Cation circle times 3 pi: Cooperative Interaction of a Cation and Three Benzenes with an Anomalous Order in Binding Energy

Cation-pi or cation-pi-pi interaction between one cation and one or two structures bearing rich pi-electrons (such as benzene, aromatic rings, graphene, and carbon nanotubes) plays a ubiquitous role in various areas. Here, we analyzed a new type interaction, cation circle times 3 pi, whereby one cation simultaneously binds with three separate pi-electron-rich structures. Surprisingly, we found an anomalous increase in the order of the one benzene binding strength of the cation circle times 3 pi interaction, with K+ > Na+ > Li+. This was at odds with the conventional ranking of the binding strength which usually increases as the radii of the cations decrease. The key to the present unexpected observations was the cooperative interaction of the cation with the three benzenes and also between the three benzenes, in which a steric-exclusion effect between the three benzenes played an important role. Moreover, the binding energy of cation circle times 3 pi was comparable to cation circle times 2 pi for K+ and Na+, showing the particular importance of cation circle times 3 pi interaction in biological systems.