In quantum mechanics, the Fock matrix is a matrix approximating the single-electron energy operator of a given quantum system in a given set of basis vectors. Fig. ... Fig. ... In mathematics, a subset B of a vector space V is said to be a basis of V if it satisfies one of the four equivalent conditions: B is both a set of linearly independent vectors and a generating set of V. B is a minimal generating set of V...

It is most often formed in computational chemistry when attempting to solve the Roothaan equations for an atomic or molecular system. The Fock matrix is actually an approximation to the true Hamiltonian operator of the quantum system. It includes the effects of electron-electron repulsion only in an average way. Importantly, because the Fock operator is a one-electron operator, it does not include the electron correlation energy. Computational chemistry is a branch of theoretical chemistry whose major goals are to create efficient mathematical approximations and computer programs that calculate the properties of molecules (such as total energy, dipole moment, vibrational frequencies) and to apply these programs to concrete chemical objects. ... The Roothaan equations are an extension of the Hartree-Fock model to molecular orbitals, and provide an approximation technique which can simplify computation. ... In physics, Hamiltonian has distinct but closely related meanings. ... This article is about operators in mathematics, for other kinds of operators see operator (disambiguation). ... Properties The electron is a subatomic particle. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrical force that one stationary, electrically charged substance of small volume (ideally, a point source) exerts on another. ... Electronic correlation refers to the interaction between electrons in a quantum system whose electronic structure is being considered. ...

The Fock matrix is defined by the Fock operator:

where:

is the Fock operator for the n-th electron in the system,

is the core Hamiltonian for the n-th electron,

is the Coulomb operator, defining the repulsive force between the j-th and n-th electrons in the system,

is the exchange operator, defining the effect of exchanging two electrons.

See also

• Roothaan equations
• Hartree-Fock