Electron density

Electron density is the expected number of electrons per unit volume at each point in space. It describes a molecule’s spatial electron distribution without specifying individual electron paths.

Many-electron wavefunction: A quantum state describing the positions and spins of all electrons in a system. Electron density is obtained from this full state by averaging over all but one electron.
Molecular orbital: A one-electron wavefunction extending over the atoms of a molecule. In orbital-based calculations, occupied orbitals are combined to construct the total density.
Atoms in molecules: A theory that partitions molecular space into atomic regions using the topology of electron density. Its boundaries and atomic properties are derived from features of the molecular density.
Spin density: The spatial difference between the densities of spin-up and spin-down electrons. It distinguishes spin imbalance, which total electron density alone does not show.
Born rule: The rule that relates a quantum state’s probability amplitudes to probabilities of measurement outcomes. It turns the wavefunction into probabilities that underlie the density at each point.
Hartree–Fock method: An approximation that represents each electron as moving in the average field of the others. Its occupied orbitals produce an approximate electron density for a molecule.
Bader charge: An atomic charge obtained by integrating electron density within a Bader basin. It converts the density’s spatial partition into an estimate of charge transfer between atoms.
Electron density matrix: A matrix representation of one-particle electron information, including density and coherence. Its off-diagonal elements contain information absent from the ordinary spatial density.
One-particle reduced density matrix: A reduced description of a many-particle quantum state containing all one-particle information. Its diagonal in position space is the electron density.
Density functional theory: A quantum method that uses electron density as its central variable to calculate ground-state properties. It computes molecular properties through functionals of the density rather than a full wavefunction.

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