Validity and Reliability of Benesi-Hildebrand Method

Benesi-Hildebrand (B-H) method is a widely used approach for determining the stoichiometry and equilibrium constants of nonbonded interactions, particularly 1:1 and 1:2 interactions. Using computer simulation, it was shown that, under certain conditions, the approach could generate inappropriate stoichiometric conclusions for 1:2 interactions. This problem could occur in the cases of both weak and strong interactions, where the 1:1 B-H plots showed a linear feature and the 1:2 B-H plots showed a nonlinear feature. In addition, effect of the initial concentrations on the accurate evaluation of equilibrium constants of 1:1 interactions was investigated. It was found that the minimum safe concentration ratio r0 between ligand and central species was 100. However, for weak nonbonding interactions, for example K<25 L·mol-1 (CP0 =4×10-4 mol·L-1), the ratio r0 has no limitation. Two conditions proposed in literatures for the safe application of the B-H method were examined. It was found that the inequation, 1/(KC0P)≥10, was a condition to secure CB/C0B >91%. The other inequation, KC0B>0.1, was not found to be the safe condition to validate the B-H method.