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Self consistent solution

  1. Jun 21, 2009 #1
    what does self consistent solution mean in for example Kohn-sham equations?
     
  2. jcsd
  3. Jun 21, 2009 #2

    Astronuc

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    Staff: Mentor

    The equations of a linear system are consistent if they possess a common solution, and consistency implies at least one solution.

    See - http://en.wikipedia.org/wiki/System_of_linear_equations#Consistency

    Self-consistency is the condition that [tex]F[n(\vec{x})]\,-\,n(\vec{x}) = 0[/tex].

    See - section 4.4 of http://people.ccmr.cornell.edu/~muchomas/P480/Notes/dft/dft.pdf
    from http://people.ccmr.cornell.edu/~muchomas/P480/

    See also the original Kohn-Sham paper - "Self-Consistent Equations Including Exchange and Correlation Effects," by W. Kohn and L. J. Sham, Physical Review 140, A1133-A1138 (1965).
    http://www.cem.msu.edu/~cem883/topics_pdf/Kohn_Sham.pdf

    and

    "Inhomogeneous Electron Gas," by P. Hohenberg and W. Kohn, Physical Review 136, B864-B871 (1964).
    http://prola.aps.org/pdf/PR/v136/i3B/pB864_1 [Broken]

    See also Electronic structure By Richard M. Martin

    This might also be of interest - KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
    http://portal.acm.org/citation.cfm?id=1499096.1499099
     
    Last edited by a moderator: May 4, 2017
  4. Sep 5, 2009 #3
    It means that on the n-th iteration of the KS loop, the density that you compute from the KS states is equal to the density computed on the (n-1)-th iteration.
     
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