electrondensity

Electrondensity is a term used to describe how electrons are distributed in space within a physical system, such as an atom, molecule, or solid. In quantum mechanics, the electron density n(r) is the probability density of finding an electron at position r. For a system with N electrons, the integral of n(r) over all space equals N. In practice, n(r) is often constructed from the occupied one-electron orbitals or obtained as a functional of the electronic wavefunction.

Mathematically, the electron density can be expressed as n(r) = ⟨Ψ| ∑_{k=1}^N δ(r − r_k) |Ψ⟩, and in many-electron theory it is approximated by summing the squared magnitudes of occupied orbitals. In density functional theory, n(r) is the central quantity from which all ground-state properties are, in principle, determined. The density provides information about where electrons are most likely found, with peaks near nuclei and characteristic shapes that reflect chemical bonding.

Electron density is accessible experimentally through methods such as X-ray crystallography, which measures electron density maps in crystals, and through other scattering techniques that probe charge distribution. Computationally, analyses of n(r) include evaluating its gradient and Laplacian to reveal bonding regions and using approaches like atoms-in-molecules topology to partition space into atomic basins.

Overall, electrondensity is a foundational concept connecting the quantum state of electrons to observable chemical structure and reactivity, serving as a bridge between theory and experiment in chemistry and materials science.