The virial theorem 2${\mathit{E}}_{\mathit{K}}$+${\mathit{E}}_{\mathit{P}}$=3pV, where p is pressure and V is volume, is known to hold for point particles with Coulomb interactions. It is often assumed to hold for electrons in a rigid jellium background but it is not obvious that such is the case. We show that the virial theorem is obeyed providing the correlation energy has the dimensionally correct form ${\mathit{e}}^4$f(${\mathit{e}}^2$${\mathit{r}}_{\mathit{s}}$), where f is an arbitrary function in units of Ry, ${\mathit{r}}_{\mathit{s}}$ is the electron sphere radius in bohrs, and ${\mathit{e}}^2$=1 is the dimensionless coupling constant.

• Received 27 August 1990

DOI:https://doi.org/10.1103/PhysRevB.43.3918