Hartree–Fock method

The Hartree–Fock method approximates a many-electron wavefunction with one optimized Slater determinant. It replaces explicit electron–electron interactions with an average field generated by the other electrons.

Slater determinant: An antisymmetric product of one-particle orbitals used to represent a fermionic many-particle state. Hartree–Fock uses one Slater determinant to enforce electron antisymmetry.
Schrödinger equation: The fundamental equation governing the evolution or stationary states of nonrelativistic quantum systems. Hartree–Fock approximates a many-electron solution to this equation.
Molecular orbital: A one-electron wavefunction extending over a molecule’s nuclei and electrons. Hartree–Fock produces optimized molecular orbitals for interpreting bonding and electronic structure.
Douglas Hartree: A British physicist who developed a self-consistent-field method for atomic calculations. His method supplied the average-field framework later extended to antisymmetric electron states.
Fock operator: An effective one-electron operator containing kinetic energy, nuclear attraction, and average Coulomb and exchange interactions. Its eigenfunctions are the orbitals optimized in the Hartree–Fock equations.
Pauli exclusion principle: The rule that identical fermions cannot occupy the same quantum state. The determinant enforces the exclusion principle for electrons.
Koopmans' theorem: An approximation relating Hartree–Fock orbital energies to ionization energies when orbitals are held fixed. It turns Hartree–Fock orbital energies into rough estimates of electron-removal energies.
Vladimir Fock: A Soviet physicist who formulated self-consistent-field equations incorporating quantum exchange. His contribution added exchange to the Hartree approach and helped establish the method.
Self-consistent field: An iterative procedure that updates a field from a solution until the field and solution agree. Hartree–Fock orbitals generate the effective field that is used to update those same orbitals.
Electron correlation: The part of electron motion not captured by an independent-particle description of their interactions. Hartree–Fock omits most correlated motion beyond its average-field treatment.

Linked from 18 pages