Norm-Conserving Pseudopotentials

The SSSP testing protocol is made of a verification part based on the Δ-factor and a performance-oriented part based on plane-wave convergence tests for phonon frequencies, band structures, cohesive energies and stress tensors.

“Our protocol, named SSSP (standard solid-state pseudopotential) testing protocol, is made of a verification part, based on the ∆ -factor (i.e. the difference between allelectron and PSP equations of state) [6, 7], and an extensive performance-oriented part based on plane-wave convergence tests for phonon frequencies, band structures, cohesive energies and stress tensors.”

Efforts of verification of the precision of pseudopotentials or projector augmented-wave approximations have been minimal.

“It is ever so more remarkable that in spite all of this, the efforts of verification of the precision of the underlying pseudopotentials (PSPs) or projector augmentedwave (PAW) approximations have been minimal.”

Only in 2016 a multi-group effort established a baseline in the calculations of the equations of state of elemental crystals.

“Only in 2016 a multi-group effort was able to establish a baseline in the calculations of the equations of state of elemental crystals [6].”

The protocol introduced by Lejaeghere et al. in 2014 was recently exploited to compare 15 different DFT codes, including all-electron and PSP codes, to verify reproducibility of PBE equations of state of elemental crystals across methods and implementations.

“This protocol was recently exploited to compare 15 different DFT codes, including both all-electron and PSP codes, in order to verify the reproducibility of the PBE equations of state of elemental crystals across different methods and implementations [6].”

The reference all-electron equations of state used are WIEN2k results from Ref. [6], except for rare-earth nitrides which use WIEN2k results from Ref. [18].

“The reference all-electron results of the equation of states chosen in this work are the ones of the WIEN2k code [24] reported in Ref. [6], with the exception of the rare-earth nitrides for which we use the WIEN2k results reported in Ref. [18].”

More Δ-factor reference data has been produced in the literature for several PSP libraries and codes than for the Δ′-factor.

“In our protocol we adopt the ∆-factor (and not the ∆ ′ -factor), as much more ∆-factor reference data has been produced in the literature [6] for several PSP libraries and codes.”

The study is restricted to the PBE functional because it is among the most popular in the electronic structure community and the only functional for which a verified set of reference all-electron results for solids exists.

“Our study on the precision and efficiency of PSPs is restricted to the PBE functional as it is among the most popular ones in the electronic structure community and the only functional for which a verified set of reference all-electron results for solids exists [6].”

The SSSP efficiency and SSSP precision have small average Δ-factors of 0.44 meV and 0.33 meV, respectively, excluding the 15 rare-earth nitrides.

“The SSSP efficiency and SSSP precision have small average ∆-factors of 0.44 meV and 0.33 meV, respectively (where the average is performed over all elements tested excluding the 15 rare-earth nitrides, following the recipe of Ref. [6]).”

The Δ-factor test for verification can currently be performed only with the PBE functional.

“So the ∆-factor test for verification can be performed, at the moment, only with the PBE functional.”