6 Figure 4: (color online) Band structure of the (LaO) 4 (FeAs) 6 slab. The thickness of the red (shadow) lines represents in turn the orbital weight of (a) surface As 4 p , (b) subsurface Fe 3 d , (c) subsurface As 4 p , and (d) central (bulk) Fe 3 d . Figure 5: The 2D FSs of the slab (LaO) 4 (FeAs) 6 . The zone center is Γ and the corner point is M . From Γ outward in turn the FSs are: 2 times bulk, 3 times surface; from M outward: two tiny surface FSs, two bulk FSs. (The small wiggles are due to the resolution of the used k mesh.) C. The As terminated surface As can be inferred from Tables II and III, the central Fe-As triple layer of (LaO) 4 (FeAs) 6 is already close to a bulk-like state. Also the Fermi level relative to the bands derived from this central layer is bulk-like. Therefore, the band structure of this slab shown in Fig. 4 may be considered as representative for a bulk crystal with an As terminated (001) surface. Observe that the slab bands do not have k$_{z}$ -dispersion due to the slab confinement of the Kohn-Sham states. As is seen in Fig. 1, the k$_{z}$ -dispersion of the bulk bands crossing Fermi level is also negligible. Therefore, in the following only the in-plane dispersion of the bands is discussed and presented in the figures. By the thickness of colored lines, the orbital character of the bands is indicated in Fig. 4 from top to bottom for basis orbitals in which the Kohn-Sham band wave- functions are expanded: of surface As 4 p -orbitals, Fe 3 d - orbitals of the Fe layer below the surface As layer, As 4 p -orbitals of the next layer below this Fe layer, and fi- nally of the Fe 3 d -orbitals in the center of the slab which corresponds to the first Fe layer below the surface triple layer of a bulk crystal. The latter Fe atoms are about 10 ˚ A below the position of the surface As atoms. The Kohn-Sham band wavefunctions in the vicinity of Fermi level are formed by the above accounted ‘chemical basis’ orbitals to about 99 percent so that the thick col- ored lines of Fig. 4 (and also of Fig. 6 below) completely represent the extension of the corresponding Kohn-Sham wavefunctions. Polarization states, and other basis states besides the explicitly discussed, of the full basis used in the calculations to not contribute to these Kohn-Sham wavefunctions. Both the surface Fe 3 d -bands and the bulk Fe 3 d -bands cross the Fermi level, however, they form quite different Fermi surfaces (FS) as shown in Fig. 5. Around Γ there are two hole cylinders of bulk bands and around M there are two electron cylinders, all much like in a bulk crys- tal calculation without surface. Note that in the slab (LaO) 4 (FeAs) 6 on which Fig. 5 is based the surfaces FSs are (almost) twofold degenerate due to the two surface FeAs triple layers on both sides of the slab (which do almost not interact due to the z -confinement of all con- duction states). Hence, each of the surface FSs is doubly degenerate which is, however, not resolved in the figure. There is next to no contribution of orbitals in the sub- surface LaO triple layer as well as in any LaO triple layer