Hartree–Fock method: Difference between revisions

In [[computational physics]] and [[Computational chemistry|chemistry]], the '''Hartree–Fock''' ('''HF''') method is a method of approximation for the determination of the [[wave function]] and the energy of a [[Many-body problem|quantum many-body system]] in a [[stationary state]].

The Hartree–Fock method often assumes that the exact ''N''-body wave function of the system can be approximated by a single [[Slater determinant]] (in the case where the particles are [[fermion]]s) or by a single [[Permanent (mathematics)|permanent]] (in the case of [[boson]]s) of ''N'' [[spin-orbital]]s. By invoking the [[variational method]], one can derive a set of ''N''-coupled equations for the ''N'' spin orbitals. A solution of these equations yields the Hartree–Fock wave function and energy of the system.

Especially in the older literature, the Hartree–Fock method is also called the '''self-consistent field method''' ('''SCF'''). In deriving what is now called the [[Hartree equation]] as an approximate solution of the [[Schrödinger equation]], [[Douglas Hartree|Hartree]] required the final field as computed from the charge distribution to be "self-consistent" with the assumed initial field. Thus, self-consistency was a requirement of the solution. The solutions to the non-linear Hartree–Fock equations also behave as if each particle is subjected to the mean field created by all other particles (see the [[Hartree–Fock#The Fock operator|Fock operator]] below), and hence the terminology continued. The equations are almost universally solved by means of an [[Iterativeiterative method|iterative]] method, although the [[fixed-point iteration]] algorithm does not always converge.<ref>{{cite journal|journal = Computer Physics Communications

|last = Froese Fischer | first = Charlotte