Analyzing the flexibility of the cages provides a more realistic picture of how much a cage cavity changes and adapts to different guests. Among the simulated cages, the [Ga4L6] 12-cage shows the largest relative change in volume, from < 1 Å 3 (not grid point can be placed inside) to 267 Å 3 (Figure ; Figure ). This flexibility is due to the rotatable central naphthalene linker. Indeed, the [Ga4L6] 12-cage has been found to bind a broad range of substrates, including quaternary ammonium cations with volumes ranging from 80-160 Å 3 . Furthermore, analysis of the interactions between the supramolecular systems and counterions can be done by computing the corresponding radial distribution functions (RDFs; Figure ).