1063/1.460205

A. D. Becke, A new mixing of Hartree???Fock and local density???functional theories, The Journal of Chemical Physics, vol.23, issue.2, pp.1372-1377, 1993.
DOI : 10.1103/PhysRevA.38.3098

J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approximations, The Journal of Chemical Physics, vol.47, issue.22, pp.9982-9985, 1996.
DOI : 10.1002/qua.560560422

M. A. Marques, J. Vidal, M. J. Oliveira, L. Reining, and S. Botti, Density-based mixing parameter for hybrid functionals, Physical Review B, vol.83, issue.3, p.35119, 2011.
DOI : 10.1103/PhysRevB.81.195103

URL : https://hal.archives-ouvertes.fr/hal-00564832

J. Toulouse, I. C. Gerber, G. Jansen, A. Savin, and J. G. Ángyán, Adiabatic-Connection Fluctuation-Dissipation Density-Functional Theory Based on Range Separation, Physical Review Letters, vol.102, issue.9, p.96404, 2009.
DOI : 10.1063/1.1543944

URL : https://hal.archives-ouvertes.fr/hal-00978055

T. Stein, H. Eisenberg, L. Kronik, and R. Baer, Fundamental Gaps in Finite Systems from Eigenvalues of a Generalized Kohn-Sham Method, Physical Review Letters, vol.105, issue.26, p.266802, 2010.
DOI : 10.1103/PhysRevLett.86.1813

J. Harris and R. O. Jones, The surface energy of a bounded electron gas, Journal of Physics F: Metal Physics, vol.4, issue.8, p.1170, 1974.
DOI : 10.1088/0305-4608/4/8/013

O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism, Physical Review B, vol.29, issue.10, pp.4274-4298, 1976.
DOI : 10.1103/PhysRevLett.29.939

W. Kohn, Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms, Physical Review Letters, vol.55, issue.17, pp.3168-3171, 1996.
DOI : 10.1103/PhysRevLett.55.2471

E. Prodan and W. Kohn, Nearsightedness of electronic matter, Proceedings of the National Academy of Sciences, vol.81, issue.814, pp.11635-11638, 2005.
DOI : 10.1088/0370-1328/81/2/311

URL : http://www.pnas.org/content/102/33/11635.full.pdf

O. Gunnarsson, M. Jonson, and B. I. Lundqvist, Descriptions of exchange and correlation effects in inhomogeneous electron systems, Physical Review B, vol.10, issue.8, pp.3136-3164, 1979.
DOI : 10.1103/PhysRevB.10.3052

S. Goedecker, M. Teter, and J. Hutter, Separable dual-space Gaussian pseudopotentials, Physical Review B, vol.44, issue.3, pp.1703-1710, 1996.
DOI : 10.1103/PhysRevB.44.8503

URL : http://arxiv.org/pdf/mtrl-th/9512004

B. I. Lundqvist, Single-particle spectrum of the degenerate electron gas, Physik der kondensierten Materie, pp.193-205, 1967.
DOI : 10.1007/bf02422716

B. I. Lundqvist, Single-particle spectrum of the degenerate electron gas, Physik der kondensierten Materie, pp.206-217, 1967.
DOI : 10.1007/bf02422716

B. I. Lundqvist, Single-particle spectrum of the degenerate electron gas, Physik der kondensierten Materie, pp.117-123, 1968.
DOI : 10.1007/bf02422716

U. Barth and B. Holm, within the random-phase approximation, Physical Review B, vol.55, issue.12, pp.8411-8419, 1996.
DOI : 10.1103/PhysRevLett.55.1912

L. H. Thomas, The calculation of atomic fields, Mathematical Proceedings of the Cambridge Philosophical Society, vol.23, issue.05, pp.542-548, 1927.
DOI : 10.1017/S0305004100011683

URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/ADCA3D21D0FACD7077B5FDBB7F3B3F3A/S0305004100011683a.pdf/div-class-title-the-calculation-of-atomic-fields-div.pdf

E. Fermi, Un Metodo Statistico per la Determinazione di alcune Prioprietà dell'Atomo, Rend. Accad. Naz. Lincei, vol.6, pp.602-607, 1927.

E. Teller, On the Stability of Molecules in the Thomas-Fermi Theory, Reviews of Modern Physics, vol.99, issue.4, pp.627-631, 1962.
DOI : 10.1103/PhysRev.99.1291

L. J. Sham and W. Kohn, One-Particle Properties of an Inhomogeneous Interacting Electron Gas, Physical Review, vol.118, issue.2, pp.561-567, 1966.
DOI : 10.1103/PhysRev.118.41

L. Hedin and B. I. Lundqvist, Explicit local exchange-correlation potentials, Journal of Physics C: Solid State Physics, vol.4, issue.14, p.2064, 1971.
DOI : 10.1088/0022-3719/4/14/022

URL : http://yjsy.xmu.edu.cn/CN/Uploads/888fab9b-b2e3-4571-90f1-d8313174c5bd/WebWork/01jpc4-2064-HL-Vxc.pdf

C. S. Wang and W. E. Pickett, Density-Functional Theory of Excitation Spectra of Semiconductors: Application to Si, Physical Review Letters, vol.24, issue.7, pp.597-600, 1983.
DOI : 10.1103/PhysRevB.24.3468

