Modeling the Equilibria of Complex Supramolecular Systems

The modeling of solution equilibria through the evaluation of multiple simultaneous equations is a ubiquitous component of undergraduate analytical chemistry. Common systems investigated include metal–ligand and acid–base equilibria as a result of their practical importance and because they typically involve ionic species allowing a charge balance equation to be used in solving for multiple unknowns (1–7). Although the basic skills needed for modeling solution equilibria are acquired early in the undergraduate curriculum, more advanced techniques can be a powerful tool for understanding more complex chemical systems. Indeed, such methods are often employed in research (8–12); particularly in the area of supramolecular chemistry (13–15). As part of our continuing studies of hydrogen-bondmediated self-assembly, we found a need to model the equilibria of complex supramolecular systems involving multiple species and numerous association modes (8–9). Although there are stochastic methods for modeling complex systems at equilibrium (16–17), we employed an analytical solution of multiple simultaneous equations, which is within the scope of undergraduate analytical chemistry courses. It is the purpose of this article to illustrate the utility of this approach and the types of data that can be generated through the modeling of lipophilic DNA base pairs and high-affinity basepair analogs in chloroform solution. These examples extend the standard undergraduate curriculum in equilibrium by introducing uncommon examples that are pertinent to recently published research (8–12) and provide a challenge to students by eliminating the charge balance equation utilized in typical equilibrium problems. Detailed derivations of two, three, and four component supramolecular systems are included in the online materials, as are the Microsoft Excel spreadsheets and Java source code that can be used to generate this and similar equilibrium data. It is our hope that this article combined with the online materials will provide a good starting point to anyone who would like to use these approaches in teaching and research.