# What is the difference between Ultrasoft, ONCV and PAW Pseudopotentials? Which is better for a spin-orbit coupled calculation?

I am trying to do spin-orbit coupled calculations for various topological insulators. I have found papers using Quantum Espresso with ONCV pseudopotentials and papers using VASP with PAW pseudopotentials. I know that PAW is also available in Quantum Espresso. But which would be better: ONCV or PAW?

Also, as a general question, why would one prefer one pseudopotential over the other?

• +1. But related? mattermodeling.stackexchange.com/q/1521/5 Aug 9 '20 at 11:24
• The area of pseudopotentials is very broad, and I don't have enough expertise to delineate the differences between them. But, I can offer some insight regarding your primary question - If you're doing SOC calculations,you should be aware that you need to use fully relativistic pseudopotentials. As far as I've seen, ultrasoft PPs (they enable you to work with lower cutoffs, hence quicker computaitons) don't have good support for this. Between PAW and NCPP, I don't think it should matter because well tested and reliable PPs are available for both. Aug 10 '20 at 19:04
• – mykd
Aug 12 '20 at 10:49

Pseudo-wavefunctions which arise from PPs are constructed to agree with the true all-electron wavefunction (where all electrons are treated explicitly) beyond a cutoff $$r_c$$. The two most common types of PPs are the norm-conserving PPs (NCPPs) and ultrasoft PPs (USPPs). NCPPs impose the restriction that the total integrated ED within $$r_c$$ has to match the all-electron electron density, whilst USPPs relax this condition, requiring fewer planewaves to describe their pseudo-wavefunctions. The ONCV pseudopotential you mention is an example of a NCPP, although it is a more ‘modern’ variant using a similar construction method to USPPs, so that it requires fewer planewaves compared to traditional NCPPs.
Projector augmented waves (PAWs) are a method of restoring the pseudo- to the all-electron wavefunctions and uses pseudopotentials which are linked closely to USPPs. It expands the all-electron wavefunction within $$r_c$$ of an atomic site $$\mathbf{R}$$ into a basis set of atomic wavefunctions $$\Phi_{u}^{\mathbf{R}}$$, called partial waves. The pseudo-wavefunctions are also expanded into a basis set of pseudo-partial waves $$\tilde{\Phi}_{u}^{\mathbf{R}}$$ which correspond to pseudised versions of the all-electron partial waves. The coefficients for the expansion of both the all-electron and pseudo-wavefunctions are the same, $$\langle {\tilde{p}_{u}^{\mathbf{R}}} | {\tilde{\phi}_{i}} \rangle$$, and they are found using projector functions $$\tilde{p}_{u}^{\mathbf{R}}$$ which are orthonormal to the pseudo-partial waves. In essence, the PAW method maps the pseudo-wavefunction to the all-electron wavefunction through a linear transformation $$\mathcal{T}$$ which evaluates the difference between the all-electron and pseudo-wavefunctions: $$$$| {\phi_{i}} \rangle= \mathcal{T} | {\tilde{\phi}_{i}} \rangle = | {\tilde{\phi}_{i}} \rangle + \sum_{\mathbf{R}} \sum_{u} \left ( | {\Phi}_{u} \rangle - | {\tilde{\Phi}}_{u} \rangle \right ) \langle {\tilde{p}_{u}^{\mathbf{R}}} | {\tilde{\phi}_{i}} \rangle$$$$