Convergence with respect to k-point sampling

Before doing anything, it is useful at this point to store the current FORCES file, which is all you will need to recalculate the frequencies should you need to, and also store the FREQ.cm file, which can then be compared with new calculations. Once this is done, edit KPOINTS and change the grid of k-points from 2 2 2 to 4 4 4 and repeat the procedure, i.e. execute runphon that will produce a new FORCES file and then phon which will produce a new FREQ.cm file. You should observe that now the frequencies agree better with the experiments, though there still are significant differences. You can now keep increasing the k-point sampling until the phonon dispersions stop changing (they are converged). You should see that once you use an 8 8 8 grid the phonon dispersions are essentially converged, but even a 4 4 4 grid produces reasonable results. Small discrepancies with the experiments still remain, but we cannot eliminate them with denser k-point grids; they must be due to something else.