W. E. Pickett and C. S. Wang, Local-density approximation for dynamical correlation corrections to single-particle excitations in insulators, Physical Review B, vol.90, issue.8, pp.4719-4733, 1984.
DOI : 10.1002/pssb.2220900229

X. Gonze, B. Amadon, P. Anglade, J. Beuken, F. Bottin et al., ABINIT: First-principles approach to material and nanosystem properties, Computer Physics Communications, vol.180, issue.12, pp.2582-2615, 2009.
DOI : 10.1016/j.cpc.2009.07.007

URL : https://digital.csic.es/bitstream/10261/95956/1/accesoRestringido.pdf

X. Gonze, G. Rignanese, M. Verstraete, J. Betiken, Y. Pouillon et al., Abstract, Zeitschrift f??r Kristallographie - Crystalline Materials, vol.51, issue.5/6, pp.558-562, 2005.
DOI : 10.1103/PhysRevB.51.8610

P. E. Blöchl, O. Jepsen, and O. K. Andersen, Improved tetrahedron method for Brillouin-zone integrations, Physical Review B, vol.3, issue.23, pp.16223-16233, 1994.
DOI : 10.1088/0953-8984/3/33/002

R. Wyckoff, Crystal structures, 1963.

N. Troullier and J. L. Martins, Efficient pseudopotentials for plane-wave calculations, Physical Review B, vol.10, issue.3, pp.1993-2006, 1991.
DOI : 10.1016/0378-4363(79)90008-1

D. R. Hamann, Optimized norm-conserving Vanderbilt pseudopotentials, Physical Review B, vol.23, issue.8, p.85117, 2013.
DOI : 10.1103/PhysRevLett.77.3865

URL : http://arxiv.org/pdf/1306.4707

J. W. Precker and M. A. Da-silva, Experimental estimation of the band gap in silicon and germanium from the temperature???voltage curve of diode thermometers, American Journal of Physics, vol.70, issue.11, pp.1150-1153, 2002.
DOI : 10.1119/1.1512658

H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Physical Review B, vol.10, issue.12, pp.5188-5192, 1976.
DOI : 10.1016/0021-9991(72)90046-0

J. P. Perdew and S. Kurth, Density Functionals for Non-relativistic Coulomb Systems in the New Century, A Primer in Density Functional Theory, 2003.
DOI : 10.1007/3-540-37072-2_1

L. Van-hove, The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal, Physical Review, vol.65, issue.6, pp.1189-1193, 1953.
DOI : 10.1088/0370-1298/65/10/305

G. Cappellini, R. Del-sole, L. Reining, and F. Bechstedt, Model dielectric function for semiconductors, Physical Review B, vol.84, issue.15, pp.9892-9895, 1993.
DOI : 10.1016/0038-1098(92)90476-P

G. A. Baraff and M. Schlüter, Migration of interstitials in silicon, Physical Review B, vol.16, issue.6, pp.3460-3469, 1984.
DOI : 10.1088/0022-3719/16/18/003

A. Schindlmayr and R. W. Godby, Approximation, Physical Review Letters, vol.8, issue.8, pp.1702-1705, 1998.
DOI : 10.1088/0022-3719/8/10/010

F. Gebhard, The Mott Metal?Insulator Transition, Models and Methods, 1997.

J. M. Tomczak, Spectral and Optical Properties of Correlated Materials, 2007.
URL : https://hal.archives-ouvertes.fr/pastel-00003163

E. W. Ng and M. Geller, A table of integrals of the Error functions, Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, vol.73, issue.1, p.1, 1969.
DOI : 10.6028/jres.073B.001

M. Geller and E. W. Ng, A table of integrals of exponential integral, Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences, vol.73, issue.3, p.191, 1969.
DOI : 10.6028/jres.073B.019

URL : http://doi.org/10.6028/jres.073b.019

K. Capelle and V. L. Campo, Density functionals and model Hamiltonians: Pillars of many-particle physics, Physics Reports, vol.528, issue.3, pp.91-159, 2013.
DOI : 10.1016/j.physrep.2013.03.002

X. Wang, C. D. Spataru, M. S. Hybertsen, and A. J. Millis, Electronic correlation in nanoscale junctions: Comparison of the GW approximation to a numerically exact solution of the single-impurity Anderson model, Physical Review B, vol.23, issue.4, p.45119, 2008.
DOI : 10.1016/0003-4916(89)90359-X

K. S. Thygesen, Characteristics of a Molecular Junction, Physical Review Letters, vol.77, issue.16, p.166804, 2008.
DOI : 10.1103/PhysRevLett.68.2512

C. Verdozzi, R. W. Godby, and S. Holloway, Approximations for the Self-Energy of a Hubbard Cluster, Physical Review Letters, vol.16, issue.12, pp.2327-2330, 1995.
DOI : 10.1103/PhysRevLett.62.2718

K. S. Thygesen and A. Rubio, scheme for nonequilibrium quantum transport in molecular contacts, Physical Review B, vol.281, issue.11, p.115333, 2008.
DOI : 10.1103/PhysRevB.28.4397

URL : http://orbit.dtu.dk/files/4804504/Kristian.pdf

M. P. Von-friesen, C. Verdozzi, and C. Almbladh, Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters, Physical Review Letters, vol.7, issue.17, p.176404, 2009.
DOI : 10.1103/PhysRevLett.74.2327