Hartree-Fock Method

In-depth explanation of Hartree-Fock Method

The Hartree-Fock method approximates the many-electron wavefunction of an atom or molecule as a single Slater determinant of one-electron orbitals, which automatically satisfies the antisymmetry requirement for electrons. Each electron is considered to move in the average field produced by all the others, and the orbitals are optimized iteratively until they are self-consistent with that field. The method gives a reasonable description of molecular geometries and orbital energies, but it neglects electron correlation, the instantaneous avoidance of electrons, which leads to errors in energies. Post-Hartree-Fock methods such as MP2 and coupled cluster CCSD(T) recover correlation energy at higher cost. Hartree-Fock is the usual starting point for these calculations.

Going deeper: Hartree-Fock Method

Key ideas: Roothaan equations FC = SCe are solved iteratively, with the self-consistent field cycle repeating until energy changes drop below a tolerance. The Hartree-Fock energy lies above the exact energy (variational principle), and correlation energy is the difference, typically about 1 eV per electron pair. Restricted HF suits closed shells and unrestricted HF suits radicals but may have spin contamination. Koopmans theorem approximates ionization energy as minus the orbital energy.

Common mistakes and connections: Students think HF includes electron correlation, but it only includes exchange. HF overestimates bond lengths for dissociating bonds and fails to describe dispersion. Larger basis sets approach the HF limit, but never the exact energy. Related to Slater determinants, Pauli principle, DFT and post-HF methods such as MP2.

Visualization of Hartree-Fock Method

The correlation energy Hartree-Fock misses, in hartree, grows with the number of electrons; MP2 and coupled cluster recover it. The interactive lesson shows this as a live animation or chart.

Worked example and use case

Hartree-Fock gives a reasonable geometry for water, while the correlation energy it misses can be recovered with MP2.

Where Hartree-Fock Method fits in Analytical, Lab & Spectroscopy

Hartree-Fock Method is topic 86 of 99 in Analytical, Lab & Spectroscopy.

Related topics

• Computational ChemistryAdvanced
• Density Functional TheoryAdvanced
• Molecular DynamicsAdvanced
• Born-Oppenheimer ApproximationAdvanced
• Particle in a BoxAdvanced
• Harmonic Oscillator ModelAdvanced

Browse all 99 topics in Analytical, Lab & Spectroscopy