Assembly of the starting Fock matrix

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 Faa 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 φa. Consider F(1,1). The total initial population of φ1 is 1.0, composed of equal amounts of α and β electron density. An electron in φ1 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:

F(1,1) = -51.7124+1/2(12.848)+2(9.6585+7.0635)+6.3622

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:


Initial Fock Matrix (eV)
Atom 1 2 3 4 5 6
1 -5.4823          
2 -3.2457 -5.4823        
3 -1.0970 -3.2457 -5.4823      
4 -0.6992 -1.0970 -3.2457 -5.4823    
5 -1.0970 -0.6992 -1.0970 -3.2457 -5.4823  
6 -3.2457 -1.0970 -0.6992 -1.0970 -3.2457 -5.4823