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All issues Volume 46 / No 2 (November-December 2012) ESAIM: M2AN, 46 2 (2012) 341-388 References
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ESAIM: M2AN
Volume 46, Number 2, November-December 2012
Page(s) 341 - 388
DOI https://doi.org/10.1051/m2an/2011038
Published online 24 October 2011
  1. A. Anantharaman and E. Cancès, Existence of minimizers for Kohn-Sham models in quantum chemistry. Ann. Inst. Henri Poincaré 26 (2009) 2425–2455. [Google Scholar]
  2. R. Benguria, H. Brezis and E.H. Lieb, The Thomas-Fermi-von Weizsäcker theory of atoms and molecules. Comm. Math. Phys. 79 (1981) 167–180. [Google Scholar]
  3. X. Blanc and E. Cancès, Nonlinear instability of density-independent orbital-free kinetic energy functionals. J. Chem. Phys. 122 (2005) 214–106. [CrossRef] [Google Scholar]
  4. M. Born and J.R. Oppenheimer, Zur quantentheorie der molekeln. Ann. Phys. 84 (1927) 457–484. [Google Scholar]
  5. G. Bourdaud and M. Lanza de Cristoforis, Regularity of the symbolic calculus in Besov algebras. Stud. Math. 184 (2008) 271–298. [CrossRef] [Google Scholar]
  6. E. Cancès, R. Chakir and Y. Maday, Numerical analysis of nonlinear eigenvalue problems. J. Sci. Comput. 45 (2010) 90–117. [Google Scholar]
  7. E. Cancès, R. Chakir, V. Ehrlacher and Y. Maday, in preparation. [Google Scholar]
  8. E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris and Y. Maday, Computational quantum chemistry: a primer, in Handbook of numerical analysis X. North-Holland, Amsterdam (2003) 3–270. [Google Scholar]
  9. E. Cancès, C. Le Bris and Y. Maday, Méthodes mathématiques en chimie quantique. Springer (2006). [Google Scholar]
  10. E. Cancès, G. Stoltz, V.N. Staroverov, G.E. Scuseria and E.R. Davidson, Local exchange potentials for electronic structure calculations. MathematicS In Action 2 (2009) 1–42. [CrossRef] [MathSciNet] [Google Scholar]
  11. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral methods: fundamentals in single domains. Springer (2006). [Google Scholar]
  12. I. Catto, C. Le Bris and P.-L. Lions, Mathematical theory of thermodynamic limits: Thomas-Fermi type models. Oxford University Press (1998). [Google Scholar]
  13. H. Chen, X. Gong, L. He and A. Zhou, Convergence of adaptive finite element approximations for nonlinear eigenvalue problems. arXiv preprint, http://arxiv.org/pdf/1001.2344. [Google Scholar]
  14. H. Chen, X. Gong and A. Zhou, Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. Math. Methods Appl. Sci. 33 (2010) 1723–1742. [CrossRef] [MathSciNet] [Google Scholar]
  15. R.M. Dreizler and E.K.U. Gross, Density functional theory. Springer (1990). [Google Scholar]
  16. A. Edelman, T.A. Arias and S.T. Smith, The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl. 20 (1998) 303–353. [CrossRef] [Google Scholar]
  17. V. Gavini, J. Knap, K. Bhattacharya and M. Ortiz, Non-periodic finite-element formulation of orbital-free density functional theory. J. Mech. Phys. Solids 55 (2007) 669–696. [CrossRef] [MathSciNet] [Google Scholar]
  18. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, 3rd edition. Springer (1998). [Google Scholar]
  19. X. Gonze et al., ABINIT: first-principles approach to material and nanosystem properties. Computer Phys. Comm. 180 (2009) 2582–2615. [CrossRef] [Google Scholar]
  20. P. Hohenberg and W. Kohn, Inhomogeneous electron gas. Phys. Rev. 136 (1964) B864–B871. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  21. W. Kohn and L.J. Sham, Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (1965) A1133–A1138. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
  22. B. Langwallner, C. Ortner and E. Süli, Existence and convergence results for the Galerkin approximation of an electronic density functional. Math. Mod. Methods Appl. Sci. 20 (2010) 2237–2265. [Google Scholar]
  23. C. Le Bris, Ph.D. thesis, École Polytechnique (1993). [Google Scholar]
  24. W.A. Lester Jr. Ed., Recent advances in Quantum Monte Carlo methods. World Sientific (1997). [Google Scholar]
  25. W.A. Lester Jr., S.M. Rothstein and S. Tanaka Eds., Recent advances in Quantum Monte Carlo methods, Part II, World Sientific (2002). [Google Scholar]
  26. M. Levy, Universal variational functionals of electron densities, first order density matrices, and natural spin-orbitals and solution of the V-representability problem. Proc. Natl. Acad. Sci. U.S.A. 76 (1979) 6062–6065. [CrossRef] [PubMed] [Google Scholar]
  27. E.H. Lieb, Thomas-Fermi and related theories of atoms and molecules. Rev. Mod. Phys. 53 (1981) 603–641. [CrossRef] [MathSciNet] [Google Scholar]
  28. E.H. Lieb, Density Functional for Coulomb systems. Int. J. Quant. Chem. 24 (1983) 243–277. [Google Scholar]
  29. Y. Maday and G. Turinici, Error bars and quadratically convergent methods for the numerical simulation of the Hartree-Fock equations. Numer. Math. 94 (2003) 739–770. [CrossRef] [MathSciNet] [Google Scholar]
  30. W. Sickel, Superposition of functions in Sobolev spaces of fractional order. A survey. Banach Center Publ. 27 (1992) 481–497. [Google Scholar]
  31. P. Suryanarayana, V. Gavini, T. Blesgen, K. Bhattacharya and M. Ortiz, Non-periodic finite-element formulation of Kohn-Sham density functional theory. J. Mech. Phys. Solids 58 (2010) 256–280. [Google Scholar]
  32. N. Troullier and J.L. Martins, A straightforward method for generating soft transferable pseudopotentials. Solid State Commun. 74 (1990) 613–616. [CrossRef] [Google Scholar]
  33. S. Valone, Consequences of extending 1matrix energy functionals from purestate representable to all ensemble representable 1 matrices. J. Chem. Phys. 73 (1980) 1344–1349. [CrossRef] [MathSciNet] [Google Scholar]
  34. Y.A. Wang and E.A. Carter, Orbital-free kinetic energy density functional theory, in Theoretical methods in condensed phase chemistry, Progress in theoretical chemistry and physics 5. Kluwer (2000) 117–184. [Google Scholar]
  35. A. Zhou, Finite dimensional approximations for the electronic ground state solution of a molecular system. Math. Methods Appl. Sci. 30 (2007) 429–447. [CrossRef] [MathSciNet] [Google Scholar]

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