Iterating Fock matrix

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):

\begin{displaymath}F(1,2) = -3.2457 - \frac{1}{2}(0.6667)(9.6583){\rm eV}.

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.