Electron correlation

Electron correlation is the part of interacting electrons’ collective motion that cannot be captured by treating each electron independently. It shapes molecular energies, bonding, and electronic structure.

Hartree–Fock method: A quantum-chemical method that approximates a many-electron state using one antisymmetrized product of orbitals. Its independent-particle approximation leaves electron correlation outside the wavefunction.
Many-electron wavefunction: A quantum state describing the coordinates and spins of all electrons in a system. Correlation is a feature of the joint state, not of isolated electron orbitals.
Coupled cluster: A family of electronic-structure methods that builds correlated states through an exponential operator acting on a reference determinant. It captures dynamic correlation accurately for many molecules near equilibrium.
Correlation energy: The difference between the exact nonrelativistic ground-state energy and the Hartree–Fock energy for the same system. It quantifies the energetic contribution omitted by the independent-particle reference.
Exchange interaction: A quantum effect arising from the antisymmetry of identical-particle wavefunctions, influencing energies and spin alignment. It is distinct from correlation caused by electrons responding to one another’s positions.
Coulomb hole: The reduced probability of finding another electron near a reference electron because of their electrostatic repulsion. It describes how electrons rearrange locally to avoid one another.
Slater determinant: An antisymmetric product of one-electron spin orbitals used to represent fermionic states. A single determinant enforces exchange antisymmetry but cannot represent all correlated motion.
Møller–Plesset perturbation theory: A family of perturbative quantum-chemistry methods that correct a Hartree–Fock reference using electron interactions. Its second-order form is a widely used estimate of correlation energy.
Covalent bond: A chemical bond formed when atoms share electron density through their quantum-mechanical states. Accurate bond energies and dissociation behavior often require correlated electrons.
Independent-particle approximation: A modeling approach that treats particles as moving independently in an effective average field. Electron correlation names the collective behavior this approximation omits.

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