The linear term of the near-nucleus expansion of the spherically averaged exchange-correlation potential ${\overline{\upsilon }}_{\mathit{xc}}\left(r\right)$ in density functional theory (DFT) is shown to be nonzero and to arise solely from the correlation-kinetic effects. Analytical expressions for it and for those of the separate exchange ${\upsilon }_x\left(\mathbf{r}\right)$ and correlation ${\upsilon }_c\left(\mathbf{r}\right)$ potentials are derived. The results were also obtained recently via quantal DFT, but here are obtained via ordinary Hohenberg-Kohn-Sham DFT. It is further pointed out that the linear term in ${\upsilon }_{\mathit{xc}}\left(\mathbf{r}\right)$ arising mainly from ${\upsilon }_c\left(\mathbf{r}\right)$ is rather small, and ${\upsilon }_{\mathit{xc}}\left(\mathbf{r}\right)$ therefore has a nearly quadratic structure near the nucleus. Implications of the results for the construction of the Kohn-Sham system are discussed and examples are given.

• Received 29 January 2007

DOI:https://doi.org/10.1103/PhysRevB.75.193104