Debugging

Run ``Geatoms.m''. (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 executable doesn't work on your computer, you can try to view the image file directly for your directory using 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 cut off 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, run ``ewald.m'', and compute the total energy per atom of the crystal. Compare this to the energy of the pseudoatom calculated at the same spatial resolution, -3.7301 H. (See Section 5 if you'd like to compute this for yourself.) Finally, using the conversion 1 hartree=27.21 eV compute your prediction for the cohesive energy of germanium. (The experimental value is 3.85 eV/atom!)