electron density function

https://doi.org/10.1351/goldbook.ET07024
The electron @[email protected] 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 @[email protected] function is that \(\rho \ \mathrm{d}\mathbf{\mathbf{r}}\) gives the @[email protected] of finding an electron in a volume element \(\mathrm{d}\mathbf{\mathbf{r}}\), i.e., @[email protected] in this volume.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1937 [Terms] [Paper]