Exact relation between density-matrix and density-functional theory forKplusLclosed shells in a bare Coulomb field

The explicit form of the first-order density matrix ρ${(\mathrm{r}}_1$,${\mathrm{r}}_2$) for independent electrons moving in a bare Coulomb field is first set up for the case of K plus L closed shells. The density matrix has a simple separable form in terms of the variables $r_1$+$r_2$ and ‖${\mathrm{r}}_1$ ${\mathrm{-}\mathrm{r}}_2$‖, a property exclusive to the Coulomb potential. Also, the off-diagonal dependence is simply quadratic in ‖${\mathrm{r}}_1$ ${\mathrm{-}\mathrm{r}}_2$‖. These two properties allow ρ${(\mathrm{r}}_1$,${\mathrm{r}}_2$) to be written solely in terms of electron and kinetic energy densities. Other implications for density-functional theory are briefly referred to.