Fragment-Based Approaches for Supramolecular Interaction Energies: Applications to Foldamers and Their Complexes with...

We explore the application of our multilayer Molecules-in-Molecules (MIM) fragment-based method for the study of the energies in supramolecular systems, viz. foldamers and their anion bound complexes. The performance of five different density functional theory (DFT) methods in conjunction with the fragmentation-based method is evaluated against the unfragmented energies for a test set of 5 foldamers (82 to 170 atoms). A systematic protocol has been developed to account for the π···π interactions in such systems in addition to the traditional fragmentation of the system along the backbone comprised of covalently bonded dimer (or trimer) units. We find a significant improvement in the performance of the method on going from a one-layer MIM1 model (errors >10 kcal/mol) to a two-layer MIM2 model (errors 0-2 kcal/mol), due to the incorporation of long-range interactions in the latter approach. Furthermore, we extend the applicability of MIM2 models to determine accurate binding energies of macromolecular receptor-anion complexes. For three different anion bound macrocycles, our MIM2 protocol provides total energies within 1.5 kcal/mol of the unfragmented energies for most of the DFT methods. The corresponding anion binding energies are calculated within 0.5 kcal/mol of the unfragmented binding energies due to systematic error cancellation between the macrocycle and the macrocycle-anion complex. Finally, we have calibrated the absolute accuracy in the calculated binding energies by comparison with unfragmented DLPNO-CCSD(T) calculations on three macromolecule-chloride anion complexes. The most accurate results are obtained using a MIM2 model using DLPNO-CCSD(T) calculations on trimer units as the high level and DFT-D3 (e.g., M06-2X-D3) as the low level of theory, yielding sub kcal/mol errors in the anion binding energies. Our protocol can be an accurate method to calculate anion binding energies for very large supramolecular systems.