The structural aspects of protein functions, e.g., molecular recognition such as enzyme-substrate and antibody-antigen interactions, are elucidated in terms of dehydration and atomic interactions. When a protein interacts with some target molecule, water molecules at the interacting regions of both molecules are removed, with loss of the hydration free energy, but gaining atomic interactions between atoms of the contact sites in both molecules. The free energies of association originating from the dehydration and interactions between the atoms can be computed from changes in the accessible surface areas of the atoms involved. The free energy due to interactions between atomic groups at the contact sites is estimated as the sum of those estimated from the changes in the accessible surface area of 7 atomic groups, assuming that the interactions are proportional to the change of the area. The chain enthalpies and entropies evaluated from experimental thermodynamic properties and hydration quantities at the standard temperature for 10 proteins were available to determine the proportional constants for the atomic groups. This method was applied to the evaluation of association constants for the dimerization of proteins and the formation of proteolytic enzyme-inhibitor complexes, and the computed constants were in agreement with the experimental ones. However, the method is not accurate enough to account quantitatively for the change in the thermal stability of mutants of T4 lysozyme. Nevertheless, this method provides a way to elucidate the interactions between molecules in solution.