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Understanding Thomas-Fermi-Like approximations: Averaging over oscillating occupied orbitals
1. | Department of Physics and Quantum Theory Group, Tulane University, New Orleans, LA 70123, United States, United States |
References:
[1] | |
[2] |
L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc., 23 (1926), 542-548.
doi: 10.1017/S0305004100011683. |
[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.
doi: 10.1007/BFb0099187. |
[5] |
J. A. Goldstein and G. R. Rieder, Recent rigorous results in Thomas-Fermi theory, Lecture Notes in Mathematics, 1394 (1989), 68-82.
doi: 10.1007/BFb0086753. |
[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.
doi: 10.1080/03605309208820914. |
[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.
doi: 10.3934/dcds.2010.28.41. |
[8] |
P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev., 136 (1964), B864-B871.
doi: 10.1103/PhysRev.136.B864. |
[9] |
W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation, Phys. Rev., 140 (1965), A11333-A1138.
doi: 10.1103/PhysRev.140.A1133. |
[10] |
S. Kurth and J. P. Perdew, Role of the exchange-correlation energy: Nature's glue, Int. J. Quantum Chem., 77 (2000), 819-830.
doi: 10.1002/(SICI)1097-461X(2000)77:5<814::AID-QUA3>3.0.CO;2-F. |
[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.
doi: 10.1103/PhysRevLett.97.223002. |
[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.
doi: 10.1103/PhysRevA.22.1827. |
[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.
doi: 10.1103/PhysRevA.29.2339. |
[14] |
E. H. Lieb, The stability of matter, Rev. Mod. Phys., 48 (1976), 553-569.
doi: 10.1103/RevModPhys.48.553. |
[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.
doi: 10.1063/1.3522767. |
[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.
doi: 10.1007/3-540-37072-2_1. |
[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.
doi: 10.1103/PhysRevB.75.155109. |
[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.
doi: 10.1103/PhysRevLett.106.236404. |
[19] |
D. C. Langreth and J. P. Perdew, The exchange-correlation energy of a metallic surface, Solid State Commun., 17 (1975), 1425-1429.
doi: 10.1016/0038-1098(75)90618-3. |
[20] |
O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules, and solids, Phys. Rev. B, 13 (1976), 4274-4298.
doi: 10.1016/0375-9601(76)90557-0. |
[21] |
D. C. Langreth and J. P. Perdew, Exchange-correlation energy of a metallic surface: Wavevector analysis, Phys. Rev. B, 15 (1977), 2884-2901. |
show all references
References:
[1] | |
[2] |
L. H. Thomas, The calculation of atomic fields, Proc. Cambridge Philos. Soc., 23 (1926), 542-548.
doi: 10.1017/S0305004100011683. |
[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.
doi: 10.1007/BFb0099187. |
[5] |
J. A. Goldstein and G. R. Rieder, Recent rigorous results in Thomas-Fermi theory, Lecture Notes in Mathematics, 1394 (1989), 68-82.
doi: 10.1007/BFb0086753. |
[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.
doi: 10.1080/03605309208820914. |
[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.
doi: 10.3934/dcds.2010.28.41. |
[8] |
P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev., 136 (1964), B864-B871.
doi: 10.1103/PhysRev.136.B864. |
[9] |
W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation, Phys. Rev., 140 (1965), A11333-A1138.
doi: 10.1103/PhysRev.140.A1133. |
[10] |
S. Kurth and J. P. Perdew, Role of the exchange-correlation energy: Nature's glue, Int. J. Quantum Chem., 77 (2000), 819-830.
doi: 10.1002/(SICI)1097-461X(2000)77:5<814::AID-QUA3>3.0.CO;2-F. |
[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.
doi: 10.1103/PhysRevLett.97.223002. |
[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.
doi: 10.1103/PhysRevA.22.1827. |
[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.
doi: 10.1103/PhysRevA.29.2339. |
[14] |
E. H. Lieb, The stability of matter, Rev. Mod. Phys., 48 (1976), 553-569.
doi: 10.1103/RevModPhys.48.553. |
[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.
doi: 10.1063/1.3522767. |
[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.
doi: 10.1007/3-540-37072-2_1. |
[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.
doi: 10.1103/PhysRevB.75.155109. |
[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.
doi: 10.1103/PhysRevLett.106.236404. |
[19] |
D. C. Langreth and J. P. Perdew, The exchange-correlation energy of a metallic surface, Solid State Commun., 17 (1975), 1425-1429.
doi: 10.1016/0038-1098(75)90618-3. |
[20] |
O. Gunnarsson and B. I. Lundqvist, Exchange and correlation in atoms, molecules, and solids, Phys. Rev. B, 13 (1976), 4274-4298.
doi: 10.1016/0375-9601(76)90557-0. |
[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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