In Kohn-Sham DFT, the Coulomb potential, which is a component of the Kohn-Sham potential, is given by:(adsbygoogle = window.adsbygoogle || []).push({});

[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 itanalyticallyjust 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]?

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# Coulomb potential in Kohn-Sham DFT

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