Pseudopotentials
Desciption of the density functional theory (DFT) pseudopotentials used in the Materials Project (MP) database.
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.

The strategy

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 (psp) 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.

Pseudopotential comments and choice

1st row elements

B, C, N, O, F\text{B, C, N, O, F}
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 have extremely high cut-offs (700 eV)

alkali and alkali-earth

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
Li
Li, Li_sv
Li_sv
0.03
0.01
all converged
Li_sv
highest e- psp chosen
Na
Na, Na_sv, Na_pv
Na_pv
0.06
0.01
all converged
Na_pv
Na_sv is extremely high in cutoff (700 eV) for marginal gain in accuracy on Na2O
K
K_pv, K_sv
K_sv
0.01
0.01
80% conv for both
K_sv
highest e- psp chosen
Cs
Cs_sv
Cs_sv
Cs_sv
Rb
Rb_pv, Rb_sv
Rb_sv
0.05
0.03
all converged
Rb_sv
highest e- psp chosen
Be
Be, Be_sv
Be
0.04
0.04
all converged
Be_sv
highest e- psp chosen
Mg
Mg, Mg_pv
Mg_pv
0.02
0.05
all converged
Mg_pv
VASP and thermo suggest Mg as they are not much different; we decided to stick with the high e- psp.
Ca
Ca_sv, Ca_pv
Ca_pv
0.06
0.03
all converged
Ca_sv
highest e- psp chosen
Sr
Sr_sv
Sr_sv
Sr_sv
Ba
Ba_sv
Ba_sv
Ba_sv

d-elements, transition metals

The table below shows the details on the psp choices. All high e- psp have been chosen except for Pd which had convergences problem with the high e- psp in PdO.
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
Sc
Sc_sv
Sc_sv
Sc_sv
Y
Y_sv
Y_sv
Y_sv
Ti
Ti, Ti_pv, Ti_sv
Ti_pv
0.13
0.23
metal conv pb with Ti and Ti_sv
Ti_pv
highest e- psp with best conv. chosen
Zr
Zr, Zr_sv
Zr_sv
0.06
0.03
all converged
Zr_sv
highest e- psp chosen
Hf
Hf, Hf_pv
Hf_pv
0.19
0.18
all converged
Hf_pv
highest e- psp chosen
V
V, V_pv, V_sv
V_pv
0.39
0.46
all converged
V_sv
highest e- psp chosen
Nb
Nb_pv
Nb_pv
Nb_pv
Ta
Ta, Ta_pv
Ta_pv
0.3
0.31
similar conv. for both
Ta_pv
highest e- psp chosen
Cr
Cr, Cr_pv
Cr_pv
0.53
0.6
all converged
Cr_pv
highest e- psp chosen
Mo
Mo, Mo_pv
Mo_pv
0.39
0.45
all converged
Mo_pv
highest e- psp chosen
W
W, W_pv
W_pv
0.47
0.48
all converged
W_pv
highest e- psp chosen
Mn
Mn, Mn_pv
Mn or Mn_pv (!)
0.29
0.31
all converged
Mn_pv
highest e- psp chosen
Tc
Tc, Tc_pv
Tc or Tc_pv
all converged (no metals BTW)
Tc_pv
highest e- psp chosen
Re
Re, Re_pv
Re
0.56
0.59
all converged
Re_pv
highest e- psp chosen
Fe
Fe, Fe_pv
Fe_pv
0.62
0.47
50% conv. on oxides for both psp
Fe_pv
highest e- psp chosen
Co
Co
Co
Co
Ni
Ni, Ni_pv
Ni
0.4
0.4
all converged
Ni_pv
highest e- psp chosen
Cu
Cu, Cu_pv
Cu
0.07
0.1
all converged
Cu_pv
highest e- psp chosen
Zn
Zn
Zn
Zn
Ru
Ru, Ru_pv
Ru
0.41
0.41
all converged
Ru_pv
highest e- psp chosen
Rh
Rh, Rh_pv
Rh
0.36
0.35
all converged
Rh_pv
highest e- psp chosen
Pd
Pd, Pd_pv
Pd
0.2
0.2
Pd_pv has one unconv. PdO
Pd
due to the conv. issue we chose Pd (recommended by VASP too).
Ag
Ag
Ag
Cd
Cd
Cd
Hg
Hg
Hg
Au
Au
Au
Ir
Ir
Ir
Pt
Pt
Pt
Pt
Os
Os, Os_pv
Os_pv
0.67
0.7
all converged
Os_pv
highest e- psp chosen

