In the present study, we attempted to apply DV-X$alpha$ method to expressing the reactivity of materials. The expression of reactivity was discussed by comparison between ${gamma}$-C$_2$G having hydraulic activity and ${gamma}$-C$_2$S not having hydraulic activity at normal conditions. It was found that the model cluster used for calculation can finely reproduce the bulk and surface states using with and without point charge, respectively. The hydration state was also represented by placing OH￣ on the surface of the cluster. It was calculated that the bond strength of the first layer (as surface) was bigger than that of inner layers (as bulk) for ${gamma}$-C$_2$S while that of the first layer for ${gamma}$-C$_2$G was smaller than that of inner layers. Subsequently a model in which OH￣ is coordinated on Ca at the surface was also calculated. The bond strength with OH￣ was stronger than that without OH￣, while for ${gamma}$-C$_2$G the bond strength with OH￣ was weaker than that without OH￣. From these results, it is concluded that the hydraulic activity depends on whether the bond strength for hydrated state becomes weaker than that unhydrated state or not.