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Hi admins,

I would like to ask about this wiki: https://www.vasp.at/wiki/index.php/Avai ... 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.

firstly, are there detailed reference paper/ citable source for the above comment?

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.

Following this comment, there's this table in the wiki.
However, if I read the Ce POTCAR file correctly, for example, one 4f electron is treated as valence electron. So the 4f electron is not placed in the core in this POTCAR file, isn't it?

Element (and appendix) default cutoff ENMAX (eV) valency
La 219 11
Ac 172 11
Ce 273 12
....

PAW_PBE Ce 23Dec2003
12.0000000000000
parameters from PSCTR are:
VRHFIN =Ce : [core= Kr 4d10]
LEXCH = PE
EATOM = 1063.0861 eV, 78.1346 Ry

TITEL = PAW_PBE Ce 23Dec2003
LULTRA = F use ultrasoft PP ?
IUNSCR = 1 unscreen: 0-lin 1-nonlin 2-no
RPACOR = 1.800 partial core radius
POMASS = 140.115; ZVAL = 12.000 mass and valenz
RCORE = 2.700 outmost cutoff radius
RWIGS = 2.500; RWIGS = 1.323 wigner-seitz radius (au A)
ENMAX = 273.042; ENMIN = 204.781 eV
RCLOC = 1.810 cutoff for local pot
LCOR = T correct aug charges
LPAW = T paw PP
EAUG = 580.196
DEXC = 0.000
RMAX = 2.749 core radius for proj-oper
RAUG = 1.300 factor for augmentation sphere
RDEP = 2.810 radius for radial grids
RDEPT = 2.162 core radius for aug-charge

Atomic configuration
14 entries
n l j E occ.
1 0 0.50 -40258.9816 2.0000
2 0 0.50 -6445.4884 2.0000
2 1 1.50 -5771.7470 6.0000
3 0 0.50 -1387.9739 2.0000
3 1 1.50 -1173.8158 6.0000
3 2 2.50 -869.9108 10.0000
4 0 0.50 -280.8706 2.0000
4 1 1.50 -210.9815 6.0000
4 2 2.50 -110.4558 10.0000
5 0 0.50 -40.5819 2.0000
6 0 0.50 -3.7444 2.0000
5 1 1.50 -23.2188 6.0000
5 2 2.50 -3.0598 1.0000
4 3 2.50 -5.3970 1.0000

Following the above table, there's this passage:

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).

that is followed by a second table:

Element (and appendix) default cutoff ENMAX (eV) valency
Ce_3 177 11
Tb_3 156 9
Pr_3 182 11

in which the 4f electron is not part of the 11 valence electrons.
-------------------

PAW_PBE Ce_3 06Sep2000
11.0000000000000
parameters from PSCTR are:
VRHFIN =Ce : [core=Xe4] s2d1f1
LEXCH = PE
EATOM = 890.3669 eV, 65.4401 Ry

TITEL = PAW_PBE Ce_3 06Sep2000
LULTRA = F use ultrasoft PP ?
IUNSCR = 1 unscreen: 0-lin 1-nonlin 2-no
RPACOR = 2.000 partial core radius
POMASS = 140.115; ZVAL = 11.000 mass and valenz
RCORE = 2.850 outmost cutoff radius
RWIGS = 3.400; RWIGS = 1.799 wigner-seitz radius (au A)
ENMAX = 176.506; ENMIN = 132.379 eV
RCLOC = 2.414 cutoff for local pot
LCOR = T correct aug charges
LPAW = T paw PP
EAUG = 304.861
DEXC = 0.000
RMAX = 2.908 core radius for proj-oper
RAUG = 1.300 factor for augmentation sphere
RDEP = 2.996 radius for radial grids
RDEPT = 2.334 core radius for aug-charge

Atomic configuration
14 entries
n l j E occ.
1 0 0.50 -40258.9816 2.0000
2 0 0.50 -6445.4884 2.0000
2 1 1.50 -5771.7470 6.0000
3 0 0.50 -1387.9739 2.0000
3 1 1.50 -1173.8158 6.0000
3 2 2.50 -869.9108 10.0000
4 0 0.50 -280.8706 2.0000
4 1 1.50 -210.9815 6.0000
4 2 2.50 -110.4558 10.0000
4 3 2.50 -5.3970 1.0000
5 0 0.50 -40.5819 2.0000
6 0 0.50 -3.7444 2.0000
5 1 1.50 -23.2188 6.0000
5 2 2.50 -3.0598 1.0000

I sort of understand the second table, which concur with the preceding passage about placing the 4f electrons in the core.
But I want to confirm whether there's anything special about the first table?

Because in the first table the f electrons remain as valence electrons, I don't see how they have been modified according to the above passages (apart from the soft versions for some elements). Aren't they just the standard POTCARs like other non-f-elements' POTCARs?

Dear alpinnovianus,

firstly, are there detailed reference paper/ citable source for the above comment?

You can find a good discussion on the topic here M.S.S. Brooks, L. Nordstrom, B. Johansson, Journal of Physics: Condensed Matter 3, 2357 (1991).

Following this comment, there's this table in the wiki.
However, if I read the Ce POTCAR file correctly, for example, one 4f electron is treated as valence electron. So the 4f electron is not placed in the core in this POTCAR file, isn't it?

Correct. The electrons placed in the core are not participating in the bonds formation. For example, in the Ce potential, if the 4f electron is treated as part of the core, such potential cannot describe the tretravalent Ce, which would involve the 4f electron.

Because in the first table the f electrons remain as valence electrons, I don't see how they have been modified according to the above passages (apart from the soft versions for some elements). Aren't they just the standard POTCARs like other non-f-elements' POTCARs?

In the standard lanthanides POTCARs, the 4f electrons are treated as valence electrons, as such potentials are more general and can be used for describing any valence and 4f magnetism. However, for compounds where the valence is known to be 2 or 3, specific potentials can be used "_2" or "_3". In these potentials, 4f electrons which do not contribute to the valence, are placed in the core.