Hartree-Fock

In computational physics and computational chemistry, the Hartree-Fock (HF) or self-consistent field (SCF) calculation scheme is a self-consistent iterative variational procedure to calculate the Slater determinant (or the molecular orbitals which it is made of) for which the expectation value of the electronic molecular Hamiltonian is minimum. Whilst it calculates the exchange energy exactly, it does not include the effect of electron correlation. The procedure is named after Douglas Hartree, who devised the self-consistent field method, and V. A. Fock, who demonstrated the rigour of Hartree's method and reformulated it into the matrix form used today. Expressed in a Slater-type or Gaussian-type basis set, the Hartree-Fock equation can be transformed into matrix form called Roothaan equations.

Weaknesses, extensions, and alternatives

Of the four simplifications outlined under Hartree-Fock algorithm, the fourth is typically the most important. Neglecting electron correlation can lead to large deviations from experimental results. A number of approaches to this weakness, collectively called post-Hartree-Fock methods, have been devised to include electron correlation to the multi-electron wave function. One of these approaches, Moller-Plesset perturbation theory, treats correlation as a perturbation of the Fock operator. Others expand the true multi-electron wavefunction in terms of a linear combination of Slater determinants - such as Multi-configurational self-consistent field, Configuration interaction, Quadratic configuration interaction, Complete active space SCF.

Related Topics:
Post-Hartree-Fock - Moller-Plesset perturbation theory - Perturbation - Multi-configurational self-consistent field - Configuration interaction - Quadratic configuration interaction - Complete active space SCF

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An alternative to Hartree-Fock calculations used in some cases is density functional theory, which gives approximate solutions to both exchange and correlation energies, but is not a purely ab initio method in pratice. Indeed, it is common to use calculations that are a hybrid of the two methods - the popular B3LYP schema is one such method.

Related Topics:
Density functional theory - Ab initio - B3LYP

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