Available PAW potentials: Difference between revisions

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Revision as of 11:08, 12 February 2021

PAW potentials for all elements in the periodic table are available. With the exception of the 1st row elements, all PAW potentials were generated to work reliably and accurately at an energy cutoff of roughly 250 eV (the default energy cutoff is read as ENMAX in the POTCAR file). The distributed PAW potentials have been generated by G. Kresse following the recipes discussed in [1], whereas the PAW method has been first suggested and used by Peter Blöchl [2]. If you use any of the supplied PAW potentials you should include these two references.

Generally the PAW potentials are more accurate than ultra-soft pseudopotentials (US-PP). There are two reasons for this: first, the radial cutoffs (core radii) are smaller than the radii used for US pseudopotentials, and second the PAW potentials reconstruct the exact valence wavefunction with all nodes in the core region. Since the core radii of the PAW potentials are smaller, the required energy cutoffs and basis sets are also somewhat larger. If such a high precision is not required, the older US-PP can be used. In practice, however, the increase in the basis set size will be usually small, since the energy cutoffs have not changed appreciably for C, N and O, so that calculations for model structures that include any of these elements are not more expensive with PAW than with US-PP.

For some elements several PAW versions exist. The standard version has generally no extension. An extension _h implies that the potential is harder than the standard potential and hence requires a greater energy cutoff. The extension _s means that the potential is softer than the standard version. The extensions _pv and _sv imply that the and semi-core states are treated as valence states (i.e. for V_pv the states are treated as valence states, and for V_sv the and states are treated as valence states). PAW files with an extension _d, treat the semi core states as valence states (for Ga_d the states are treated as valence states).

In the following we will present the available PAW potentials. All distributed potentials have been tested using standard DFT-"benchmark" runs (see the data_base file in the released tar files). We strongly recommend to use the potentials only in VASP.5.4 or higher.

Recommended potentials are always reported in bold face.

The corresponding distribution directory of the potential is created by adding underscores between the elemental name and the extensions "_", e.g Li sv becomes Li_sv. All reported potentials are for PBE calculations. The reported cutoffs might differ slightly for LDA potentials.

Recommended potentials for DFT calculations

The following table lists the standard PAW potentials for VASP.

Important Note: If dimers with short bonds are present in the compound (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.

Element (and appendix) default cutoff ENMAX (eV) valency
H 250 1
H AE 1000 1
H h 700 1
H s 200 1
He 479 2
Li 140 1
Li sv 499 3
Be 248 2
Be sv 309 4
B 319 3
B h 700 3
B s 269 3
C 400 4
C h 700 4
C s 274 4
N 400 5
N h 700 5
N s 280 5
O 400 6
O h 700 6
O s 283 6
F 400 7
F h 700 7
F s 290 7
Ne 344 8
Na 102 1
Na pv 260 7
Na sv 646 9
Mg 200 2
Mg pv 404 8
Mg sv 495 10
Al 240 3
Si 245 4
P 255 5
P h 390 5
S 259 6
S h 402 6
Cl 262 7
Cl h 409 7
Ar 266 8
K pv 117 7
K sv 259 9
Ca pv 120 8
Ca sv 267 10
Sc 155 3
Sc sv 223 11
Ti 178 4
Ti pv 222 10
Ti sv 275 12
V 193 5
V pv 264 11
V sv 264 13
Cr 227 6
Cr pv 266 12
Cr sv 395 14
Mn 270 7
Mn pv 270 13
Mn sv 387 15
Fe 268 8
Fe pv 293 14
Fe sv 391 16
Co 268 9
Co pv 271 15
Co sv 390 17
Ni 270 10
Ni pv 368 16
Cu 295 11
Cu pv 369 17
Zn 277 12
Ga 135 3
Ga d 283 13
Ga h 405 13
Ge 174 4
Ge d 310 14
Ge h 410 14
As 209 5
As d 289 15
Se 212 6
Br 216 7
Kr 185 8
Rb pv 122 7
Rb sv 220 9
Sr sv 229 10
Y sv 203 11
Zr sv 230 12
Nb pv 209 11
Nb sv 293 13
Mo 225 6
Mo pv 225 12
Mo sv 243 14
Tc 229 7
Tc pv 264 13
Tc sv 319 15
Ru 213 8
Ru pv 240 14
Ru sv 319 16
Rh 229 9
Rh pv 247 15
Pd 251 10
Pd pv 251 16
Ag 250 11
Ag pv 298 17
Cd 274 12
In 96 3
In d 239 13
Sn 103 4
Sn d 241 14
Sb 172 5
Te 175 6
I 176 7
Xe 153 8
Cs sv 220 9
Ba sv 187 10
La 219 11
La s 137 9
Ce 273 12
Ce h 300 12
Ce 3 177 11
Pr 273 13
Pr 3 182 11
Nd 253 14
Nd 3 183 11
Pm 259 15
Pm 3 177 11
Sm 258 16
Sm 3 177 11
Eu 250 17
Eu 2 99 8
Eu 3 129 9
Gd 256 18
Gd 3 154 9
Tb 265 19
Tb 3 156 9
Dy 255 20
Dy 3 156 9
Ho 257 21
Ho 3 154 9
Er 2 120 8
Er 3 155 9
Er 298 22
Tm 257 23
Tm 3 149 9
Yb 253 24
Yb 2 113 8
Lu 256 25
Lu 3 155 9
Hf 220 4
Hf pv 220 10
Hf sv 237 12
Ta 224 5
Ta pv 224 11
W 223 6
W pv 223 12
Re 226 7
Re pv 226 13
Os 228 8
Os pv 228 14
Ir 211 9
Pt 230 10
Pt pv 295 16
Au 230 11
Hg 233 12
Tl 90 3
Tl d 237 13
Pb 98 4
Pb d 238 14
Bi 105 5
Bi d 243 15
Po 160 6
Po d 265 16
At 161 7
At d 266 17
Rn 152 8
Fr sv 215 9
Ra sv 237 10
Ac 172 11
Th 247 12
Th s 169 10
Pa 252 13
Pa s 193 11
U 253 14
U s 209 14
Np 254 15
Np s 208 15
Pu 254 16
Pu s 208 16
Am 256 17
Cm 258 18

