# Tag Info

22

To complement mykd's already excellent answer, I will just add that the approximant we all learn in school (the Taylor approximant) is nice to teach and easy to help students learn the concept of approximations, but in practice it's one of the worst options in terms of it's accuracy-to-complexity ratio. The Taylor approximant matches the $n^{\textrm{th}}$ ...

17

Disclaimer: I am a developer of the Fleur code. I hope that I don't put too much bias into this answer. At least I try to not do that... When you want to solve the Kohn-Sham equations you have the problem that the potential has singularities at the atomic nuclei. There are different ways to deal with this. On the one hand you can make the pseudopotential ...

16

PADE refers to the mathematician Henri Padé, who developed the Padé approximation, which can approximate a function using rational polynomial functions. For ex: $$\sin(x)\approx {\frac {(12671/4363920)x^{5}-(2363/18183)x^{3}+x}{1+(445/12122)x^{2}+(601/872784)x^{4}+(121/16662240)x^{6}}}$$ This feature is used to approximate the total correlational ...

15

Three criteria to consider are Performance and size of basis set USPPs generally require a lower plane-wave cut-off and smaller basis, but a larger density grid. However performance may not be straightforwardly related to cut off as there are additional terms to compute which may have a significant computational cost. Accuracy USPPs usually have 2 (or more)...

14

When to include relativistic corrections or modeling of any kind in computational methods is a rather complex one. Full Dirac methods as you asked about (DHF) recapture two important factors, so called scalar relativistic effects, and spin effects. I'll elaborate on each and when including them is important. Scalar Relativistic Effects - This largely ...

12

The clearest example in my mind is if you want to understand the orbital-based contributions to some phenomena (e.g. bonding, a reaction energy), particularly if the periodic material being modeled is more like a molecular solid where the chemical picture of orbitals is more intuitive than bands. There are several schemes out there that try to go from PAW to ...

11

Great question, will allow me to advertize our newly-released DFT code :](https://github.com/JuliaMolSim/DFTK.jl/). The rloc parameter is the characteristic distance at which the pseudopotential acts. At distances bigger than rloc, the potential starts to behave like a Coulomb potential. Note that the nonlocal potential also has a characteristic size, ...

10

Summary of the "milestone" pseudopotential (PP) papers Since it wasn't available anywhere & took me a few hours, it's an answer rather than question-edit: Local pseudo-potentials: 1935: Zusatzpotential / Hellmann (Generally credited as the first pseudopotential). 1936: Fermi pseudopotential (for s-wave scattering of a free neutron by a nucleus)...

9

I think the best place to start is the original paper¹ proposing norm conserving pseudopotentials (NCPPs). It's very short and gives a nice explanation of why they were developed. I'll just give a brief summary here. Norm conservation (specifically of the charge density $\rho$) ensures that the electrostatic potential for $r>r_c$ is accurate as a result ...

9

It is well known that using pseudopotentials generated with a functional which is inconsistent with the functional used in the plane-wave calculation can lead to serious problems, see here for example. It was also shown that for a potential-only meta-GGA (TB), the choice of pseudopotential makes a huge difference in the band gap, and in particular using PBE ...

9

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 ...

9

I am quoting from the book Materials Modelling Using Density Functional Theory: Properties and Predictions by Feliciano Giustino How do we decide which wavefunctions should be considered ‘core’ and which ones ‘valence’ states? As a rule of thumb, in the context of DFT calculations the ‘valence’ corresponds to the outermost shell of the atom in the ...

8

The GPAW code can do GW/BSE and it uses purely PAW potentials. So it's absolutely possible to do GW/BSE with PAW sets. The involvement for the implementation, however, is another topic. From Kevin J. M.'s answer, the primary block is fairly clear: PAWs are quite involved to implement. Doing all of the atom-centered corrections and then getting them onto your ...

8

USPP is not a format of pseudopotential. It is a type of pseudopotential that enables you to work with lower cutoffs. On the other hand, upf is a popular file extension for pseudopotentials. If your question is regarding the availability of fully relativistic Ultrasoft PPs, they aren't very popular but PSLibrary offers that support. For Norm-conserving and ...

7

Only a partial answer: some setups are surely better suited than others for a given property. Some developers recognize this and thus do not bother implementing properties for which their setup will be bad, other developers simply lack the time. One example that I am familiar with are NMR/ESR properties. The ADF package (using Slater basis functions) can ...

