Binding of organic cations to a cyclophane host as studied with molecular dynamics simulations and free energy calculations

We have studied the binding of two organic cations, an iminium (IM) and a guanidinium (GU), to a cyclophane host P4--4Na(+), using molecular dynamics simulations and free energy calculations. A proper treatment of the long-range electrostatic forces is essential for the stability of these highly charged complexes, and a simple cutoff at 12 Angstrom results in an artifactual dissociation of the IM-P4--4Na(+) complex. Since the host is highly aromatic and the guests cationic, cation-pi interactions play an important role in the complex stability. In free energy calculations, using a simple additive force field, we calculate that the relative free energy of association of IM and GU binding to the host is 2.3 kcal/mol favoring IM, which is of the correct sign but 1.4 kcal/mol too small in magnitude. Differences in van der Waals interaction energies are mainly responsible for the different binding strengths, and the host adopts different shapes when accommodating IM compared to GU. To approximately estimate the contribution to the complex stability from the polarization energy, we calculated the in vacuo interaction energies in the two complexes, using a nonadditive force field, previously shown to accurately describe alkali cation-aromatic interaction energies in vacuo, Adding the contribution from the polarization energy upon forming the two complexes in this calculation to the estimate from the free energy calculation, we obtain an improved relative binding free energy (-4.0 kcal/mol), which is in close agreement with the experimental value of -3.7 kcal/mol.