The recently proposed local hard-soft acid-base principle characterizes the reactive centers of two systems on the basis of equal Fukui functions or/and equal local softnesses. We make a quantum chemical study of this principle using ab initio and density functional calculations in cases where the global softnesses of the reacting systems are different. We consider reactions of a dimer cluster model of faujasite X-type zeolite with the probe molecules CO, NH3, and H2O.