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.

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, as well as the effects of electron exchange energy . Importantly, it does not include the electron correlation energy.

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