Example: Pseudopotentials for Oxygen

It is very important that pseudopotentials are tested before used in large scale applications. We will show here some important points that should be considered whenever a new pseudopotential was created. Our test example are pseudopotentials for oxygen.

Figure 4: Troullier-Martins pseudopotential for Oxygen. Core radius was set to 1.05 Bohr for s and p angular momentum.

We will compare pseudopotentials generated according the recipe by Troullier and Martins [96] with cutoff radii of 1.05 and 1.40 Bohr. The pseudopotentials are used within the Kleinman-Bylander approximation using the p potential as local part (TM105p, TM140p) or the d potential as local part (TM140d). In addition we will also compare to a dual-space pseudopotential (HGH) [102] that uses a single s-type nonlocal projector.

Figure 5: Convergence of the bond length of the $O_2$ molecule for different types of pseudopotentials. See text for details.

• The first property to check is if the pseudo wavefunctions overlap with the all-electron wavefunction outside the cutoff region. See top left plot in figure 4 for the TM105 case. From this plot we immediately see that this pseudopotential will need a rather high cutoff as the p function was almost not pseudized.
• The oxygen pseudopotentials will be used without nonlinear core corrections. We have to see if there is considerable overlap between the valence density and the core density. This is not the case and the approximation though justified (see upper left plot in figure 4).
• The lower plots show the s and p potentials in the screened and unscreened form. We see that both potentials are rather smooth. There is the danger that for too large values of the core radius the potential will exhibit oscillations.
• As a further test we compare bond length is of the oxygen molecule (triplet state using LSD) as a function of the plane wave cutoff. As can be seen in figure 5 the calculations with the TM140 pseudopotentials need the smallest cutoff (about 60 Rydberg). However, a cutoff of 1.4 Bohr means that the core regions will overlap for the oxygen molecule and special care is needed. It can be seen that the converged bond length of the TM140p potential has an error of about 2 %. Including also the p potential as a nonlocal function improves the result considerably, at the cost of four projector functions compared to one in the other case. The HGH and TM105p potentials have converged bond lengths close to the all-electron value using a single projector of s type. However, convergence is only achieved at about 100 to 125 Rydberg.