Computation of binding constants from spectrophotometric titration data is a very popular application of chemometric hard modeling. However, the calculated values are meaningless and misleading if the correct binding model is not used. Given that many supramolecular systems of interest feature unknown speciation, a priori determination of binding stoichiometry constitutes an important unsolved problem in chemometrics. We present a new and reliable algorithm for accomplishing this task, implemented using a hybrid particle swarm optimization technique. Simultaneous optimization of stoichiometry ratios and binding constants allows the optimal binding model to be calculated in just a few minutes for systems with up to four reactions. Simulated data studies demonstrate that the algorithm finds the correct stoichiometry with up to nine reactions in the absence of noise, including accurately determining species with unusual stoichiometry, such as H₂G₅. Application to four experimental datasets shows the algorithm is robust to experimental errors for a variety of chemical systems and binding models. This algorithm will facilitate the discovery of complex binding models, increase efficiency in titration analysis, and avert incorrect stoichiometry models, thereby improving the reliability of binding constant information in spectrophotometric titrations.

RMSE optimization surfaces for H<sub>h</sub>G<sub>g</sub>, with minimum at h = g = 1, for two different parameterizations of the problem. (a) Straightforward parameterization based on <i>h </i>and<i> g</i> shows strong correlation between the two parameters, greatly hampering convergence to the global minimum with respect to either parameter due to the diagonal channel. (b) Parameterization as ratio (<i>g</i>/<i>h</i>) and nuclearity (<i>h</i>) shows the correlation has been removed so that the optimal ratio value may be precisely determined independently from the nuclearity.

RMSE optimization surfaces for H_hG_g, with minimum at h = g = 1, for two different parameterizations of the problem. (a) Straightforward parameterization based on h and g shows strong correlation between the two parameters, greatly hampering convergence to the global minimum with respect to either parameter due to the diagonal channel. (b) Parameterization as ratio (g/h) and nuclearity (h) shows the correlation has been removed so that the optimal ratio value may be precisely determined independently from the nuclearity.

Nathanael Kazmierczak

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