A class A ${eta}$-lactamase from Staphylococcus aureus PC1 complexed with 3R,5R-clavulanate is studied. The starting geometry for the computation is the crystal structure of the ${eta}$-lactamase. Docking of the clavulanate to the enzyme is done exploiting the requirements of electrostatic and shape complementarity between the enzyme and clavulanate. This structure is then hydrated by water molecules and refined by energy minimization and short molecular dynamics simulation. In the energy refined structure of this complex, the carboxyl group of the clavulanate is hydrogen bonded to Lys-234, and the the carbonyl carbon atom of the clavulanate is adjacent to the $O_{gamma}$ of Ser-70. It is found that a crystallographic water molecule initially located at the oxyanion hole, which is formed by the two -NH group of Ser-70 and Gln-237, is replaced by the carbonyl oxygen atom of the 3R,5R-clavulanate after docking and energy reginement. The crystallographic water molecules are proved to be important in ligand binding. Glu-166 residue is found to be repulsive to the binding of clavulanate, which is in agreement with experimental observation. Arg-244 residue is found to be important to the binding of clavulanate as well as to interaction with C2 side chain of the clavulanate. The electron density redistribution of the clavulanate on binding to the ${eta}$-lactamase in studied by an ab initio quantum-mechanical calculation. A significant redistribution of electron density of the clavulanate is induced by the enzyme, toward the enzyme, toward the transition state of the enzymatic reaction.