Pseudo-potentials
Description of the pseudo-potentials (PSP) used in the GGA and GGA+U calculations.
Last updated
Description of the pseudo-potentials (PSP) used in the GGA and GGA+U calculations.
Last updated
On 2023-05-02, we changed the Yb PSP in all VASP input sets from Yb_2
to Yb_3
as Yb_2
gives incorrect thermodynamics for most systems with Yb3+. See pymatgen#2968 for details. We are also recomputing all Yb compounds in MP for an upcoming database release. The release notes will highlight this change.
Pseudopotentials are used to reduce computation time by replacing the full electron system in the Coulombic potential by a system only taking explicitly into account the "valence" electrons (i.e., the electrons participating into bonding) but in a pseudopotential. This approach not only reduces the electron number but also the energy cutoff necessary (this is critical in plane-wave-based computations). All computations in the materials project have been performed using a specific type of very efficient pseudopotentials: the projector augmented wave (PAW) pseudopotentials. [1] We used the library of PAW pseudopotentials provided by VASP but for a given element there are often several possibilities in the VASP library. This wiki presents how the choices between the different pseudopotential options were made.
As a test set, we ran all elements and binary oxides present in the ICSD with the available PAW pseudopotentials. As it is difficult to test for all properties (structural, electronic, etc...), we chose to be inclusive and to select the pseudopotential with the largest number of electrons (high e) except if convergence issues were seen on our test set, or if previous experience excluded a specific pseudopotential. We also excluded pseudopotentials with too large an energy cutoff.
We also compared to recommendations from the VASP manual present in 1.
Finally, as we had energies for elements and binary oxides, we compared binary oxide formation energies with the available pseudopotentials. The oxygen molecule energy was obtained from Wang et al. Please note that this data is pure GGA and some chemistries (e.g., transition metals) will give extremely bad formation energy results in GGA. This is not an issue with the pseudopotential but with the functional, so we do not focus on that issue in this wiki.
Usually, they have three pseudopotentials: a soft _s, a hard _h, and a standard. The standard is recommended by VASP and will be used for all. The hard ones have extremely high cut-offs (700 eV)
The table below indicates our choices. Basically, we chose all high e- pseudopotentials except for Na where we excluded Na_sv
due to its very high cutoff (700 eV).
element | options | VASP | Low elec: oxide form_enth (exp-comp) eV per fu | High elec: oxide form_enth (exp-comp) eV per fu | High e- conv. Stats | our choice | rem |
---|---|---|---|---|---|---|---|
The table below shows the details on the PSP choices. All high e- PSPs have been chosen except for Pd which had convergences problem with the high e- PSP in PdO.
Si, P, Cl, S will be used in their standard form (not hard) as suggested by VASP manual.
The Al_h
psp was found to be definitely wrong in terms of band structure. There were "ghost" states found in the DOS.
Pb is interesting as the high e- psp shows significantly higher error in formation energies. We kept the high e- psp (Pb_d
), but it might be interesting to study this a little more. One hypothesis relies on a recent result showing that lead oxide formation energies need the use of spin-orbit coupling to be accurate. [2] Our computations do not include any relativistic corrections for valence electrons. However, spin-orbit coupling is taken into account during the psp construction. This would explain why a psp with more core electrons (treated indirectly with spin-orbit coupling) would give more accurate results than a psp with fewer electrons.
Bi_d
shows a convergence problem, so the decision on Bi has been postponed to further analysis.
Finally, Po and At, while referred to in the VASP manual, are not present in the VASP PAW library.
These are probably the most problematic to use as pseudopotentials. Here is what the VASP manual says about them:
Due to self-interaction errors, f-electrons are not handled well by presently available density functionals. In particular, partially filled states are often incorrectly described, leading to large errors for Pr-Eu and Tb-Yb where the error increases in the middle (Gd is handled reasonably well, since 7 electrons occupy the majority shell). These errors are DFT and not VASP related. Particularly problematic is the description of the transition from an itinerant (band-like) behavior observed at the beginning of each period to localized states towards the end of the period. For the elements, this transition occurs already in La and Ce, whereas the transition sets in for Pu and Am for the elements. A routine way to cope with the inabilities of present DFT functionals to describe the localized electrons is to place the electrons in the core. Such potentials are available and described below. Furthermore, PAW potentials in which the states are treated as valence states are available, but these potentials are not expected to work reliable when the electrons are localized.
In summary, the pseudopotentials can either include or not include f electrons; how accurate including them or not is depends on the nature of the bonding for each particular system (localized or not).
What we found is that convergence issues are often seen for high electron psp (e.g., Pr, Nd, Sm). Also, some pseudopotentials (e.g., Er_2
, Eu_2
) freeze too many electrons and therefore have issues with oxidation states that make one of the frozen electron participate in bonding (e.g., Eu2O3, Er2O3). Finally, there is a major problem with Tb. Only Tb_3
exists but Tb is known to also form Tb4+ compounds (e.g., TbO2). For those Tb4+ compounds, this psp is likely to be extremely wrong. There is currently no fix for this except waiting for someone to develop a PAW Tb_4
psp.
U, Ac, Th, Pa, Np, Pu, Am
Following VASP suggestion, we decided to use the standard (and not the soft) version for all those pseudopotentials.
To cite the Materials Project, please reference the following work:
A. Jain, G. Hautier, C. J. Moore, S. P. Ong, C. C. Fischer, T. Mueller, K. A. Persson, and G. Ceder, A high-throughput infrastructure for density functional theory calculations, Computational Materials Science, vol. 50, 2011, pp. 2295-2310. DOI:10.1016/j.commatsci.2011.02.023
Geoffroy Hautier
[1]: P.E. Blöchl, Physical Review B 50, 17953-17979 (1994).
[2]: R. Ahuja, A. Blomqvist, P. Larsson, P. Pyykkö, and P. Zaleski-Ejgierd, Physical Review Letters 106, 1-4 (2011).
element | options | VASP | Low elec: oxide form_enth (exp-comp) eV per fu | High elec: oxide form_enth (exp-comp) eV per fu | High e- conv. Stats | our choice | rem |
---|---|---|---|---|---|---|---|
element | options | VASP | Low elec: oxide form_enth (exp-comp) eV per fu | High elec: oxide form_enth (exp-comp) eV per fu | High e- conv. Stats | our choice | rem |
---|---|---|---|---|---|---|---|
element | options | VASP | Low elec: oxide form_enth (exp-comp) eV per fu | High elec: oxide form_enth (exp-comp) eV per fu | High e- conv. Stats | our choice | rem |
---|---|---|---|---|---|---|---|