main group

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.
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
Ga
Ga, Ga_d, Ga_h
Ga_d
0.05
0.01
all converged
Ga_d
Ga_h seems best (0.01 instead of 0.02) but same problem as Al_h?
Ge
Ge, Ge_d, Ge_h
Ge_d
0.06
0.06
all converged
Ge_d
Ge_h seems best (Ge_h and Ge_d similar though) but same problem as Al_h ?
Al
Al, Al_h
Al
0.03
0.01
all converged
Al
Good energetics but pb in band structure
As
As
Se
Se
Br
Br
In
In, In_d
In_d
0.13
0.1
all converged
In_d
highest e- psp chosen
Sn
S, Sn_d
Sn_d
0.16
0.12
all converged
Sn_d
highest e- psp chosen
Tl
Tl, Tl_d
Tl_d
0.26
0.31
all converged
Tl_d
highest e- psp chosen
Pb
Pb, Pb_d
Pb_d
0.17
0.36
all converged
Pb_d
highest e- psp chosen
Bi
Bi, Bi_d
Bi_d
convergence pb
?
Po
Po, Po_d
Po
no Po psp is available in the PAW library!
At
At, At_d
At_d
no At psp is available in the PAW library

rare-earth, f-electrons

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 not much fix to this for now except waiting for someone to develop a PAW Tb_4 psp.
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
La
La, La_s
La
0.12
0.17
all converged
La
La_s means soft
Ce
Ce_3, Ce
/
1.18
0.26
all converged
Ce
thermo data on CeO2 is terrible with Ce_3, cf Ce4+ thermo data on Ce2O3 is similar with both
Pr
Pr_3, Pr
/
0.00
0.09
Pr metal did not converge
Pr_3
Pr_3 better oxide thermo (surprisingly good!) and convergence in metal.
Nd
Nd_3, Nd
/
0.04
0.01
Nd metal conv. problem
Nd_3
convergence pb
Pm
Pm_3, Pm
/
/
/
Pm_3
no real data to compare, it is between Nd and Sm in the periodic table, so we decided to pick a _3 as Nd and Sm
Sm
Sm_3, Sm
/
0.1
/
Sm metal conv. pb
Sm_3
conv pb
Eu
Eu_2, Eu
/
0.68
0.25
all converged
Eu
Both EuO and Eu2O3 thermo worse with Eu_2
Gd
Gd_3, Gd
/
0.2
0.12
all converged
Gd
Gd has better thermo and highest e-
Tb
Tb_3
/
all converged
Tb_3
There is a major pb with Tb. It can 4+ and we have only a 3+ psps
Dy
Dy_3
/
all converged
Dy_3
Ho
Ho_3
/
Ho_3
Er
Er_2, Er_3
/
1.16
0.15
all converged
Er_3
thermo data on Er2O3 off with Er_2
Tm
Tm, Tm_3
/
0.2
?
could not converge any metal with Tm
Tm_3
Yb
Yb_2, Yb
/
1.03
0.59
all converged
Yb
thermo data off with Yb_2
Lu
Lu_3, Lu
/
0.43
?
Lu could not be converged
Lu_3

transuranides, f-electrons

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.

Citation

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

Authors

  1. 1.
    Geoffroy Hautier

References

[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).
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The strategy
Pseudopotential comments and choice
1st row elements
alkali and alkali-earth
d-elements, transition metals
main group
rare-earth, f-electrons
transuranides, f-electrons
Citation
Authors
References