Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-13T01:08:17.888Z Has data issue: false hasContentIssue false
  • English
  • Français

Climbing the ladder of density functional approximations

Published online by Cambridge University Press:  12 September 2013

John P. Perdew
John P. Perdew*
Affiliation:
Department of Physics, Temple University; perdew@temple.edu
Get access

Abstract

Kohn–Sham density functional theory is the most widely used method of electronic-structure calculation in materials physics and chemistry because it reduces the many-electron ground-state problem to a computationally tractable self-consistent one-electron problem. Exact in principle for the ground-state energy and electron density, it requires in practice an approximation to the density functional for the exchange-correlation energy. Common approximations fall on the rungs of a ladder, with higher rungs being more complicated to construct and use but potentially more accurate. Each rung of the ladder introduces an additional ingredient to the energy density. From bottom to top, the rungs are (1) the local spin density approximation, (2) the generalized gradient approximation (GGA), (3) the meta-GGA, (4) the hybrid functional, and (5) the generalized random phase approximation. The semi-local rungs (1–3) are important, because they are computationally efficient, they can be constructed non-empirically, they can serve as input to fourth-rung functionals, and the meta-GGA by itself can be accurate for equilibrium properties. Recent and continuing improvements to the meta-GGA are emphasized here.

Keywords

electronic structurebondinginteratomic arrangementscrystalsurface chemistry
Type
Research Article
Information
MRS Bulletin , Volume 38 , Issue 9: Quantum dot light-emitting devices , September 2013 , pp. 743 - 750
Copyright
Copyright © Materials Research Society 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kohn, W., Sham, L.J., Phys. Rev. 140, A1133 (1965).CrossRefGoogle Scholar
Parr, R.G., Yang, W., Density Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989).Google Scholar
Dreizler, R.M., Gross, E.K.U., Density Functional Theory (Springer, Berlin, 1990).CrossRefGoogle Scholar
Fiolhais, C., Nogueira, F., Marques, M., Eds., A Primer in Density Functional Theory (Springer, Berlin, 2003).CrossRefGoogle Scholar
Martin, R.M., Electronic Structure: Basic Theory and Practical Methods (Cambridge University Press, UK, 2004).CrossRefGoogle Scholar
Engel, E., Dreizler, R.M., Density Functional Theory: An Advanced Course (Springer, Berlin, 2011).CrossRefGoogle Scholar
“18 Most Cited Physics Papers 1981–2010”; http://tulane.edu/sse/pep/news-and-events/upload/most-cited-papers-1981-2010.pdf.Google Scholar
Kohn, W., Rev. Mod. Phys. 71, 1253 (1999).CrossRefGoogle Scholar
Kurth, S., Perdew, J.P., Int. J. Quantum Chem. 75, 889 (1999).3.0.CO;2-8>CrossRefGoogle Scholar
Perdew, J.P., Wang, Y., Phys. Rev. B 45, 13244 (1992).CrossRefGoogle Scholar
Vosko, S.H., Wilk, L., Nusair, M., Can. J. Phys. 58, 1200 (1980).CrossRefGoogle Scholar
Langreth, D.C., Perdew, J.P., Solid State Commun. 17, 1425 (1975); Phys. Rev. B 15, 2884 (1977).CrossRefGoogle Scholar
Gunnarsson, O., Lundqvist, B.I., Phys. Rev. B 13, 4274 (1976).CrossRefGoogle Scholar
Perdew, J.P., Schmidt, K., in Density Functional Theory and Its Applications to Materials, Van Doren, V.E., Van Alsenoy, K., Geerlings, P., Eds. (American Institute of Physics, Melville, NY, 2001).Google Scholar
