$f$-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