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Coulomb potential in Kohn-Sham DFT

  1. Nov 20, 2012 #1
    In Kohn-Sham DFT, the Coulomb potential, which is a component of the Kohn-Sham potential, is given by:

    [itex]v_H(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|}d\mathbf{r'}[/itex]

    where [itex]\rho(\mathbf{r'})[/itex] is the electron density.

    For molecular systems with exponential densities, this potential is known to be finite at any [itex]\textbf{r}[/itex].

    How to prove it analytically just based on its definition?

    Would a potential

    [itex]v(\mathbf{r}) = \int \frac{\rho(\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^n}d\mathbf{r'}[/itex]

    (where [itex] n [/itex] is some nonnegative integer)

    be also finite at any [itex] \mathbf{r}[/itex]?
  2. jcsd
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