Theoretical Methods

  • Manuela Mura
Part of the Springer Theses book series (Springer Theses)


Many of the properties of the solid state and chemical systems can be determined solving the Schrödinger equation for a given system. However, states of most of electrons and nuclei have to be accounted for. The solution to many electrons can be obtained by the Hartree Fock (HF) method, using the wavefunction of the electrons, or density functional theory (DFT) based methods, using the density function of the electrons instead of solving the Schrödinger equation. The former method is a base for other approaches used in the quantum chemistry community, whereas the latter method has been largely used in the physics community to study the electronic structure of solids. However, over the last 20 years due to the increased efficiency of computers and the accuracy of the DFT functionals, the number of systems studied using DFT method has increased. As a result of this expansion, systems typically studied using quantum chemistry methods, such as organic and inorganic molecules, are being increasingly often studied with DFT methods because of much better efficiency and high quality which is close to that of the quantum chemistry (QC) methods. Another way to address many body problem is the classical molecular dynamics that is used to derive physical properties of the system from empirical potentials.


Density Functional Theory Generalise Gradient Approximation Local Density Approximation Correlation Energy Density Functional Theory Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Kantorovich LN (2004) Quantum theory of the solid state: an introduction. Fundamental theories of physics. Kluwer Academic Publishers, DordrechtGoogle Scholar
  2. 2.
    Hohenberg P, Kohn W (1964) Phys Rev Lett 136:864BGoogle Scholar
  3. 3.
    Kohn W, Sham LJ (1965) Phys Rev Lett 140:1133AGoogle Scholar
  4. 4.
    Sanchez-Portal D, Ordejon P, Artacho E, Soler JM (1997) Density functional method for very large systems with lcao bas is sets. Int J Quantum Chem 65:453CrossRefGoogle Scholar
  5. 5.
    Kleinman L (1980) Phys Rev B 21:2630CrossRefGoogle Scholar
  6. 6.
    Bachelet GB, Schluter M (1982) Phys Rev B 25:2103CrossRefGoogle Scholar
  7. 7.
    Troullier N, Martins JL (1991) Phys Rev B 43:1993CrossRefGoogle Scholar
  8. 8.
    Kleinman L, Bylander DM (1982) Phys Rev Lett 48:1425CrossRefGoogle Scholar
  9. 9.
    Louie SG, Froyen S, Cohen ML (1982) Phys Rev B 26:1738CrossRefGoogle Scholar
  10. 10.
    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865CrossRefGoogle Scholar
  11. 11.
    Kelly REA, Lee YJ, Kantorovich LN (2005) J Phys Chem B 109:22045CrossRefGoogle Scholar
  12. 12.
    Kelly REA, Kantorovich LN (2006) J Mater Chem 16:1894CrossRefGoogle Scholar
  13. 13.
    Kelly REA, Lee YJ, Kantorovich LN (2005) J Phys Chem B 109:11933CrossRefGoogle Scholar
  14. 14.
    Kelly REA, Lee YJ, Kantorovich LN (2006) J Phys Chem B 110:2249CrossRefGoogle Scholar
  15. 15.
    Sponer J, Leszczynski J, Hobza P J Phys ChemGoogle Scholar
  16. 16.
    Boys F, Bernardi F (1970) Mol Phys 19:553CrossRefGoogle Scholar
  17. 17.
    Grimme S (2004) J Comput Chem 25:1463CrossRefGoogle Scholar
  18. 18.
    von Lilienfeld OA, Tavernelli I, Rothlisberger U, Sebastiani D Phys Rev LettGoogle Scholar
  19. 19.
    Dion M, Rydberg H, Schroeder E, Langreth DC, Lundqvist BI (2004) Phys Rev Lett 92:246401CrossRefGoogle Scholar
  20. 20.
    Langreth DC, Dion M, Rydberg H, Schroder E, Hyldgaard P, Lundqvist BI (2005) J Quantum Chem 101:599CrossRefGoogle Scholar
  21. 21.
    Thonhauser T, Cooper VR, Li S, Puzder A, Hyldgaard P, Langreth DC (2007) Phys Rev B 76:125112CrossRefGoogle Scholar
  22. 22.
    Cooper VR, Thonhauser T, Puzder A, Schroeder E, Lundqvist BI, Langreth DC (2008) J Am Chem Soc 130:1304CrossRefGoogle Scholar
  23. 23.
    Langreth DC, Lundqvist BI, Chakarova-Draxl SD, Cooper VR, Dion M, Hyldgaard P, Kelkkanen A, Kleis J, Kong LZ, Li S, Moses PG, Murray E, Puzder A, Rydberg H, Schroder E, Rydberg T, Thonhauser H (2009) Cond Matter 21:084203CrossRefGoogle Scholar
  24. 24.
    Gulans A, Puska MJ, Nienminen RN Phys Rev BGoogle Scholar
  25. 25.
    Roman-Perez G, Soler JM Phys Rev LettGoogle Scholar
  26. 26.
    Mura M, Gulans A, Thonhauser T, Kantorovich L (2009) Role of van der waals interaction in forming molecule-metal junctions: flat organic molecules on the au(111) surface. Phys Chem Chem Phys (submitted)Google Scholar
  27. 27.
    Bardeen J (1961) Phys Rev Lett 6:57CrossRefGoogle Scholar
  28. 28.
    Tersoff J, Hamann DR (1985) Stm Theory Phys Rev B 31:805CrossRefGoogle Scholar
  29. 29.
    Cerdá J, Van Hove MA, Sautet P, Salmeron M (1997) Efficient method for the simulation of stm images. i. generalized green-function formalism. Phys Rev B 56(24):15885–15899CrossRefGoogle Scholar
  30. 30.
    Cerdá J, Van Hove MA, Sautet P, Salmeron M (1997) Efficient method for the simulation of stm images. ii. application to clean rh(111) and rh(111)+c(4x2)-2s. Phys Rev B 56(24):15900–15918CrossRefGoogle Scholar
  31. 31.
    Büttiker M, Imry Y, Landauer R, Pinhas S (May 1985) Generalized many-channel conductance formula with application to small rings. Phys Rev B 31(10):6207–6215CrossRefGoogle Scholar
  32. 32.
    Kantorovich LN, Trevethan T, Polesel-Maris J, Foster A Self consistent image dorce interaction + virtual AFM machineGoogle Scholar
  33. 33.
    Piana S, Bilic A (2006) J Phys Chem B 110:23467CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.University of Central Lancashire PrestonLancashireUK

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