Pseudo-potentials

Description of the pseudo-potentials (PSP) used in the GGA and GGA+U calculations.

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.

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 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

$\text{B, C, N, O, F}$

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 ones 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- PSPs 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_pv	balance of high e-psp and compute cost
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 currently no fix for this 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_3, Yb_2, Yb	/	1.03	0.59	all converged	Yb_3	thermo data off with Yb_2 and Yb has convergence issues
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. 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).