von Barth, U., Hedin, L., J. Phys. C: Solid State Phys. 5, 1629 (1972).CrossRefGoogle Scholar
Langreth, D.C., Perdew, J.P., Solid State Commun. 31, 567 (1979); Phys. Rev. B 21, 5469 (1980).CrossRefGoogle Scholar
Langreth, D.C., Mehl, M.J., Phys. Rev. B 28, 1809 (1983).CrossRefGoogle Scholar
Becke, A.D., Phys. Rev. A 38, 3098 (1988).CrossRefGoogle Scholar
Perdew, J.P., Burke, K., Ernzerhof, M., Phys. Rev. Lett. 77, 3865 (1996).CrossRefGoogle Scholar
Becke, A.D., J. Chem. Phys. 109, 2092 (1998).CrossRefGoogle Scholar
Perdew, J.P., Kurth, S., Zupan, A., Blaha, P., Phys. Rev. Lett. 82, 2544 (1999).CrossRefGoogle Scholar
Tao, J., Perdew, J.P., Staroverov, V.N., Scuseria, G.E., Phys. Rev. Lett. 91, 146401 (2003).CrossRefGoogle Scholar
Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Constantin, L.A., Sun, J., Phys. Rev. Lett. 103, 026403 (2009).CrossRefGoogle Scholar
Sun, J., Xiao, B., Ruzsinszky, A., J. Chem. Phys. 137, 051101 (2012).CrossRefGoogle Scholar
Sun, J., Haunschild, R., Xiao, B., Bulik, I.W., Scuseria, G.E., Perdew, J.P., J. Chem. Phys. 138, 044113 (2013).CrossRefGoogle Scholar
Becke, A.D., J. Chem. Phys. 98, 5648 (1993).CrossRefGoogle Scholar
Perdew, J.P., Ernzerhof, M., Burke, K., J. Chem. Phys. 105, 9982 (1996).CrossRefGoogle Scholar
Ernzerhof, M., Scuseria, G.E., J. Chem. Phys. 110, 5029 (1999).CrossRefGoogle Scholar
Adamo, C., Barone, V., J. Chem. Phys. 110, 6158 (1999).CrossRefGoogle Scholar
Furche, F., Phys. Rev. B 64, 195120 (2001).CrossRefGoogle Scholar
Harl, J., Schimka, L., Kresse, G., Phys. Rev. B 81, 115126 (2010).CrossRefGoogle Scholar
Ma, S.-K., Brueckner, K.A., Phys. Rev. 165, 18 (1968).CrossRefGoogle Scholar
Antoniewicz, P.R., Kleinman, L., Phys. Rev. B 31, 6779 (1985).CrossRefGoogle Scholar
Svendsen, P.S., von Barth, U., Phys. Rev. B 54, 17392 (1996).CrossRefGoogle Scholar
Levy, M., Perdew, J.P., Phys. Rev. A 32, 1010 (1985).CrossRefGoogle Scholar
Levy, M., Phys. Rev. A 43, 4637 (1991).CrossRefGoogle Scholar
Lieb, E.H., Oxford, S., Int. J. Quantum Chem. 19, 427 (1981).CrossRefGoogle Scholar
Gunnarsson, O., Lundqvist, B.I., Wilkins, J.W., Phys. Rev. B 10, 1319 (1974).CrossRefGoogle Scholar
Jaramillo, J., Scuseria, G.E., Ernzerhof, M., J. Chem. Phys. 118, 1068 (2003).CrossRefGoogle Scholar
Perdew, J.P., Staroverov, V.N., Tao, J., Scuseria, G.E., Phys. Rev. A 78, 052513 (2008).CrossRefGoogle Scholar
Moroni, S., Ceperley, D.M., Senatore, G., Phys. Rev. Lett. 69, 1837 (1992).CrossRefGoogle Scholar
Perdew, J.P., Ruzsinszky, A., Csonka, G.I., Constantin, L.A., Zhou, X., Vydrov, O.A., Scuseria, G.E., Burke, K., Phys. Rev. Lett. 100, 136406 (2008).CrossRefGoogle Scholar
Armiento, R., Mattsson, A.E., Phys. Rev. B 62, 10046 (2000).Google Scholar
Wu, Z., Cohen, R.E., Phys. Rev. 73, 235116 (2006).CrossRefGoogle Scholar
Sun, J., Marsman, M., Ruzsinszky, A., Kresse, G., Perdew, J.P., Phys. Rev. B 83, 121410 (2011).CrossRefGoogle Scholar
Hao, P., Sun, J., Csonka, G.I., Philipsen, P.H.T., Perdew, J.P., Phys. Rev. B 85, 014111 (2012).CrossRefGoogle Scholar
Perdew, J.P., Zunger, A., Phys. Rev. B 23, 5048 (1981).CrossRefGoogle Scholar
Brothers, E.N., Izmaylov, A.F., Normand, J.O., Scuseria, G.E., J. Chem. Phys. 129, 011102 (2008).CrossRefGoogle Scholar
Yan, Z., Perdew, J.P., Kurth, S., Phys. Rev. B 61, 16430 (2000).CrossRefGoogle Scholar
Xiao, B., Sun, J., Ruzsinszky, A., Feng, J., Perdew, J.P., Phys. Rev. B 86, 094109 (2012).CrossRefGoogle Scholar