Structure determination, valence, and superexchange in the dimerized low temperature phase of alpha '-NaV2O5

We report results of a new analysis for the low-temperature structure of al pha ' -NaV2O5 from synchrotron X-ray diffraction experiments. We confirm th e existence of two inequivalent ladder structures in each vanadium layer. B ased on our structural data we perform a bond-valence calculation for the v anadium sites in the low temperature state. Due to an asymmetric charge ord ering we obtain only two different vanadium valences despite the three ineq uivalent sites. This explains the V-51-NMR observation of only two resonant peaks in the charge ordered phase. By use of a Slater-Koster method to obt ain hopping matrix elements and cluster calculations we obtain effective va nadium-vanadium hoppings which compare well to LDA results. Using these in a cluster calculation we obtain a superexchange of 0.047 eV between electro ns on neighbouring rungs of the same ladder for the undistorted phase. For the distorted phase we find a significant alternation in the shifts of the oxygen atoms along the legs of one of the two ladder types which leads to a significant exchange dimerisation delta (J) approximate to 0.25.