Comprehensive Energy Analysis for Various Types of π-Interaction

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