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- Created 2012-03-29
) method is a method of approximation for the determination of the
and the energy of a
quantum many-body system
The Hartree–Fock method often assumes that the exact,
-body wave function of the system can be approximated by a single
(in the case where the particles are
s) or by a single
(in the case of
s. By invoking the
, one can derive a set of
-coupled equations for the
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
). In deriving what is now called the
as an approximate solution of the
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 Fock operator below) and hence the terminology continued. The equations are almost universally solved by means of an
method, although the
algorithm does not always converge.
This solution scheme is not the only one possible and is not an essential feature of the Hartree–Fock method.
The Hartree–Fock method finds its typical application in the solution of the
for atoms, molecules, nanostructures and solids but it has also found widespread use in
for a discussion of its application in nuclear structure theory). In
theory, calculations may be for a spectrum with many excited energy levels and consequently the Hartree–Fock method for atoms assumes the wave function is a single configuration state function with well-defined
and that the energy level is not necessarily the
For both atoms and molecules, the Hartree–Fock solution is the central starting point for most methods that describe the many-electron system more accurately.
The rest of this article will focus on applications in electronic structure theory suitable for molecules with the atom as a special case.
The discussion here is only for the Restricted Hartree–Fock method, where the atom or molecule is a closed-shell system with all orbitals (atomic or molecular) doubly occupied.
systems, where some of the electrons are not paired, can be dealt with by one of two Hartree–Fock methods:
Restricted open-shell Hartree–Fock
from Wikipedia (last updated: 06 December), licensed under
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Introduction by C. David Sherrill
Quantum chemistry computer programs
Clemens C. J. Roothaan
George G. Hall
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