  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.
