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$ 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.

La 219 Ce 273 Pr 272 Nd 253 Pm 258 Sm 257 Eu 249 Gd 256
    Tb 264 Dy 255 Ho 257 Er 298 Tm 257 Yb 253 Lu 255
Ac 172 Th 247 Pa 252 U 252 Np 254 Pu 254 Am 255    
    Th_s 169 Pa_s 193 U_s 209 Np_s 207 Pu_s 207        
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 (6 $ f$ electrons and 2 $ s$ electrons). In most compounds Sm, however, 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).

Ce_3 176 Pr_3 181 Nd_3 182 Pm_3 176 Sm_3 177 Eu_3 129 Gd_3 154
                    Eu_2 99    
Tb_3 155 Dy_3 155 Ho_3 154 Er_3 155 Tm_3 149     Lu_3 154
            Er_2 119     Yb_2      

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