7

The short answer is DEPENDS on your system and property of interest you are after (among other things). Anyway, I see the order of physical basis/complexity increasing as NC --> USPP --> PAW. But I may be wrong here. However, you should look at https://www.vasp.at/vasp-workshop/pseudopp2.pdf and the original USPP paper by Vanderbilt https://journals.aps....

7

The Augmented Plane Wave (APW) method, and by extension Linearly-Augmented Plane Wave method are both generalizations of the Muffin Tin Approximation. In both the APW and LAPW methods, the potential $V(r)$ is defined as a piecewise function  with a single parameter: the muffin-tin radius $r_\mathrm{MT}$.  V(r) = % \begin{cases} \sum_{lm} V_{lm} (r) Y_{...

7

Spin-orbit coupling is related to relativity which is increasingly important for heavier elements. If you're aiming for ultra-high precision, as in this post on our site: How accurate are the most accurate calculations?, you will need to include every possible effect, including spin-orbit coupling, for all elements including hydrogen. For most applications, ...

6

But in the case of the pseudo-potentials included, should I use fully relativistic pseudopotentials for all three elements? Yes, you should use the fully relativistic pseudopotentials if you are considering spin-orbit coupling calculations. When you should consider spin-orbit coupling? If the investigated materials contain heavy atoms then you should ...

6

This 2017 paper titled "Shape and Energy Consistent Pseudopotentials for Correlated Electron systems" defines energy-consistent psuedopotentials this way: "A combined reproduction of core scattering, core polarisation, and atomic excitation energies allows the generation of a new pseudopotential from correlated electron calculations, referred ...

6

I don't think there is a consensus of norm conserving PP being more accurate. There are some references I am aware of which have calculated dielectric tensor using NC-PP, but without justification though: Yu, E. K.; Stewart, D. A.; Tiwari, S. Ab Initio Study of Polarizability and Induced Charge Densities in Multilayer Graphene Films. Phys. Rev. B - Condens. ...

6

The advantages and disadvantages are discussed in this review paper which was cited in Susi Lehtola's answer to: What are the types of pseudopotentials? and then again in my answr to: What is the meaning of energy-consistent and shape-consistent in the context of pseudopotentials?. My quotes below will be from that review paper: Disadvantages of shape-...

6

There is a discussion on this limitation on VASP page. Maybe the approach of a frozen f valence PAW pseudopotential could help you. Although magnetic properties might not be as well represented. I'm quantum espresso user and when their PAW potentials show problems (not so rare) I go to a norm-conserving solution like pseudodojo library, if you can do this in ...

6

This error has been resolved now. Though I am not an expert but here are few thoughts. There may be several reasons for this error: This error might appear due to numerical instability from overlapping atoms. As mentioned by @Phil Hasnip, if the S-matrix eigenvalues are really small. Some pseudopotential may not fit with calculation, USPP giving non-...

5

To add to Nike's list, one should also differentiate between the energy consistent pseudopotentials used in quantum chemistry and the shape consistent pseudopotentials that dominate in the solid state community. Energy consistent pseudopotentials are also shape consistent, while shape consistent pseudopotentials result in much larger errors in the energy ...

5

Why would you want to generate a pseudopotential for a cation/anion? The pseudopotential is only for the inner core electrons. The only case where you'd want to do this is when the charge state of the system is so extreme that the inner shells are disturbed as well. (Also note that anions are ill-described by DFT so setting up an anion pseudopotential would ...

5

Shape consistent pseudopotentials are just commonly used for some reason, even though energy consistent pseudopotentials are "the right way to do it". The reason why shape consistent pseudopotentials keep on being used is that the errors in the density functional approximations themselves are so large that the extra error from the pseudopotentials ...

5

The question is related essentially to solve the Kohn-Sham equation with an atomic-like basis set. In fact, different implementations of DFT are distinguished mainly by their basis set and how they orthogonalize themselves to the core levels. In particular, the choice of basis set forms the core of any electronic structure method. Dedepending on the choice ...

5

The "pn" column here gives the principal quantum number ("n") for the states of the pseudoatom, which is the "atom" that remains after the core electrons are removed and the original Coulomb potential is replaced with the pseudopotential. For example, in the file you show, the $n=1$, $l=0$ state of the pseudo-atom corresponds to ...

4

New functionals often use PBE as a base. This is due to the benefit that everyone is using the same slightly incorrect psuedopotential, meaning it is reproducible. In VASP the psuedopotentials cannot be generated by the user but codes like CASTEP and GPAW can generate them on the fly as needed. Using PBE as a base for SCAN is not ideal, but its consistent ...

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