Pseudopotentials Choice

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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 is often several possibility in the VASP library. This wiki presents how the choice between the different pseudopotential option was operated detailing what pseudopotential we chose and for what reason.


The strategy

As a test set, we ran all elements and binary oxides present in the ICSD with the several PAW pseudopotentials available. 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 EXCEPT if convergence issues were seen on our test set, or previous experience excluded a specific pseudopotential. We also excluded pseudopotentials with a too large 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 oxides formation energies with the several pseudopotentials available. 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 per se with the pseudopotential but with the functional and we did not focus on this in this wiki.

Pseudopotential comments and choice

1st row elements

B, C, N, O, F

Usually they have three psp 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- psp 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 was "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 are without 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 undirectly with SO coupling) would give more accurate results than a psp with fewer electrons.

Bi_d shows convergence problem and 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

Those are probably the more problematic to use as pseudopotentials. Here is what the VASP manual says about them:

"Due to self-interaction errors, -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."

Please note that basically what it says is that the pseudopotentials can include or not f electrons and how accurate you would be by including them or not will depend on the nature of the bonding (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 somehow too many electron and 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+ 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.

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).

Authors

  1. Geoffroy Hautier