Abstract
Since the inception of Density Functional Theory (DFT) the remarkable success of the Local Density Approximation (LDA) has been difficult to improve in a systematic way. Originally Hohenberg, Kohn and Sham introduced LDA as the first term in a gradient expansion of the exchange-correlation energy functional[1]. It success in a wide variety of systems, such as atoms molecules and solids[2, 3], was somewhat surprising, since the density gradients are not small. The accuracy of LDA was attributed to the sum rules which it satisfies[4] and to the range of validity of the small gradient approximation being larger than expected[5, 6]. Well defined gradient expansions[7] were carried out, however the most accurate numerical results for real systems require either a semi-empirical approach[8] or a detailed model for the exchange-correlation hole[9]. A large number of exact constraints have also been placed upon the possible functionals which are beginning to lead to more systematic improvements[10].
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References
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965).
R.O. Jones and O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).
R.G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford, 1989).
O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B. 13, 4274 (1976).
V. Sahni, J. Gruenebaum, and J.P. Perdew, Phys. Rev. B. 26, 4371 (1982).
D.C. Langreth and M.J. Mehl, Phys. Rev. B. 28, 1809 (1983).
D.J.W. Geldart and M. Rasolt, in “Single Particle Density in Physics and Chemistry”, (Academic Press, 1987).
A.D. Becke, J. Chem. Phys. 84, 4524 (1986).
A.D. Becke, Phys. Rev. A 38, 3089 (1988).
J.P. Perdew and W. Yue, Phys. Rev. B 33, 8800 (1986).
L.C. Wilson and M. Levy, Phys. Rev. B. 41, 12930 (1990).
J.F. Annett, Phys. Rev. Lett. 69, 2244 (1992).
M.C. Payne et.al. Rev. Mod. Phys. 64, 1045 (1992).
O. Gunnarsson, J. Harris and R.O. Jones, Phys. Rev. B. 15, 3027 (1977).
U. von Barth and CD. Gelatt, Phys. Rev. B. 21, 2222 (1980).
D.R. Hamman, M. Schlüter and C. Chiang, Phys. Rev. Lett. 43, 1494 (1974).
G.B. Bachelet, D.R. Hamann and M. Shluter, Phys. Rev. B 26, 4199 (1982).
S.G. Louie, S. Froyen and M.L. Cohen, Phys. Rev. B. 26, 1738 (1982).
D.M. Bylander and L. Kleinman, Phys. Rev. B. 43, 12070 (1991).
M. Levy, Proc. Natl. Acad. Sci. USA. 76, 6062 (1979).
S. Valone, Phys. Rev. B 44 1509 (1991).
R.L. Kelly, J. Phys. Chem. Ref. Data 16, Suppl 1, (1987).
The LSDA parameterization used was from: J.P. Perdew and Y. Wang, Phys. Rev. B. 45, 13244 (1992).
E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables 14 177 (1974).
E.L. Shirley, R.M. Martin and G.B. Bachelet, Phys. Rev. B. 42, 5057 (1990).
F.R. Vukajlovic, E.L. Shirley and R.M. Martin, Phys. Rev. B 43, 3994 (1991).
D.M. Bylander and L. Kleinman, Phys. Rev. B. 43, 12070 (1991).
B.L. Hammond, P.J. Reynolds, and W.A. Lester Jr., Phys. Rev. Lett. 61 2312 (1988).
S. Fahy, X. W. Wang and S.G. Louie, Phys. Rev. Lett. 61, 1631 (1988).
G. B. Bachelet, D.M. Ceperley and M.G.B. Chiocchetti, Phys. Rev. Lett. 62, 2088 (1989).
L. Mitas, E.L. Shirley and D.M. Ceprley, J. Chem. Phys. 95, 3467 (1991).
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© 1995 Springer Science+Business Media New York
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Annett, J.F. (1995). Valence Density Functionals. In: Gross, E.K.U., Dreizler, R.M. (eds) Density Functional Theory. NATO ASI Series, vol 337. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9975-0_20
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DOI: https://doi.org/10.1007/978-1-4757-9975-0_20
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