Choosing pseudopotentials

For many elements several pseudopotential choices exist. The usual tradeoff between computational cost and accuracy and transferability applies. The choice of pseudopotential variant is not always straight forward. For the PBE generated latest PAW potential set (potpaw_PBE) we provide some recommendations for calculations involving a significant number of states far above the Fermi energy, and for those that are mainly evolved with states below or around the Fermi level.

Step-by-step instructions

Step 1: Select a pseudopotential release.

Generally we recommend to use the latest release of pseudopotentials (currently potpaw.64), but for consistency reasons or to accurately reproduce another calculation, you might need to use another release. Please consult the Construction:Lists_of_pseudopotentials for a list of all available potentials.

Step 2: Analyze your structure.

Your pseudopotential choice depends on the type of structure you have and the species it contains. Not all variants are available for all elements. E.g. there are no _GW potentials for the lanthanides. Bond lengths are also critical.

Step 3: Be sure what you want to calculate.

If you are interested in a quick and rough structure optimization only, soft potentials with minimal valency may be sufficient. The same can be true for phonon calculations, which often require very large supercells. However, when carefully optimizing a magnetic structure, it might be necessary to include a lot of semicore states in the valence, and optical properties should be calculated with potentials that are optimized for the description of empty states.

Step 4: Check if your calculation method involves a significant number of unoccupied states, you are doing Hartree-Fock, or switch the exchange-correlation functional.

For any calculation involving unoccupied states significantly above the Fermi energy, the _GW variants of potentials are superior and should be used. This is especially true for all kinds of many-body perturbation calculations which need a high number of empty bands. Hartree-Fock and hybrid caluclations should not be performed with soft potentials, as should be any calculations where you switch the exchange-correlation functional. However, for "plain" DFT-ground-state calculations it is usually not necessary to use _GW or _h potentials unless a specific reason exists.

Step 5: Test your setup.

Even if you have taken a lot of care to optimize your pseudopotential choice, it is always good to perform some test calculations with other potentials, if necessary on a small prototype system. You might realize that you need extra accuracy, or that you are leaving performance on the table by using unnecessarily hard POTCARs for your problem.

Recommendations and advice

Hydrogen-like atoms with fractional valence

Twelve hydrogen-like potentials are supplied for a valency between 0.25 and 1.75. (Further potentials might become available, please check Construction:List_of_pseudopotentials.). These are useful to e.g. passivate dangling surface bonds.

Mind: The POTCAR files restricts the number of digits for the valency (typically 2, at most 3 digits). Therefor, using three H.33 potentials does not yield 0.99 electrons and not 1.00 electron. This can cause hole- or electron-like states that are undesirable. Set the NELECT tag in the INCAR file to correct the total number of electrons.

First row elements

For the 1st row elements B, C, N, O, and F, three potential versions exist, the plain one, a hard version, and a soft version. For most purposes, the standard version of PAW potentials is most appropriate. They yield reliable results for energy cutoffs between 325 and 400 eV, where 370-400 eV are required to predict vibrational properties accurately. Binding geometries and energy differences are already well reproduced at 325 eV. The typical bond-length errors for first row dimers (N₂, CO, O₂) are about 1% compared to more accurate DFT calculations. The hard pseudopotentials _h give results that are essentially identical to the best DFT calculations presently available (FLAPW, or Gaussian with very large basis sets). The soft potentials are optimized to work around 250-280 eV. They yield reliable description for most oxides, such as V_xO_y, TiO₂, CeO₂, but fail to describe some structural details in zeolites, i.e., cell parameters, and volume.

For Hartree-Fock (HF) and hybrid functional calculations, we strictly recommend using the standard, standard GW, or hard potentials. For instance, the O_s potential can cause unacceptably large errors even in transition metal oxides. Generally, the soft potentials are less transferable from one exchange-correlation functional to another and often fail when the exact exchange needs to be calculated.

Tip: If dimers with short bonds are present in the system (O2, CO, N2, F2, P2, S2, Cl2), we recommend to use the _h potentials. Specifically, C_h, O_h, N_h, F_h, P_h, S_h, Cl_h, or their _GW counterparts. Otherwise the standard version is often the best choice for first row elements.

Alkali and alkali-earth elements (simple metals)

For Li (and Be), a standard potential and a potential that treats the $1s$ shell as valence states are available (Li_sv, Be_sv). One should use the _sv potentials for many applications since their transferability is much higher than the standard potentials.

