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DFPT second order energy variational form

  1. Nov 11, 2015 #1
    I am referring to perturbation expansion of density functional Kohn Sham energy expression in
    Phys. Rev. A 52, 1096.

    In equation (92) the variational form of the second order energy is listed, but I cannot seem to work out the last 3 terms involving XC energy and density. Particularly, the interaction energy potential is given as:
    [tex] v_{HXC}^{(i)} = \frac{1}{i!} \frac{d^i}{d\lambda^i} \left[ \frac{\delta E_{HXC} \left[ \sum_{j=0}^i \lambda^j n^{(j)} \right] }{\delta(n(r))} \right] \Bigg|_{\lambda=0} [/tex]

    In Phys. Rev. B 55, 10337 by the same author, it is listed that
    [tex] v_{HXC}^{(1)} = \int \frac{\delta^2 E_{HXC}}{\delta(n(r))\delta(n(r'))} \bigg|_{n^(0)} n^{(1)}(r') \,dr' + \frac{d}{d\lambda} \frac{\delta E_{HXC}}{\delta(n(r))} \bigg|_{n^(0)} [/tex]
    which I don't know the rationale behind the expansion.

    From the general expression Eq (50) in Phys. Rev. A 52, 1096, I am lost at finding the terms which contribute to the last 3 terms in the variational expression.

    Thank you for any help.
  2. jcsd
  3. Nov 16, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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