We attempt to find out the origin of rate difference of the $S_N2$ reaction in the gas phase and in the aqueous solution which is about twenty orders of magnitude. To do this, we calculate the interaction energies of both reactant-complex and activated-complex of the $S_N2$ reaction with the hydrated water molecules and their interaction energy differences, varying the number of hydrated water molecules step by step. The calculated results show that the rate of the $S_N2$ reaction decreases with an increase of the number of hydrated water molecules due to the increase of the reaction barrier height and also about sixty as more water molecules are needed to explain the rate difference of the $S_N2$ reaction in the gas phase and solution. Potential functions of polarization model for water are used to study the proton transfer in water clusters with optimum geometries, $(H_2O)_n$ (n=2,3,4,5,6). Proton transfer reaction in dimer shows single proton transfer and single-well potential energy profile, while proton transfer reactions in trimer, tetramer, pentamer, and hexamer show simultaneous proton transfers and double-well potential energy profiles. Ab initio SCF calculation with the STO-3G basis set have been performed to obtain the potential energy profiles for proton transfers in DNA base pairs, Guanine-Cytosine base pair and Adenine-Thymine base pair. Double proton transfers in DNA base pairs have produced double-well potential energy profiles.