What are some of the advantages and disadvantages when using shape consistent pseudopotentials as compared to energy consistent pseduopotentials

Question

From the literature as well as the answer to the question What is the meaning of energy-consistent and shape-consistent in the context of pseudopotentials? I can see that the key difference between these two types of pseudopotential is based on how they are fitted.

I can also see that energy consistent pseudopotentials provide more accurate information concerning the energy of the atoms/molecules however shape consistent ones are a lot easier to construct. Additionally, it seems that that energy consistent are also shape-consistent but the reverse is not necessarily true.

I was wondering if anyone knew of any more advantages/disadvantages of these types of pseudopotentials. If one could elaborate on the typical circumstances when one pseudopotential may be preferable to the other that would also be greatly appreciated.

Answer 1

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-consistent PPs:

"This technique has the disadvantage that it requires inversion of the Fock equation to produce angular-momentum-dependent pseudopotentials, resulting in a large number of Gaussian fitting functions.

The author then mentions that this disadvantage can be overcome by directly fitting to the shape of the valence orbital, and such PPs are sometimes called "compact effective core potentials" or CEPs.

Advantages of shape-consistent PPs:

"Shape-consistent pseudopotentials have the advantage that the fitting technique used is fast and efficient."

However the author then says:

"energy-consistent pseudopotentials choosing a rather large valence spectrum in the fit procedure fulfil the shape-consistent requirement extremely well (not necessarily vice versa) if the spectrum is accurately adjusted".

Final remarks:

As Susi's answer to the present question, and to this one: What are the types of pseudopotentials?, says: energy-consistent PPs can fulfill the shape-consistent requirement very well while also providing accurate energies, whereas shape-consistent PPs may not provide accurate energies, so the best energy-consistent PPs will often be preferable for all-around accuracy over any "shape-consistent PP" in the literature.

Answer 2

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 can be disregarded.