Mixed Explicit–Implicit Solvation Approach for Modeling of Alkane Complexation in Water-Soluble Self-Assembled Capsules

The host-guest binding properties of a water-soluble resorcinarene-based cavitand are examined using density functional theory methodology. Experimentally, the cavitand has been observed to self-assemble in aqueous solution into both 1:1 and 2:1 host/guest complexes with hydrophobic guests such as n-alkanes. For n-decane, equilibrium was observed between the 1:1 and 2:1 complexes, while 1:1 complexes are formed with shorter n-alkanes and 2:1 complexes are formed with longer ones. These findings are used to assess the standard quantum chemical methodology. It is first shown that a rather advanced computational protocol (B3LYP-D3(BJ)/6-311+G(2d,2p) with COSMO-RS and quasi-rigid-rotor-harmonic-oscillator) gives very large errors. Systematic examination of the various elements of the methodology shows that the error stems from the implicit solvation model. A mixed explicit-implicit solvation protocol is developed that involves a parametrization of the hydration free energy of water such that water cluster formation in water is predicted to be thermoneutral. This new approach is demonstrated to lead to a major improvement in the calculated binding free energies of n-alkanes, reproducing very well the 1:1 versus 2:1 host/guest binding trends.