Term: electron density function
https://doi.org/10.1351/goldbook.ET07024

Definition:
The electron probability distribution function, ρ, 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 Ψ 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 electron density function is that ρ d r gives the probability of finding an electron in a volume element dr, i.e., electron density in this volume.

Related Terms:
1) probability (http://doi.org/10.1351/goldbook.P04855).
2) electron density (http://doi.org/10.1351/goldbook.E01986).

Source: PAC, 1999, 71, 1919. 'Glossary of terms used in theoretical organic chemistry' on page 1937 (https://doi.org/10.1351/pac199971101919)

Citation: 'electron density function' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.ET07024

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