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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
Pages: 5319 - 5325, Issue 11/12, November/December 2013

doi:10.3934/dcds.2013.33.5319      Abstract        References        Full text (258.5K)           Related Articles

John P. Perdew - Department of Physics and Quantum Theory Group, Tulane University, New Orleans, LA 70123, United States (email)
Adrienn Ruzsinszky - Department of Physics and Quantum Theory Group, Tulane University, New Orleans, LA 70123, United States (email)

1 A. Messiah, "Quantum Mechanics," Dover, 1999.
2 L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc., 23 (1926), 542-548.
3 E. Fermi, Un metodo statistico per la determinazione di alcune proprieta dell atomo, Rend. Accad. Naz. Licei, 6 (1927), 602-607.
4 J. A. Goldstein and G. R. Rieder, Some extensions of Thomas-Fermi theory, Lecture Notes in Mathematics, 1223 (1986), 110-121.       
5 J. A. Goldstein and G. R. Rieder, Recent rigorous results in Thomas-Fermi theory, Lecture Notes in Mathematics, 1394 (1989), 68-82.       
6 P. Benilan, J. A. Goldstein and G. R. Rieder, Nonlinear elliptic system arising in electron-density theory, Communications in Partial Differential Equations, 17 (1992), 2079-2092.       
7 G. R. Rieder, J. A. Goldstein and N. Naima, A convexified energy functional for the Fermi-Amaldi correction, Discrete and Continuous Systems, 28 (2010), 41-65.       
8 P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev., 136 (1964), B864-B871.       
9 W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation, Phys. Rev., 140 (1965), A11333-A1138.       
10 S. Kurth and J. P. Perdew, Role of the exchange-correlation energy: Nature's glue, Int. J. Quantum Chem., 77 (2000), 819-830.
11 J. P. Perdew, L. A. Constantin, E. Sagvolden and K. Burke, Relevance of the slowly-varying electron gas to atoms, molecules, and solids, Phys. Rev. Lett., 97 (2006), 223002, 4 pages.
12 J. Schwinger, Thomas-Fermi model: The leading correction, Phys. Rev. A, 22 (1980), 1827-1832; Thomas-Fermi model: The second correction, ibid., 24 (1981), 2353-2361.       
13 B. G. Englert and J. Schwinger, Statistical atom: Some quantum improvements, Phys. Rev. A, 29 (1984), 2339-2352; Semiclassical atom, ibid., 32 (1985), 26-35.       
14 E. H. Lieb, The stability of matter, Rev. Mod. Phys., 48 (1976), 553-569.       
15 L. A. Constantin, J. C. Snyder, J. P. Perdew and K. Burke, Ionization potentials in the limit of large atomic number, J. Chem. Phys., 133 (2010), 241103, 4 pages.
16 J. P. Perdew and S. Kurth, Density functionals for non-relativistic Coulomb systems in the new century, in "A Primer in Density Functional Theory" ( eds. C. Fiolhais, F. Nogueira and M. Marques), Lecture Notes in Physics, 620 (2003), 1-55.
17 J. P. Perdew and L. A. Constantin, Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy, Phys. Rev. B, 75 (2007), 155109, 9 pages.
18 A. Cangi, D. Lee, P. Elliott, K. Burke and E. K. U. Gross, Electronic structure via potential functional approximations, Phys. Rev. Lett., 106 (2011), 236404, 4 pages.
19 D. C. Langreth and J. P. Perdew, The exchange-correlation energy of a metallic surface, Solid State Commun., 17 (1975), 1425-1429.
20 O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules, and solids, Phys. Rev. B, 13 (1976), 4274-4298.
21 D. C. Langreth and J. P. Perdew, Exchange-correlation energy of a metallic surface: Wavevector analysis, Phys. Rev. B, 15 (1977), 2884-2901.

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