We propose a computational strategy within the full quantum embedded cluster methodology for modeling reactivity in extended systems. This method takes advantages of the embedded cluster methodology for treating interactions in the active region accurately while allowing interactions with the remaining crystal framework to be treated fully quantum mechanically by using the ab initio tight-binding theory. We have applied this method to study proton siting in chabazite. We found that our calculated relative stability of proton at four different oxygen sites agree well with those from previously periodic calculations, though the computational demand for the present approach is much less.