Accurate prediction of cucurbituril binding affinities from guest molecular formulae

The binding affinities of 24 ammonium salts were determined by isothermal titration calorimetry (ITC). The affinities were predicted with three empirical models that do not invoke the macrocycle explicitly. Once head groups common to all guests are removed, and the remaining fragments are transferred from aqueous solution to a virtual gas phase, the free energy of transfer from the gas phase to the CB[7] cavity is correlated with (a) the dispersive component of their interaction with a non-polar, non-polarizable hard sphere fluid, (b) their free energy of solvation in tetramethylglycoluril, that mimics the main building block of CB[7], and (c) a sum of individual guest atom free energy contributions via multiple linear regression. The latter method, which simply correlates binding affinities with the guest molecular formulae, is the most precise and accurate one, except for tight-fitting guests, with mean absolute errors as low as 0.16 kcal mol^-1, thereby rivaling experimental error (0.06 kcal mol^-1 on average). Accuracy exceeds density functional theory calculations that treat the host explicitly.