electron density function

The electron @P04855@ distribution function, \(\rho \), defined as \[\rho (\mathbf{r}) = n\ \int \Psi ^{\text{*}}\left[\mathbf{r}(1),\mathbf{r}(2)\,\text{...}\,\mathbf{r}(n)\right]\ \Psi \left[\mathbf{r}(1),\mathbf{r}(2)\,\text{...}\,\mathbf{r}(n)\right]\text{d}\mathbf{r}(2)\,\text{...}\,\text{d}\mathbf{r}(n)\] where \(\Psi \) is an electronic wave-function and integration is made over the coordinates of all but the first electron of \(n\). The physical interpretation of the @E01986@ function is that \(\rho \ \mathrm{d}\mathbf{\mathbf{r}}\) gives the @P04855@ of finding an electron in a volume element \(\mathrm{d}\mathbf{\mathbf{r}}\), i.e., @E01986@ in this volume.
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1937 [Terms] [Paper]