Figure 3: (color online) The atom layer distances as functions of the stretched c axis lattice constant. In the upper panel the Fe-O layer distances are shown, the two upper curves across the slit and the two lower curves between the surface and subsurface triple layer on both sides of the slit (FeAs and LaO terminated, respectively. On the lower panel the behavior of layer distances within the triple layers La/O/La and As/Fe/As, respectively, are shown, again for the bulk and for the surface triple layers. Observe the different scales of the ordinates. For more explanation see the text. 3 4 6 8 10 Fe-O distance [  o A] slit Fe-O of rigid bulk slit Fe-O bulk Fe-O FeAs-surface Fe-O LaO-surface Fe-O 16 18 20 22 24 doubled c-lattice constant [  o A] 1.1 1.2 1.3 layer distances [ A] bulk Fe-As bulk O-La As-surface Fe-As La-surface O-La ferent codes differ in doing so (if they make such an as- signment at all). However, with such a charge partition- ing procedure fixed, the stability of the assigned charges with respect to slab and spacer thickness can be taken as a criterion for size convergence. Here, the site charges recorded in the FPLO protocol file are used. As a result of these checks, while the slab (LaO) 4 (FeAs) 6 turned out to be representative, the thicker slab (LaO) 10 (FeAs) 8 had to be considered for the La terminated case. Finally, for the geometrically relaxed slabs Kohn-Sham band structures were calculated and projected onto var- ious basis orbitals of the ‘chemical basis’ used in the FPLO code. This allows to distinguish bulk from sur- face bands and to estimate the spatial extension of the corresponding states. We mention here that FPLO works with a well designed small basis consisting at most of one ‘chemical’ basis state (site orbital) and one polarization state per atomic orbital. The chemical relevance of the ‘chemical’ part of the basis is emphasized by the fact that the polarization states are typically occupied by less than 0.01 electron in a converged calculation, although relaxed structures and total energies compete well in accuracy with any available full potential density functional code like for instance FLAPW. Geometry relaxation was done by direct calculation of the forces on atom sites and minimizing them with the corresponding tool of FPLO9.00. Convergence was accepted when all forces were smaller than 10 − 3 eV/ ˚ A. Only for the thickest slabs this was hard to achieve, and the relaxation was stopped when the atom positions did not change any more within 0.01 ˚ A accuracy over several force steps (in an oscillating behavior) which keeps the band energies close to Fermi level within about 20 meV of accuracy. slit width as measured between the Fe and O layers form- ing the centers of the adjacent tetrahedra layers would be that of the black straight line in the upper panel of Fig. 3. For z -strain not exceeding about 10 p.c. (leftmost line segments in Fig. 3) the tetrahedra behave indeed as nearly rigid, but every La-As distance is homogeneously strained by one fourth of the black line. Observe that the ordinate scale is stretched by about a factor of 20 in the lower panel of Fig. 3 compared to the upper, so the changes in the La-O and Fe-As distances within the triple layers are really negligible compared to the change of the distance between the triple layers (smaller roughly by a factor of seven). Hence, for not to large strain the crys- tal behaves as a system of nearly rigid triple atom layers La/O/La and As/Fe/As which are elastically bonded to- gether. For a sufficiently small c -strain of the crystal the orig- inal periodicity is preserved. However, as said the lattice essentially expands only between La and As layers while the La-O and As-Fe layer distances hardly change. There are four neighboring La-As layer pairs in the doubled unit III. RESULTS AND DISCUSSION A. Cleavage behavior Cleavage is ideally considered as expanding a bulk crys- tal in z -direction until it disintegrates into parts. On the computer, a bulk crystal with a unit cell doubled in z - direction and with the in-plane lattice constant fixed to its equilibrium bulk value a = 4 . 041 ˚ A, but with reduced space group to the orthorhombic group Pmm2 and with an increasing sequence of c lattice constants is treated. Pmm2 (still with b = a ) is the highest symmetry of our situation which leaves all z Wyckoff parameters of all atom layers undetermined. For each value of the c lat- tice constant these Wyckoff parameters were relaxed in GGA. The crystal structure of LaOFeAs can be imagined as a stacking of layers of tetrahedra with their corners oc- cupied with La and As sites, respectively, and which are centered by O and Fe ions (triple atom layers, Fig. 2). If the bulk structure of the crystal were rigid and the crys- tal would split between every fourth La-As layer pair, the