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First Principles Electronic Structure Methods

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Part of the book series: NATO Science Series ((NAII,volume 9))

Abstract

The behavior of amorphous solids, as in any other material, depends ultimately on their electronic properties. The electrons are the ultimate responsible for the binding of the atoms that build the material, and the structure of the electronic states in space and energy determines its properties and its response to the environment. Since the early days of quantum mechanics, the prospect of being able to solve the equations that govern the microscopic behavior of electrons and nuclei, has made us dream of being capable of understanding and predicting the properties of condensed matter in detail. Legend has it that Paul Dirac, shortly after the first demonstrations of the success of the Schrödinger equation, pointed out this possibility, although he was skeptical due to the great complexity of the equations, which allowed solution only in the most simple systems. Although the basic quantum theory has remained unperturbed, our capability to solve its equations has improved tremendously. Both the development of powerful numerical techniques (hand in hand with the advent and continuous improvement of the power of digital computers), and the derivation of approximate schemes to simplify the coupled many-body quantummechanical problem, has brought us to a situation in which it is possible to solve systems as complex as biological molecules such as DNA.

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References

  1. Hohenberg, P. and Kohn, W., (1964), Phys. Rev. 136, 864.

    Article  MathSciNet  ADS  Google Scholar 

  2. Kohn, W. and Sham, L.J. (1965) Phys. Rev. 145, 561.

    MathSciNet  Google Scholar 

  3. Kohn, W. (1998) Rev. Mod. Phys. 71, 1253.

    Article  ADS  Google Scholar 

  4. Car, R. and Parrinello, M. (1985) Phys. Rev. Lett. 55, 2471.

    Article  ADS  Google Scholar 

  5. Allen, M.P., and Tildesley, DJ. (1987) Computer Simulations on Liquids, Clarendon, Oxford.

    Google Scholar 

  6. Payne, M.C., Teter, M.P., Allan, D.C., Arias, T.A. and Joannopoulos, J.D. (1992) Rev. Mod. Phys. 64, 1045.

    Article  ADS  Google Scholar 

  7. Ordejön, P. (1998) Computational Materials Science 12, 157.

    Article  Google Scholar 

  8. Goedecker, S. (1999) Rev. Mod. Phys. 71, 1085.

    Article  ADS  Google Scholar 

  9. Born, M. and Oppenheimer, J.R. (1927), Ann. der Phys. 84, 457.

    Article  ADS  MATH  Google Scholar 

  10. Messiah, A. (1961) Quantum Mechanics, North-Holland, Amsterdam.

    Google Scholar 

  11. Hellmann, H. (1937) Einfürung in die Quantenchemie, Deutike, Leipzig; Feynman, R.P. (1939) Phys. Rev. 56, 340.

    Google Scholar 

  12. Goringe, CM., Bowler, D.R. and Hernandez, E. (1997) Rep. Prog. Phys. 60, 1447.

    Article  ADS  Google Scholar 

  13. Szabo, A. and Ostlund, N.S. (1989) Modern Quantum Chemistry: introduction to advanced electronic structure theory, McGraw-Hill, New York.

    Google Scholar 

  14. Kohn, W. (1996) Phys. Rev. Lett. 76, 3168.

    Article  ADS  Google Scholar 

  15. Mahan, G.D. (1990) Many Particle Physics, Plenum, New York.

    Book  Google Scholar 

  16. Perdew, J.P. and Zunger, A. (1981) Phys. Rev. B 23, 5048.

    Article  ADS  Google Scholar 

  17. Ceperley, D.M. and Alder, B.J. (1980) Phys. Rev. Lett. 45, 556.

    Article  ADS  Google Scholar 

  18. Parr, R.G. and Yang, W. (1989) Density Functional Theory of Atoms and Molecules, Oxford.

    Google Scholar 

  19. von Barth, U. and Hedin, L. (1979) J. Phys. C 12, 5419.

    Article  Google Scholar 

  20. Vosko, S.H., Wilk, L. and Nusair, M. (1980) Can. J. Phys. 58, 1200.

    Article  ADS  Google Scholar 

  21. Filipi, A., Umrigar, C. and Taut, M. (1994) J.Chem. Phys. 100, 1295.

    ADS  Google Scholar 

  22. Perdew, J.P. and Kurth, S. (1998), in Density Functionals: Theory and Applications, edited by D. Joubert, Springer, Berlin.

    Google Scholar 

  23. Sanchez-Portal, D., Artacho, E. and Soler, J.M. (1996) J. Phys.: Condens. Matter 8, 3859.

    Article  ADS  Google Scholar 

  24. Slater, P.C. and Koster, G.F. (1954) Phys. Rev. 94, 1598.

    Article  ADS  Google Scholar 

  25. Mulliken, R.S. (1955) J. Chem. Phys. 23, 1833.

    Article  ADS  Google Scholar 

  26. Boys, S.F. (1966), in Quantum Theory of Atoms, Molecules and the Solid State, edited by P.-O. Löwdin, Academic Press, New York.

    Google Scholar 

  27. Huzinaga, S., Andzelm, J., Klobukowski, M., Radzio-Andzelm, E., Sakai, Y. and Tatewaki, H. (1984), Gaussian Basis Sets for Molecular Calculations, Elsevier Publ. Co., Amsterdam/New York.

    Google Scholar 

  28. Poirier, R., Kari, R. and Csizmadia, R. (1985) Handbook of Gaussian Basis Sets, Elsevier Publ. Co., Amsterdam/New York.