Hydrogen like potentials are supplied for a valency between 0.25 and 1.75 as listed in the table below:

Element (and appendix) default cutoff ENMAX (eV) valency
H .25 250 0.2500
H .33 250 0.3300
H .42 250 0.4200
H .5 250 0.5000
H .58 250 0.5800
H .66 250 0.6600
H .75 250 0.7500
H 1.25 250 1.2500
H 1.33 250 1.3300
H 1.5 250 1.5000
H 1.66 250 1.6600
H 1.75 250 1.7500

Recommended potentials for GW/RPA calculations

The available GW potentials are listed in the Table below. As documented in the data_base file released with the PAW potentials, for density functional calculations, the GW potentials yield virtually identical results as the standard potentials, and it is safe to assume that one can use the GW potentials instead of standard LDA/GGA potentials for groundstate calculations without deteriorating the results. In fact, we believe the GW potentials are generally at least as good as the DFT standard potentials, but might be much better for excited state properties.

In general, the GW potentials yield much better scattering properties at high energies well above the Fermi-level (typically up to 10-20 Ry above the vacuum level). This is believed to be important for GW and RPA calculations.

Important Note: If dimers with short bonds are present in the compound (O2, CO, N2, F2, P2, S2, Cl2), we recommend to use the _h potentials. Specifically, C_GW_h, O_GW_h, N_GW_h, F_GW_h.

Element (and appendix) default cutoff ENMAX (eV) valency
H GW 300 1
H h GW 700 1
He GW 405 2
Li sv GW 434 3
Li GW 112 1
Li AE GW 434 3
Be sv GW 537 4
Be GW 248 2
B GW 319 3
C GW 414 4
C GW new 414 4
C h GW 741 4
N GW 421 5
N GW new 421 5
N h GW 755 5
N s GW 296 5
O GW 415 6
O GW new 434 6
O h GW 765 6
O s GW 335 6
F GW 488 7
F GW new 488 7
F h GW 848 7
Ne GW 432 8
Ne s GW 318 8
Na sv GW 372 9
Mg sv GW 430 10
Mg GW 126 2
Mg pv GW 404 8
Al GW 240 3
Al sv GW 411 11
Si GW 245 4
Si GW new 245 4
Si sv GW 548 12
P GW 255 5
S GW 259 6
Cl GW 262 7
Ar GW 290 8
K sv GW 249 9
Ca sv GW 281 10
Sc sv GW 378 11
Ti sv GW 383 12
V sv GW 382 13
Cr sv GW 384 14
Mn sv GW 384 15
Mn GW 278 7
Fe sv GW 387 16
Fe GW 321 8
Co sv GW 387 17
Co GW 323 9
Ni sv GW 389 18
Ni GW 357 10
Cu sv GW 467 19
Cu GW 417 11
Zn sv GW 401 20
Zn GW 328 12
Ga d GW 404 13
Ga GW 135 3
Ga sv GW 404 21
Ge d GW 375 14
Ge sv GW 410 22
Ge GW 174 4
As GW 209 5
As sv GW 415 23
Se GW 212 6
Se sv GW 469 24
Br GW 216 7
Br sv GW 475 25
Kr GW 252 8
Rb sv GW 221 9
Sr sv GW 225 10
Y sv GW 339 11
Zr sv GW 346 12
Nb sv GW 353 13
Mo sv GW 344 14
Tc sv GW 351 15
Ru sv GW 348 16
Rh sv GW 351 17
Rh GW 247 9
Pd sv GW 356 18
Pd GW 251 10
Ag sv GW 354 19
Ag GW 250 11
Cd sv GW 361 20
Cd GW 254 12
In d GW 279 13
In sv GW 366 21
Sn d GW 260 14
Sn sv GW 368 22
Sb d GW 263 15
Sb sv GW 372 23
Sb GW 172 5
Te GW 175 6
Te sv GW 376 24
I GW 176 7
I sv GW 381 25
Xe GW 180 8
Xe sv GW 400 26
Cs sv GW 198 9
Ba sv GW 238 10
La GW 313 11
Ce GW 305 12
Hf sv GW 283 12
Ta sv GW 286 13
W sv GW 317 14
Re sv GW 317 15
Os sv GW 320 16
Ir sv GW 320 17
Pt sv GW 324 18
Pt GW 249 10
Au sv GW 306 19
Au GW 248 11
Hg sv GW 312 20
Tl d GW 237 15
Tl sv GW 316 21
Pb d GW 238 16
Pb sv GW 317 22
Bi d GW 261 17
Bi GW 147 5
Bi sv GW 323 23
Po d GW 267 18
Po sv GW 326 24
At d GW 266 17
At sv GW 328 25
Rn d GW 268 18
Rn sv GW 331 26

