We have investigated various types of pi-interactions, where one of the interacting pi-systems is represented by an aromatic benzene molecule. The system includes Rg-pi, CH-pi, pi-pi(D), pi-pi(T), H-pi(T), pi(+)-pi(D), pi(+)-pi(T), H+-pi(T), pi(+2)-pi(D), M+-pi, M+2-pi complexes, where Rg denotes a rare gas or noble atom, M denotes a metal, and D/T indicates displaced-stacked/T-shaped structure. The microsolvation effect is also considered. We note that the interaction between a cationic pi system and a neutral pi system (pi(cation)-pi interaction) is so far ambiguously considered as either pi-pi or cation-pi interaction. In terms of total binding energy, the pi(cation)-pi interaction is weaker than the cation-pi interaction, but much stronger than the pi-pi interaction. When the hydrophilic (N-H)(+) or (C-H)(+) group in a singly charged pi(+) system (as in protonated histidine, arginine, pyridine, or dimethyl imidazolium) interacts with pi-system, the complex favors a T-shaped form [pi+-pi(T) complex]. However, in the presence of polar solvating molecules or counteranions, these species interact with the (N-H)(+)/(C-H)(+) group, while the pi(+) system interacts with the neutral aromatic ring. Then, the displaced-stacked form [pi(+)-pi(D) complex] is favored or otherwise nearly isoenergetic to the pi(+)-pi(T) form. The pi(+)-pi systems are stabilized mainly by both dispersion and electrostatic energies. Ternary diagrams using either attractive energy components or both attractive and repulsive energy components show that the pi(+)-pi(D) complexes have more contribution from dispersion energy but less contribution from induction energy than the pi(+)-pi(T) complexes, while both complexes have similar percentage contributions from electrostatic and exchange energy components. In particular, the pi(+)-pi(D) complexes are found to be distinctly different from the pi-pi complexes and the non-pi organic or metallic cation-pi complexes.
