We have performed ab-initio calculations of exchange couplings in the layered
vanadates CaV2O5, MgV2O5, CaV3O7 and CaV4O9. The uniform susceptibility of the
Heisenberg model with these exchange couplings is then calculated by quantum
Monte Carlo method; it agrees well with the experimental measurements. Based on
our results we naturally explain the unusual magnetic properties of these
materials, especially the huge difference in spin gap between CaV2O5 and
MgV2O5, the unusual long range order in CaV3O7 and the "plaquette resonating
valence bond (RVB)" spin gap in CaV4O9