The Benesi–Hildebrand method is a mathematical approach used in physical chemistry for the determination of the equilibrium constant K and stoichiometry of non-bonding interactions.
This method was first developed by Benesi and Hildebrand in 1949,[2] as a means to explain a phenomenon where iodine changes color in various aromatic solvents.
This was attributed to the formation of an iodine-solvent complex through acid-base interactions, leading to the observed shifts in the absorption spectrum.
Following this development, the Benesi–Hildebrand method has become one of the most common strategies for determining association constants based on absorbance spectra.
It has been observed that the existence of these 2:1 complexes generate inappropriate parameters that significantly interfere with the accurate determination of association constants.
The two parameters, K or ε are determined by using the Solver module a spreadsheet, by minimizing a sum of squared differences between observed and calculated quantities with respect to the equilibrium constant and molar absorbance or chemical shift values of the individual chemical species involved.
Although initially used in conjunction with UV/Vis spectroscopy, many modifications have been made that allow the B–H method to be applied to other spectroscopic techniques involving fluorescence,[8] infrared, and NMR.
[10] The equation that they developed is as follows: Their method relied on a set of chosen values of ε and the collection of absorbance data and initial concentrations of the host and guest.
When the procedure is repeated for a series of concentrations and plotted on the same graph, the lines intersect at a point giving the optimum value of εHG and K−1.
This approach relies on a more complex mathematical rearrangement of the Benesi–Hildebrand method but has proven to be quite accurate when compared to standard values.