## electron density function

https://doi.org/10.1351/goldbook.ET07024
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.
Source:
PAC, 1999, 71, 1919. (Glossary of terms used in theoretical organic chemistry) on page 1937 [Terms] [Paper]