Editing Hartree–Fock method (section)

== Weaknesses, extensions, and alternatives ==

Of the five simplifications outlined in the section "Hartree–Fock algorithm", the fifth is typically the most important. Neglect of [[electronic correlation|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, [[Møller–Plesset perturbation theory]], treats correlation as a [[perturbation theory|perturbation]] of the Fock operator. Others expand the true multi-electron wave function in terms of a linear combination of Slater determinants—such as [[multi-configurational self-consistent field]], [[configuration interaction]], [[quadratic configuration interaction]], and [[multi-configurational self-consistent field#Complete active space SCF|complete active space SCF (CASSCF)]].  Still others (such as [[Variational Monte Carlo|variational quantum Monte Carlo]]) modify the Hartree–Fock wave function by multiplying it by a correlation function ("Jastrow" factor), a term which is explicitly a function of multiple electrons that cannot be decomposed into independent single-particle functions.

An alternative to Hartree–Fock calculations used in some cases is [[density functional theory]], which treats both exchange and correlation energies, albeit approximately. Indeed, it is common to use calculations that are a hybrid of the two methods—the popular B3LYP scheme is one such [[hybrid functional]] method.
Another option is to use [[modern valence bond]] methods.