Decomposition of the factors that govern binding site preference in a multiple rotaxane

A particularly interesting class of multiple rotaxanes consists of complexes where one long shaft threads two rings. If the shaft contains three or more potential binding sites for the rings, multiple co-conformations are possible. Such a complex is a molecular topological analogue to an abacus. Here we address the question, how does strength of ring binding to the shaft vary with respect to position on the shaft? Previous studies have found that a shaft with three binding sites exhibits strongest ring binding at the center site. Here a five-binding-site shaft is studied. We employ a novel method to partition the total energy of the system into contributions from intercomponent binding and intracomponent distortion. The method uses the output of quantum mechanical electronic structure calculations to determine fitting parameters in a set of coupled equations. The solution of the equations yields the energy partitioning and reveals the influence of long-range intercomponent interactions.