In the Hartree–Fock method of 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.
[1] 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.
In its general form the Fock operator writes: Where i runs over the total N spin orbitals.
For the restricted case which assumes closed-shell orbitals and single- determinantal wavefunctions, the Fock operator for the i-th electron is given by:[2] where: The Coulomb operator is multiplied by two since there are two electrons in each occupied orbital.