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 alpha'-NaV2O5 from synchrotron x-ray diffraction experiments. We confirm the existence of two inequivalent ladder structures in each vanadium layer. Based on our structural data we perform a bond-valence calculation for the vanadium sites in the low temperature state. Due to an asymmetric charge ordering we obtain only two different vanadium valences despite the three inequivalent sites. This explains the 51V-NMR observation of only two resonant peaks in the charge ordered phase. By use of a Slater-Koster method to obtain hopping matrix elements and cluster calculations we obtain effective vanadium-vanadium hoppings which compare well to LDA results. Using these in a cluster calculation we obtain a superexchange of 0.047 eV between electrons 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 \approx 0.25. 
A. Bernert, T. Chatterji, P. Thalmeier, P. Fulde