Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Silicon Nitride Ceramics Read chapter Read first chapter

2011 | OriginalPaper | Chapter

2. Theoretical Methods and Approximations

Author : Weronika Walkosz

Published in: Atomic Scale Characterization and First-Principles Studies of Si₃N₄ Interfaces

Publisher: Springer New York

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter describes the theoretical approaches and approximations used in standard first principles calculations. First, the Born Oppenheimer approximation is stated. Next, an overview of the basic formulation of density functional theory (DFT) is given, underlying its merits in describing various materials and their properties, but also pointing out the aspects which need further improvements. The Kohn–Sham ansatz, which provides a means of calculating properties of many-body system using independent-particle methods, is presented along with practical schemes for solving the resulting Kohn–Sham equations. Finally, the DFT+U method and its implementation within a pseudopotential-plane wave framework are introduced.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
previous chapter Silicon Nitride Ceramics
next chapter Overview of Experimental Tools
Literature
1.
Hohenberg, P., Kohn, W.: Zur Quantentheorie der Molekeln. Ann. Phys. (Leipzing) 84, 456 (1927)
2.
Hohenberg, P., Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136(3B), B864–B871 (1964)CrossRef
3.
Kohn, W., Sham, L. J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), A1133–A1138 ( 1965)CrossRef
4.
Janak, J.F.: Proof that \({\frac{\partial E}{\partial n_{i}}}=\varepsilon\) in density-functional theory. Phys. Rev. B. 18(12), 7165–7168 (1978)
5.
Perdew, J.P., Parr, R.G., Levy, M., Balduz, J.L.: Density-functional theory for fractional particle number: derivative discontinuities of the energy. Phys. Rev. Lett. 49(23), 1691–1694 (1982)CrossRef
6.
Wigner, E.: On the interaction of electrons in metals.: Phys. Rev. 46(11), 1002–1011 (1934)CrossRef
7.
Vosko, S.H., Wilk, L., Nusair, M.: Accurate spin-dependent electron liquid correlation energies for local spin-density calculations—a critical analysis. Can. J. Phys. 58, 1200 (1980)CrossRef
8.
Ceperley, D.M., Alder, B.J.: Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45(7), 566–569 (1980)CrossRef
9.
Perdew, J.P., Zunger, A.: Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B. 23(10), 5048–5079 (1981)CrossRef
10.
Harris, J., Jones, R.O.: The surface energy of a bounded electron gas. J. Phys. F Metal Phys. 4, 1170–1186 (1974)CrossRef
11.
Gunnarsson, O., Lundqvist, B.I.: Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 13(10), 4274–4298 (1976)CrossRef
12.
Langreth, D.C., Perdew, J.P.: Exchange-correlation energy of a metallic surface: wave-vector analysis. Phys. Rev. B. 15(6), 2884–2901 (1977)CrossRef
13.
Perdew, J.P., Burke, K., Ernzerhof, M.: Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865–3868 (1996)CrossRef
14.
Perdew, J.P., Wang, Y.: Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 45(23), 13244–13249 (1992)CrossRef
15.
Chadi, D.J., Cohen, M.L.: Special points in the Brillouin zone. Phys. Rev. B 8(12), 5747–5753 (1973)CrossRef
16.
Monkhorst, H.J., Pack, J.D.: Special points for Brillouin-zone integrations. Phys. Rev. B 13(12), 5188–5192 (1976)CrossRef
17.
Evarestov, R.A., Smirnov, V.P.: Special points of the Brillouin-zone and thier use in the solid-State theory. Phys. Status Solidi B 119, 9–40 (1983)
18.
Phillips, J.C.: Energy-band interpolation scheme based on a pseudopotential. Phys. Rev. 112(3), 685–695 (1958)CrossRef
19.
Yin, M.T., Cohen, M.L.: Theory of ab initio pseudopotential calculations. Phys. Rev. B 25(12), 7403–7412 (1982)CrossRef
20.
Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50(24), 17953–17979 (1994)CrossRef
21.
Qian, G.X., Martin, R.M., Chadi, D.J.: First-principles study of the atomic reconstructions and energies of Ga- and As-stabilized GaAs(100) surfaces. Phys. Rev. B 38(11), 7649–7663 (1988)CrossRef
22.
Mosey, N.J., Carter, E.: Ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations. Phys. Rev. B 57, 1505–1509 (1998)CrossRef
23.
Anisimov, V.I., Zaanen, J., Andersen, O.K.: Band theory and Mott insulators: Hubbard U instead of Stoner I. Phys. Rev. B 44(3), 943–954 (1991)CrossRef
24.
Anisimov, V.I., Solovyev, I.V., Korotin, M.A., Czyzyk, M.T., Sawatzky, G.A.: Density-functional theory and NiO photoemission spectra. Phys. Rev. B 48(23), 16929–16934 (1993)CrossRef
25.
Solovyev, I.V., Dederichs, P.H., Anisimov, V.I.: Corrected atomic limit in the local-density approximation and the electronic structure of impurities in Rb. Phys. Rev. B 50(23), 16861–16871 (1994)CrossRef
26.
Dudarev, S.L., Botton, G.A., Savrasov, S.Y., Humphreys, C.J., Sutton, A.P.: Electron-energy loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998)CrossRef
Metadata
Title
Theoretical Methods and Approximations
Author
Weronika Walkosz
Copyright Year
2011
Publisher
Springer New York
Book
Atomic Scale Characterization and First-Principles Studies of Si₃N₄ Interfaces

Print ISBN: 978-1-4419-7816-5

Electronic ISBN: 978-1-4419-7817-2

Copyright Year: 2011

DOI
https://doi.org/10.1007/978-1-4419-7817-2_2

Premium Partners

    Image Credits