The second Fock matrix can then be constructed using this density matrix. The
on-diagonal terms are identical to those in the first Fock matrix, since the
atomic orbital electron densities are unchanged, but the off-diagonal terms are
now changed. The off-diagonal terms are modified to allow for exchange
interactions. (Note that not all exchange terms are stabilizing.)

Let us evaluate the matrix element F(1,2):

The second Fock matrix is thus:

Second Fock Matrix (eV)

Atom

1

2

3

4

5

6

1

-5.4823

2

-6.4652

-5.4823

3

-1.0970

-6.4652

-5.4823

4

+0.3611

-1.0970

-6.4652

-5.4823

5

-1.0970

+0.3611

-1.0970

-6.4652

-5.4823

6

-6.4652

-1.0970

+0.3611

-1.0970

-6.4652

-5.4823

Diagonalization of this matrix yields the same set of eigenvectors as we had
initially. In general, several iterations are necessary in order to obtain an
SCF; however, a few systems exist for which symmetry restrictions on the form
of the eigenvectors allow them to achieve an SCF in one iteration. Hexagonal
H_{6} is one such system. Although the eigenvectors are the same, the
eigenvalues obviously have to be different.

Exercise: Verify that the SCF energy levels of H_{6} are -20.2457, -11.2116,
-11.2116, 2.4411, 2.4411, and 4.8929 eV.

Once an SCF is achieved we need to calculate the heat of formation.