For the other alkali and alkali-earth elements, the semi-core $s$ and $p$ states should be treated as valence states as well. For lighter elements (Na-Ca) it is usually sufficient to treat the $2p$ and $3p$ states as valence states (_pv), respectively. For Rb-Sr the $4s$, $4p$, and $5s$, $5p$ states, respectively, must be treated as valence states (_sv). The standard potentials are listed below. The default energy cutoffs are specified as well but might vary from one release to the other.

Tip: For alkali and alkaline earth metals, the _sv variants should be chosen, other than for very light elements Na, Mg, K, and Ca, where _pv is usually sufficient

p-elements

For Ga, Ge, In, Sn, Tl-At, the lower-lying $d$ states should be treated as valence states (_d potential). For these elements, alternative potentials that treat the $d$ states as core states are also available but should be used with great care.

d-elements

For the $d$ elements the same as for the as for the alkali and earth-alkali metals applies: the semi-core $p$ states and possibly the semi-core $s$ states should be treated as valence states. In most cases, however, reliable results can be obtained even if the semi-core states are kept frozen.

When to switch from X_pv potentials to the X potentials depends on the required accuracy and the row for the $3d$ elements, even the Ti, V, and Cr potentials give reasonable results but should be used with uttermost care. $4d$ elements are most problematic, and we advice to use the X_pv potentials up to Tc_pv. For $5d$ elements the $5p$ states are rather strongly localized (below 3 Ry), since the $4f$ shell becomes filled. One can use the standard potentials starting from Hf, but we recommend performing test calculations. For some elements, X_sv potentials are available (e.g. Nb_sv, Mo_sv, Hf_sv). These potentials usually have very similar energy cutoffs as the _pv potentials and can also be used. For HF-type and hybrid functional calculations, we strongly recommend using the _sv and _pv potentials whenever possible.

Tip: As a rule of thumb the $p$ states should be treated as valence states for d-elements, if their eigenenergy $\epsilon$ lies above 3 Ry.

f-elements

Due to self-interaction errors, $f$ electrons are not handled well by the presently available density functionals. In particular, partially filled $f$ states are often incorrectly described. For instance, all $f$ states are pinned at the Fermi-level, leading to large overbinding for Pr-Eu and Tb-Yb. The errors are largest at quarter, and three-quarter filling, e.g., Gd is handled reasonably well since 7 electrons occupy the majority $f$ 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 $4f$ elements, this transition occurs already in La and Ce, whereas the transition sets in for Pu and Am for the $5f$ elements. A routine way to cope with the inabilities of present DFT functionals to describe the localized $4f$ electrons is to place the $4f$ electrons in the core. Such potentials are available and described below; however, they are expected to fail to describe magnetic properties arising $f$ orbitals. Furthermore, PAW potentials in which the $f$ states are treated as valence states are available, but these potentials are expected to fail to describe electronic properties when $f$ electrons are localized. In this case, one might treat electronic correlation effects more carefully, e.g., by employing hybrid functionals or introduce on-site Coulomb interaction.

For some elements, soft versions (_s) are available as well. The semi-core $p$ states are always treated as valence states, whereas the semi-core $s$ states are treated as valence states only in the standard potentials. For most applications (oxides, sulfides), the standard version should be used since the soft versions might result in $s$ ghost-states close to the Fermi-level (e.g., Ce_s in ceria). For calculations on intermetallic compounds, the soft versions are, however, expected to be sufficiently accurate.

Lanthanides with fixed valence

In addition, special GGA potentials are supplied for Ce-Lu, in which $f$ electrons are kept frozen in the core, which is an attempt to treat the localized nature of $f$ electrons. The number of f electrons in the core equals the total number of valence electrons minus the formal valency. For instance: According to the periodic table, Sm has a total of 8 valence electrons, i.e., 6 $f$ electrons and 2 $s$ electrons. In most compounds, Sm adopts a valency of 3; hence 5 $f$ electrons are placed in the core when the pseudopotential is generated. The corresponding potential can be found in the directory Sm_3. The formal valency n is indicted by _n, where n is either 3 or 2. Ce_3 is, for instance, a Ce potential for trivalent Ce (for tetravalent Ce, the standard potential should be used).

Warning: f-elements are notoriously hard to describe with DFT due to self-interaction errors in the strongly localized orbitals. Placing some, or all, $4f$ electrons in the core can rectify this issue, but then the description of magnetism will fail.

Tip: If you are not interested in $4f$-magnetism, and know the valency of your lanthanide, use the _2 or _3 potentials.