Choosing the Plane Wave Cutoff

After getting familiar with the input and output of CPMD, we now have to run a test on the validity of the pseudopotential and its cutoff requirements for the subsequent calculations (geometry optimization and molecular dynamics). For that purpose we make a copy of the input file from the wavefunction optimization and add the keyword PRINT FORCES ON to the &CPMD section and then re-run the wavefunction optimization for a series of wavefunction cutoff values ranging from 10ryd up to 200-500ryd (depending on the available memory. Take note of the values of total energy, and force for each cutoff value. Since the convergence behavior can be different for each pseudopotential (and each property), we exchange the pseudopotential file as well using H_BHS_LDA.psp as replacement. When plotting the relative errors from those calculations, we get a graph similar to the following:

Energy and forces have a the same convergence trend, but for the forces we have a not as regular behavior in the relative error. Next we see that for both pseudopotentials, the relative error in the force reaches some kind of plateau starting at 50ryd, with the Martins-Troullier (MT) potential behaving a bit better than the BHS-type pseudopotential parameters. For problems requiring even more accurate forces, a choice of 100-120ryd would be better. Please note, however, that these errors only document the convergence behavior of the pseudopotential with respect to the basis set size (= cutoff), they do not include systematic error contributions, e.g. the error from using DFT altogether in or from the choice of pseudization cutoff radius (which can be chose to make a ``softer'' pseudopotential at the expense of the transferability of the pseudopotential). Typical errors on bond lengths or lattice constants from DFT calculations relative to experiment are of the order of one to a few percent. For all subsequent calculations on hydrogen we will use the H_MT_LDA.psp file and a wavefunction cutoff of 60ryd.