Debugging

Run ``GeSolid.m'' with S=[48; 48; 48]. (This will take about 1/2 hour!) The code should produce (and will try to display) two graphics, ``100.ppm'' and ``110.ppm''. If the display doesn't work on your computer, you can try to view the images with some other application.

The graphics show a brightness proportional to the total charge density at each point in a plane cutting through the solid. The sky-blue graphic (``100.ppm'') shows a slice across the top of the cubic cell. The atoms should appear as rings of round charge distributions with low density (dark regions) centered on the nuclei. The reason why there are no electrons on the nuclei is that we are using a pseudopotential and are not computing the core electrons. You should see one atom in the center of the 100 slice and four atoms cutoff at the corners. This reflects the basic faced-centered cubic (fcc) structure of the germanium crystal. The 110 graphic is more exciting. This cut slices through the centers of neighboring atoms, showing significant buildup of charge right in between them. These are the bonds which hold the crystal together!!!

Finally, adding your final energy from ``GeSolid.m'' to the 8 atom result of ``poissonGeSolid.m'' and subtracting 8 times the energy that you got for an isolated pseudoatom (calculated with the same $S$ and $R$ is best) gives your result for the binding energy of an 8 atom cell of germanium. (Your result should be negative: because the crystal is stable, it's energy should be lower than that of the same number of isolated atoms.) Divide this number by 8, convert units (1 hartree=27.21 eV), and compare to the experimental cohesive energy of germanium of 3.85 eV/atom!