Optional: Variable fillings and verification of pseudopotential

Our final tasks are to compute the total energy of an isolated atom of germanium as described by our pseudopotential and to convince ourselves that the pseudopotential we are using reproduces the influence on the valence electrons of the nucleus and core electrons of the germanium atom. We shall do this by using our software to compute the electronic structure of an isolated atom of germanium.

For germanium, the calculation of an isolated atom requires variable fillings. The valence electrons of Ge have the configuration 4s$^2$4p$^2$. The 4p$^2$ means that the three $p$ states share two electrons equally. This means that the fillings vector $\vec f$ should be f=[2;2/3;2/3;2/3]. Our current software, however, assumes constant fillings, f=[2;2;2;...]. We must modify the current DFT software to include the appropriate general expressions.

To prepare for this create a final copy of all of your ``.m'' files in ``$\sim$/A4'' in a new directory, ``$\sim$/A4'' and begin working there.