When thinking about orbitals, we are often given an orbital vision which ( even if it is not spelled out ) is heavily influenced by this Hartree – Fock approximation, which is one way to reduce the complexities of molecular orbital theory.

The first ab initio Hartree – Fock calculations on diatomic molecules were carried out in 1956 at MIT, using a basis set of Slater orbitals.

The simplest type of ab initio electronic structure calculation is the Hartree – Fock ( HF ) scheme, an extension of molecular orbital theory, in which the correlated electron – electron repulsion is not specifically taken into account ; only its average effect is included in the calculation.

As the basis set size is increased, the energy and wave function tend towards a limit called the Hartree – Fock limit.

Many types of calculations ( known as post-Hartree – Fock methods ) begin with a Hartree – Fock calculation and subsequently correct for electron – electron repulsion, referred to also as electronic correlation.

The Hartree – Fock wave function is a single configuration or determinant.

Some methods combine the density functional exchange functional with the Hartree – Fock exchange term and are known as

Semi-empirical quantum chemistry methods are based on the Hartree – Fock formalism, but make many approximations and obtain some parameters from empirical data.

They are very important in computational chemistry for treating large molecules where the full Hartree – Fock method without the approximations is too expensive.

This approach is the conceptional basis of the Hartree – Fock method and further post Hartree – Fock methods.

Though this method is less developed than post Hartree – Fock methods, its significantly lower computational requirements ( scaling typically no worse than with respect to basis functions ) allow it to tackle larger polyatomic molecules and even macromolecules.

Calculations by these methods produced accurate Hartree – Fock self-consistent field ( SCF ) molecular orbitals and were used to study boranes and carboranes.

For instance, by separating the total interaction of physisorption into two contributions-a short-range term depicted by Hartree – Fock theory and a long-range van der Waals attraction, the equilibrium position of physisorption for rare gases adsorbed on jellium substrate can be determined.

Møller – Plesset perturbation theory uses the difference between the Hartree – Fock Hamiltonian and the exact non-relativistic Hamiltonian as the perturbation.

The first-order energy is the Hartree – Fock energy and electron correlation is included at second-order or higher.

Now it is also known as the Hartree – Fock method.

* Hartree – Fock method, a calculation scheme in the field of computational chemistry

-Hartree – Fock Talk: Hartree – Fock

Later in the 1930s, Douglas Hartree, Vladimir Fock and John Slater developed the so-called Hartree-Fock wavefunction as an improvement over the Thomas-Fermi model.

Those who used the techniques of calculus included Louis de Broglie, Erwin Schrödinger, Paul Dirac, Hermann Weyl, Oskar Klein, Walter Gordon, Douglas Hartree and Vladimir Fock.

In 1927, Hartree and Fock made the first step in an attempt to solve the N-body wave function, and developed the self-consistency cycle: an iterative algorithm to approximate the solution.

* the multi-configuration time-dependent Hartree method ( MCTDH ),

To begin the work of the group, Slater " distilled his experience with the Hartree self-consistent field method " into ( 1 ) a simplification that became known as the Xα method, and ( 2 ) a relationship between a feature of this method and a magnetic property of the system.

It essentially takes the basic Hartree – Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation.

In computational physics and chemistry, the Hartree – Fock ( HF ) method is a method of approximation 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.

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.

The Hartree – Fock method is also called, especially in the older literature, the self-consistent field method ( SCF ).

This solution scheme is not the only one possible and is not an essential feature of the Hartree – Fock method.

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.

The origin of the Hartree – Fock method dates back to the end of the 1920s, soon after the derivation of the Schrödinger equation in 1926.

In 1927 D. R. Hartree introduced a procedure, which he called the self-consistent field method, to calculate approximate wave functions and energies for atoms and ions.

His first proposed method of solution became known as the Hartree method.

However, many of Hartree's contemporaries did not understand the physical reasoning behind the Hartree method: it appeared to many people to contain empirical elements, and its connection to the solution of the many-body Schrödinger equation was unclear.

A. Gaunt independently showed that the Hartree method could be couched on a sounder theoretical basis by applying the variational principle to an ansatz ( trial wave function ) as a product of single-particle functions.

Hence the square of α is the ratio between the Hartree energy () and the electron rest mass ( 511 keV ).

The hartree ( symbol: E < sub > h </ sub > or Ha ), also known as the Hartree energy, is the atomic unit of energy, named after the British physicist Douglas Hartree.

where is a Slater determinant usually constructed from Hartree – Fock molecular orbitals.

For molecules, Hartree – Fock is the central starting point for most ab initio quantum chemistry methods.

Of the five simplifications outlined in the section " Hartree – Fock algorithm ", the fifth is typically the most important.

The Hartree method used the Pauli exclusion principle in its older formulation, forbidding the presence of two electrons in the same quantum state.

The Hartree – Fock method, despite its physically more accurate picture, was little used until the advent of electronic computers in the 1950s due to the much greater computational demands over the early Hartree method and empirical models.

Following the basic postulates of quantum mechanics, the Hartree – Fock wave function can then be used to compute any desired chemical or physical property within the framework of the Hartree – Fock method and the approximations employed.

An alternative to Hartree – Fock calculations used in some cases is density functional theory, which treats both exchange and correlation energies, albeit approximately.

This expression is used in the Hartree – Fock method as an ansatz for the many-particle wave function and is known as a Hartree product.

A differential analyzer could have been used if more integrators had been available, so Hartree set up his group as three " CPUs " to work on mechanical desk calculators in parallel.

Multi-configurational self-consistent field ( MCSCF ) is a method in quantum chemistry used to generate qualitatively correct reference states of molecules in cases where Hartree – Fock and density functional theory are not adequate ( e. g., for molecular ground states which are quasi-degenerate with low lying excited states or in bond breaking situations ).