Further recommendations for the potentials

In the following we further explanation the potentials for very important element groups.

1st row elements

Element (and appendix) default cutoff ENMAX (eV)
B 318 3
B_h 700 3
B_s 250 3
C 400 4
C_h 700 4
C_s 273 4
N 400 5
N_h 700 5
N_s 250 5
O 400 6
O_h 700 6
O_s 250 6
F 400 7
F_h 700 7
F_s 250 7
Ne 343 8

For the 1st row elements three PAW versions exist. For most purposes the standard versions should be used. They yield reliable results for cutoffs between 325 and 400 eV, where 370-400 eV are required to accurately predict vibrational properties, but binding geometries and energy differences are 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, not experiment). The hard pseudopotentials _h give results that are essentially identical to the best DFT calculations presently available (FLAPW, or Gaussian with huge basis sets). The soft potentials are optimised to work around 250-280 eV. They yield very reliable description for most oxides, such as VxOy, TiO2, CeO2, but fail to describe some structural details in zeolites (i.e. cell parameters, and volume).

For HF and hybrid tpye calculations, we strictly recommend the use of the standard, standard GW, or of the hard potentials. For instance, the O_s potential can cause unacceptably large error even in transition metal oxides, even though the potential works reliable at the PBE level.

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). For many applications one should use the _sv potential since their transferability is much improved compared to 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 the 2p and 3p states, respectively, as valence states (_pv), whereas for Rb-Sr the 4s, 4p and 5s, 5p states, respectively, must be treated as valence states (_sv). The standard potentials are listed below (default energy cutoffs are specified as well but might vary from one release to the other):

Element (and appendix) default cutoff ENMAX (eV) valency
H 250 1
H_h 700 1
Li 140 1
Li_sv 500 3
Na 100 1
Na_pv 260 7
Na_sv 700 9
K_pv 120 7
K_sv 260 9
Rb_pv 120 7
Rb_sv 220 9
Cs_sv 220 9
Be 300 2
Be_sv 308 4
Mg 210 2
Mg_pv 400 8
Mg_sv 495 10
Ca_pv 120 8
Ca_sv 270 10
Sr_sv 230 10
Ba_sv 190 10


Contrary to the common believe, these elements are exceedingly difficult to pseudize in particular in combination with strongly electronegative elements (F) errors can be larger then usual. The present potentials are very precise, and should offer a very reliable description. For X_pv potentials the semicore p states are treated as valence (2p in Na and Mg, 3p in K and Ca etc.). For X_sv potentials, the semicore s states are treated as valence (1s in Li and Be, 2s in Na etc.)

d-elements

The same applies to d-elements as for the alkali and earth-alkali metals: 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. As a rule of thumb the p states should be treated as valence states, if their eigenenergy lies above 3 Ry.

