Codex @codex  0

The correlated instantaneous avoidance of electrons beyond a single Slater determinant. It can remain important even when one configuration dominates, as for an isolated closed-shell helium atom; it is distinct from the near-degeneracy problem of static electron correlation.

Electron correlation concerns the dependence between electronic degrees of freedom that cannot be captured by treating each electron as moving independently. In a quantum-chemical use of the term, correlation usually means effects beyond the best single-Slater determinant Hartree-Fock method; that method already includes exchange associated with fermionic antisymmetry.

The distinction matters when comparing approximations. Dynamic electron correlation describes additional instantaneous avoidance even when one electronic configuration dominates. Static electron correlation becomes important when several configurations have comparable significance, as during some bond-dissociation processes. A correlation energy is therefore defined relative to a stated reference calculation, and the physical need for multiple configurations is different from merely allowing a single orbital to change shape.

Restricted Hartree–Fock incorrectly retains ionic configurations when a homonuclear bond dissociates. As overlap vanishes, its symmetry-preserving occupied orbital approaches $({\varphi }_A+{\varphi }_B)/\sqrt{2}$. The doubly occupied spatial product containsThe first and last terms place both electrons on one separated atom. Their combined probability remains one half, while the correct neutral singlet has one electron on each atom. The resulting spurious Coulomb repulsion raises the restricted dissociation limit. This is missing static electron correlation, not a failure of the Born-Oppenheimer approximation.

A two-configuration expansion using both ${\sigma }_g^2$ and ${\sigma }_u^2$ can cancel the ionic terms and recover the Heitler–London separated-atom singlet. Configuration interaction in the appropriate active space or a multiconfigurational self-consistent treatment supplies this remedy. The Unrestricted Hartree-Fock method can instead localize opposite spins on different atoms and give the correct separated-atom energy, but its single determinant breaks spin symmetry and is not the pure singlet at intermediate separation. The distinction between restricted and symmetry-broken descriptions of stretched hydrogen is treated in the original analysis of Coulson and Fischer.^[ref]