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?

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    $\begingroup$ +1. But related? mattermodeling.stackexchange.com/q/1521/5 $\endgroup$ – Nike Dattani Aug 9 '20 at 11:24
  • $\begingroup$ 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. $\endgroup$ – Xivi76 Aug 10 '20 at 19:04
  • $\begingroup$ Useful Post: lists.quantum-espresso.org/pipermail/users/2019-April/… $\endgroup$ – mykd Aug 12 '20 at 10:49

Pseudopotentials (PPs) describe the effective interaction between the valence electrons and a nuclei screened by frozen core electrons. This approximation makes DFT calculations less computationally expensive as only valence electrons are treated explicitly and the resulting valence wavefunctions no longer oscillate rapidly near the cores to ensure orthogonality with core electron wavefunctions, thus, converging with fewer plane waves.

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: \begin{equation} | {\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 \end{equation}

There is no systematic manner for deciding which pseudopotential is ‘better’ as a pseudopotential that works well for obtaining one property may not work well for another property. In general, you would expect the PAW pseudopotential to be more accurate compared to the ultrasoft pseudopotential since the projector augmented waves should restore the pseudo-wavefunction up to the all-electron wavefunction behaviour, but this does not always guarantee that it would be more accurate than USPPs or NCPPs. I am not familiar with spin-orbit calculations for topological insulators but the only way to truly determine which pseudopotential is ‘best’ for determining a specific materials property is to benchmark the different pseudopotentials against the same property obtained from an all-electron DFT method on an example system as all of these pseudopotentials are trying approximate it.

  • $\begingroup$ +10. A second answer is always good, especially when it's this detailed! $\endgroup$ – Nike Dattani Aug 14 '20 at 4:03
  • $\begingroup$ PAW and USP formalisms are almost identical and the all-electron properties can be recovered with either of them. (USPs have an additional pseudisation step, and IIRC linearise one extra term.) $\endgroup$ – Phil Hasnip Nov 16 '20 at 10:30

Spin-orbit coupling is an effect that is dependent on the relativistic effect. So you should use fully relativistic PP(pseudopotentials) whatever you use. Another thing is that PP often varies from your material structure. So, the efficiency of PP is highly dependent on what your simulation output parameter is. There are a lot of things related to the performance of the simulation. So, my suggestion is you can benchmark on a small scale. You can see this paper below I wrote for benchmarking. Though it's on Quantum espresso but I think the process is similar. http://dx.doi.org/10.13140/RG.2.2.25087.23207


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