Element (and appendix) default cutoff ENMAX (eV) valency
Sc 154 3
Sc_sv 222 11
Fe 267 8
Fe_pv 293 14
Fe_sv 390 16
Y_sv 203 11
Ru 213 8
Ru_pv 240 14
Ru_sv 319 16
Os 228 8
Os_pv 228 14
Ti 178 4
Ti_pv 222 10
Ti_sv 274 12
Co 267 9
Co_pv 271 15
Co_sv 390 17
Zr_sv 229 12
Rh 228 9
Rh_pv 250 15
Hf 220 4
Hf_pv 220 10
Ir 210 9
V 192 5
V_pv 263 11
V_sv 263 13
Ni 269 10
Ni_pv 367 16
Nb_pv 207 11
Nb_sv 293 13
Pd 250 10
Pd_pv 250 16
Ta 223 5
Ta_pv 223 11
Pt 230 10
Pt_pv 294 16
Cr 227 6
Cr_pv 265 12
Cr_sv 395 14
Cu 290 11
Cu_pv 368 17
Mo 224 6
Mo_pv 224 12
Mo_sv 242 14
Ag 249 11
Ag_pv 298 17
W 223 6
W_pv 223 12
Au 229 11
Mn 269 7
Mn_pv 269 13
Mn_sv 387 15
Zn 276 12
Tc 228 7
Tc_pv 263 13
Tc_sv 318 15
Cd 274 12
Re 226 7
Re_pv 226 13
Hg 233 12


For X_pv potentials, the semi core p states are treated as valence, whereas for X_sv pseudopotentials, the semi core s states are treated as valence. X_pv potentials are required for early transition metals, but one can freeze the semi-core p states for late transition metals (in particular noble metals).

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 I 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 to perform test calculations. For some elements, X_sv potential are available (e.g. Nb_sv, Mo_sv, Hf_sv). These potential usually have very similar cutoffs as the _pv potentials, and can be used as well. For HF type and hybrid functional calculations, we strongly recommend the use of the _sv and _pv potentials whenever possible.

p-elements including first row

Element (and appendix) default cutoff ENMAX (eV) valency
B_h 700 3
B 318 3
B_s 250 3
Al 240 3
Ga 134 3
Ga_d 282 13
Ga_h 404 13
In 95 3
In_d 239 13
Tl 90 3
Tl_d 237 13
C_h 700 4
C 400 4
C_s 273 4
Si 245 4
Ge 173 4
Ge_d 310 14
Ge_h 410 14
Sn 103 4
Sn_d 241 14
Pb 97 4
Pb_d 237 14
N_h 700 5
N 400 5
N_s 250 5
P 260 5
P_h 390 5
As 208 5
As d 289 15
Sb 172 5
Bi 105 5
Bi_d 242 15
O_h 700 6
O 400 6
O_s 250 6
S 260 6
S_h 402 6
Se 211 6
Te 174 6
Po 159 6
Po_d 264 16
F_h 700 7
F 400 7
F_s 250 7
Cl 260 7
Cl_h 409 7
Br 216 7
I 175 7
At 161 7
At_d 266 17
Ne 343 8
Ar 266 8
Kr 185 8
Xe 153 8
Rn 152 8

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

f-elements

Due to self-interaction errors, f-electrons are not handled well by presently available density functionals. In particular, partially filled f 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 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. Furthermore, PAW potentials in which the f states are treated as valence states are available, but these potentials are not expected to work reliable when the f electrons are localized. Expertise using hybrid functionals or an LDA+U like treatment are not particularly large, but hybrid functionals should improve the description, if the f electrons are localized, although the most likely fail of the f electrons for band-like (itinerant) states.

Element (and appendix) default cutoff ENMAX (eV)
La 219
Ac 172
Ce 273
Tb 264
Th 247
Th_s 169
Pr 272
Dy 255
Pa 252
Pa_s 193
Nd 253
Ho 257
U 252
U_s 209
Pm 258
Er 298
Np 254
Np_s 207
Sm 257
Tm 257
Pu 254
Pu_s 207
Eu 249
Yb 253
Am 255
Gd 256
Lu 255

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 ghoststates close to the Fermi-level (e.g. Ce_s in ceria). For calculations on inter-metallic compounds the soft versions are, however, sufficiently accurate.

In addition, special GGA potential are supplied for Ce-Lu, in which f electrons are kept frozen in the core (standard model for the treatment of localised 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 (6f electrons and 2s electrons). In most compounds Sm, however, adopts a valency of 3, hence 5f 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).

Element (and appendix) default cutoff ENMAX (eV)
Ce_3 176
Tb_3 155
Pr_3 181
Dy_3 155
Nd_3 182
Ho_3 154
Pm_3 176
Er_3 155
Er_2 119
Sm_3 177
Tm_3 149
Eu_3 129
Eu_2 99
Yb_2 113
Gd_3 154
Lu_3 154

References