The quantum chemical (density functional) analysis of the antiferromagnetic interactions between the two iron centers incorporated into the gamma-silicotungstate is performed. The influence of the polyoxometalate framework on the exchange coupling within the diiron core unit is studied. The dependence of the strength of antiferromagnetic exchange on the protonation of the core bridges is considered. It is shown that the magnetic coupling is very sensitive to the distortions in core geometry. Variations in the core structure induced by the environment (such as the polyoxometalate framework) change the significance of superexchange pathways and give rise to new superexchange mechanisms. This effect is especially pronounced in the case of the hydroxo-bridged diiron core.