Fock Matrix

The Fock matrix $\hat{F}$ is an approximation of the single electron energy operator of a given system.

In Hartree-Fock thoery, the Fock matrix will be given by:

$$\hat{F} = \hat{H}_{core} + 2 \hat{J} - \hat{K}$$

where $\hat{J}$ is the Coulomb operator i.e. the repulsion between two electrons in the system and $\hat{K}$ is the Exchange operator i.e. arising from the exchange any two (indistinguishable) electrons.