    Google Scholar 

  29. Boys, S.F. and Bernardi, F. (1970) J. Mol. Phys. 19, 553.

    Article  ADS  Google Scholar 

  30. Pulay, P. (1969) Mol. Phys. 17, 197.

    Article  ADS  Google Scholar 

  31. Boys, S.F. (1950) Proc. R. Soc. London, A 200, 542.

    Article  ADS  MATH  Google Scholar 

  32. Baerends, E.J., Ellis, D.E. and Ross, E. (1973), Chem. Phys. 2, 41.

    Article  Google Scholar 

  33. Delley, B. (1990) J. Chem. Phys. 92, 508.

    Article  ADS  Google Scholar 

  34. Lippert, G., Hutter, J., Ballone, P. and Parrinello, M. (1996) J. Chem. Phys. 100, 6231.

    Article  Google Scholar 

  35. Artacho, E., Sanchez-Portal, D., Ordejön, P., Garcia, A. and Soler, J.M. (1999) Phys. Slat. Sol (b) 215, 80

    Article  ADS  Google Scholar 

  36. Galli, G. and Parrinello, M. (1991) in Computer Simulations in Materials Sciences, ed. by M. Meyer and V. Pontikis, Kluwer Academic Publishers, the Netherlands.

    Google Scholar 

  37. White, C, Johnson, B., Gill, P. and Head-Gordon, M. (1994) Chem. Phys. Lett. 230, 8.

    Article  ADS  Google Scholar 

  38. Kudin, K.N. and Scuseria, G. (1998) Chem. Phys. Lett. 289, 611.

    Article  ADS  Google Scholar 

  39. Lippert, G., Hutter, J. and Parrinello, M. (1997) Mol. Phys. 92, 477.

    ADS  Google Scholar 

  40. Sanchez-Portal, D., Ordejön, P., Artacho, E. and Soler, J.M. (1997) Int J. Quantum Chem. 65, 453.

    Article  Google Scholar 

  41. Bendt, P. and Zunger, A. (1983) Phys. Rev. Lett. 50, 1688; Wood, D.M. and Zunger, A. (1985) J. Phys. A 18, 1343.

    Article  ADS  Google Scholar 

  42. Ordejön, P., Artacho, E. and Soler, J.M. (1996) Phys. Rev. B 53, 10441.

    Article  ADS  Google Scholar 

  43. Haynes, P.D. and Payne, M.C. (1997) Comp. Phys. Comm. 102, 17.

    Article  ADS  Google Scholar 

  44. Sankey, O.F. and Niklewski, D.J. (1989) Phys. Rev. B 40, 3979.

    Article  ADS  Google Scholar 

  45. Williams, A. and Soler, J.M. (1987) Bull. Am. Phys. Soc. 32, 562.

    Google Scholar 

  46. Press, H.W., Flannery, P.B., Teukolsky, S.A. and Vetterling, W.T. (1986) Numerical Recipes, Cambridge University Press, Cambridge.

    Google Scholar 

  47. Methfessel, M. and van Schilfgaarde, M. (1993) Phys. Rev. B 48, 4937.

    Article  ADS  Google Scholar 

  48. Heine, V. (1980) in Solid State Physics: Advances in Research and Applications, edited by F. Seitz, C. Turnbull and H. Ehrenreich, Academic Press, New York.

    Google Scholar 

  49. Yang, W. (1991) Phys. Rev. Lett. 66, 1438.

    Article  ADS  Google Scholar 

  50. Wannier, G.H. (1937) Phys. Rev. 52, 191.

    Article  ADS  Google Scholar 

  51. Kohn, W. (1959) Phys. Rev. 115, 809.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Marzari, N. and Vanderbilt, D. (1997) Phys. Rev. B 56, 12847.

    Article  ADS  Google Scholar 

  53. Goedecker, S. (1998) Phys. Rev. B 58, 3501.

    Article  ADS  Google Scholar 

  54. Baer, R. and Head-Gordon, M. (1997) Phys. Rev. Lett. 79, 3962.

    Article  ADS  Google Scholar 

  55. Ismail-Beigi, S. and Arias, T. (1999) Phys. Rev. Lett. 82, 2127.

    Article  ADS  Google Scholar 

  56. Mauri, F., Galli, G. and Car, R. (1993) Phys. Rev. B 43, 9973.

    Article  ADS  Google Scholar 

  57. Mauri, F. and Galli, G. (1994) Phys. Rev. B 50, 4316.

    Article  ADS  Google Scholar 

  58. Ordejön, P., Drabold, D.A., Grumbach, M.P. and Martin, R.M. (1993) Phys. Rev. B 48, 14646.

    Article  ADS  Google Scholar 

  59. Ordejön, P., Drabold, D.A., Martin, R.M. and Grumbach, M.P. (1995) Phys. Rev. B 51, 1456.

    Article  ADS  Google Scholar 

  60. Li, X.-P, Nunes, R. and Vanderbilt, D. (1993) Phys. Rev. B 47, 10891.

    Article  ADS  Google Scholar 

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Ordejón, P. (2001). First Principles Electronic Structure Methods. In: Thorpe, M.F., Tichý, L. (eds) Properties and Applications of Amorphous Materials. NATO Science Series, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0914-0_12

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  • DOI: https://doi.org/10.1007/978-94-010-0914-0_12

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-0-7923-6811-3

  • Online ISBN: 978-94-010-0914-0

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