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Ab-Initio Calculations

  • Francisco ChinestaEmail author
  • Emmanuelle Abisset-Chavanne
Chapter
Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)

Abstract

Due to the difficulties found in the direct solution of the Schrödinger equation, different simplified approaches were proposed and are nowadays widely used. Among them, those most usually employed are the Hartree–Fock and the Density Functional Theory, which we revisit in the present chapter. The former makes use of nonstandard numerical approximations in order to calculate the wavefunction while circumventing the curse of dimensionality, whereas the latter involves the electronic density that is now defined in three dimensions but requires deeper analyses to retain the most relevant features present in the wavefunction description in a coarse 3D model.

Keywords

Hartree-Fock Hohenberg and Kohn Theorems Density Functional Theory 

References

  1. 1.
    D.B. Cook, Handbook of Computational Chemistry (Oxford University Press, Oxford, 1998)Google Scholar
  2. 2.
    A. Ammar, F. Chinesta, P. Joyot, The nanometric and micrometric scales of the structure and mechanics of materials revisited: An introduction to the challenges of fully deterministic numerical descriptions. Int. J. Multiscale Comput. Eng. 6(3), 191–213 (2008)Google Scholar
  3. 3.
    E. Cancès, M. Defranceschi, W. Kutzelnigg, C. Le Bris, Y. Maday, Computational quantum chemistry: a primer. Handb. Numer. Anal. 10, 3–270 (2003)Google Scholar
  4. 4.
    C. Le Bris (ed.), Handbook of Numerical Analysis, Computational Chemistry (Elsevier, New York, 2003)Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Francisco Chinesta
    • 1
    Email author
  • Emmanuelle Abisset-Chavanne
    • 2
  1. 1.ENSAM Paris TechParisFrance
  2. 2.École Centrale de NantesNantesFrance

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