Argentophilic Interactions, Flexibility, and Dynamics of Pyrrole Cages Encapsulating Silver(I) Clusters

Recently, pyrrole cages have been synthesized that encapsulate ion pairs and silver(I) clusters to form intricate supramolecular capsules. We report here a computational analysis of these structures using density functional theory combined with a semiempirical tight-binding approach. We find that for neutral pyrrole cages, the Gibbs free energies of formation provide reliable predictions for the ratio of bound ions. For charged pyrrole cages, we find strong argentophilic interactions between Ag ions on the basis of the calculated bond indices and molecular orbitals. For the cage with the Ag₄ cluster, we find two minimum-geometry conformations that differ by only 6.5 kcal/mol, with an energy barrier <1 kcal/mol, suggesting a very flexible structure as indicated by molecular dynamics. The predicted energies of formation of [Ag_n⊂1]^n-3+ (n = 1-5) cryptands provide low energy barriers of formation of 5-20 kcal/mol for all cases, which is consistent with the experimental data. Furthermore, we also examined the structural variability of mixed-valence silver clusters to test whether additional geometrical conformations inside the organic cage are thermodynamically accessible. In this context, we show that the time-dependent density functional theory UV-vis spectra may potentially serve as a diagnostic probe to characterize mixed-valence and geometrical configurations of silver clusters encapsulated into cryptands.