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
H6 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 H6 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.
