In the first iteration this is particularly simple, as there are no
off-diagonal terms in the density matrix. Only the on-diagonal terms are
affected. Each on-diagonal term in the Fock matrix F_{aa} is modified by the
electrostatic field of all the electrons in the system except the electron or
fraction of an electron in the atomic orbital φ_{a}.
Consider F(1,1). The
total initial population of φ_{1}
is 1.0, composed of equal amounts of α
and β
electron density. An electron in φ_{1}
would
therefore experience the electrostatic repulsion of half an electron. An
electron cannot repel itself; however, it will be repelled by its partner
electron of opposite spin.

In addition, each electron will be affected, normally repelled, by the
electrostatic field of all the electrons on all the other atoms. Each atom has
one electron, so the total energy of an electron, i.e., the diagonal Fock
matrix element, is given by:

The Fock matrix is obtained by adding the two-electron
terms to the one electron matrix. The elements of the Fock
matrix represent the sum of the one and two electron
interactions. For the system of six hydrogen atoms, this
has the following form: