In
computational physics and
chemistry, the
Hartree–Fock (
HF) method is an approximate method for the determination of the
ground-state wave function and
ground-state energy of a
quantum many-body system.
The Hartree–Fock method 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 fermions) or by a single permanent (in the case of bosons) of N spin-orbitals. By invoking the variational principle, one can derive a set of N-coupled equations for the N spin orbitals. Solution of these equations yields the Hartree–Fock wave function and energy of the system, which are approximations of the exact ones.
The Hartree–Fock method finds its typical application in the solution of the electronic Schrödinger equation of atoms, molecules, and solids but it has also found widespread use in nuclear physics. (See Hartree–Fock–Bogolyubov for a discussion of its application in nuclear structure theory.) The rest of this article will focus on applications in electronic structure theory.
The Hartree–Fock method is also called, especially in the older literature, the self-consistent field method (SCF). The solutions to the resulting non-linear equations behave as if each particle is subjected to the mean field created by all other particles (see the Fock operator below). The equations are almost universally solved by means of an iterative, fixed-point type algorithm (see the following section for more details). This solution scheme is not the only one possible and is not an essential feature of the Hartree–Fock method.
