Abstract
To begin the topic of DFT, this chapter overviews how the Kohn–Sham method was developed historically and then introduces various extensions of this method. The Thomas–Fermi method, which is the first form of DFT, is first explained, focusing on the local density approximation of kinetic and exchange energy density functionals, in Sect.4.1. Then, the Hohenberg–Kohn theorem, which is the basic theory of DFT, is reviewed, with a mention of the constrained search formulation used to solve the V -representability problem, in Sect. 4.2. The Kohn–Sham method based on this theorem is introduced, along with the corresponding computational methods, in Sect. 4.3. As the extension of the Kohn–Sham method to include general functionals, the generalized Kohn–Sham method is surveyed in Sect. 4.4. The constrained search method, which directly constructs a Kohn–Sham potential from the electron density, is explained, and as a consequence of this method, it is clarified why the Kohn–Sham method can accurately reproduce chemical behavior in Sect. 4.5. Finally, the time-dependent and coupled-perturbed Kohn–Sham methods are reviewed as methods with which to apply the Kohn–Sham method to calculations of photoexcitation spectra and response properties, respectively, in Sects. 4.6 and 4.7.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Casida, M.E.: In: Seminario, J.J. (ed.) Recent Developments and Applications of Modern Density Functional Theory. Elsevier, Amsterdam (1996)
Dirac, P.A.M.: Camb. Phil. Soc. 26, 376–385 (1930)
Eschrig, H.: The Fundamentals of Density Functional Theory, 2nd edn. EAGLE, Leipzig (2003)
Fermi, E.: Z. Phys. 48, 73–79 (1928)
Fermi, E., Amaldi E.: Accad. Ital. Rome 6, 117–149 (1934)
Feynman, R.P.: Phys. Rev. 56, 340–343 (1939)
Fock V.: Z. Phys. 61, 126–148 (1930)
Gilbert, T.L.: Phys. Rev. B 12, 2111–2120 (1975)
Gross, E.K.U., Burke, K.: Lect. Notes Phys. 706, 1–17 (2006)
Gross, E.K.U., Ullrich, C.A., Gossmann, U.A.: In: Dreizler, R., Gross, E.K.U. (eds.), Density Functional Theory, NATO ASI Series B. Plenum, New York (1995)
Hirata, S., Head-Gordon, M.: Chem. Phys. Lett. 314, 291–299 (1999)
Hohenberg, P., Kohn, W.: Phys. Rev. B 136, 864–871 (1964)
Jensen F.: Introduction to Computational Chemistry. Wiley, Chichester (2006)
Kohn, W., Sham, L.J.: Phys. Rev. A 140, 1133–1138 (1965)
Kutzelnigg, W.: J. Mol. Struct. Theochem 768, 163–173 (2006)
Lee, A.M., Colwell, S.M.: J. Chem. Phys. 101, 9704–9709 (1994)
Levy, M.: Proc. Natl. Acad. Sci. USA 76, 6062–6065 (1979)
Lieb, E.H.: Int. J. Quantum Chem. 24, 243–277 (1983)
Marques M.A.L., Castro, A., Rubio, A.: J. Chem. Phys. 115, 3006–3014 (2001)
McWeeny, R.: Methods of Molecular Quantum Mechanics, 2nd edn. Academic Press, San Diego (1992)
Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford University Press, New York (1994)
Runge, E., Gross, E.K.U.: Phys. Rev. Lett. 52, 997–1000 (1984)
Schipper, P.R.T., Gritsenko, O.V., Baerends, E.J.: Phys. Rev. A 57, 1729–1742 (1998)
Schrödinger, E.: Ann. Phys. 80, 437–490 (1926)
Seidl, A., Görling, A., Vogl, P., Majewski, J.A., Levy, M.: Phys. Rev. B 53, 3764–3774 (1986)
Thomas, L.H.: Proc. Cam. Phyl. Soc. 23, 542–548 (1927)
Ullrich, C.A.: Time-Dependent Density-Functional Theory. Oxford University Press, New York (2012)
van Leeuwen, R.: Lect. Notes Phys. 706, 17–31 (2006)
von Weizsäcker, C.F.: Z. Phys. 96, 431–458 (1935)
Yabana, K., Bertsch, G.F.: Phys. Rev. B 54, 4484–4487 (1996)
Yang, Z., Burke, K.: Phys. Rev. A 88, 042514(1–14) (2013)
Zhao, Q., Morrison, R.C., Parr, R.G.: Phys. Rev. A 50, 2138–2142 (1994)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Japan
About this chapter
Cite this chapter
Tsuneda, T. (2014). Kohn–Sham Method. In: Density Functional Theory in Quantum Chemistry. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54825-6_4
Download citation
DOI: https://doi.org/10.1007/978-4-431-54825-6_4
Published:
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-54824-9
Online ISBN: 978-4-431-54825-6
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)