Dynamic and Static Behavior of Intramolecular π-π Interactions in [2.2]- and [3.3]Cyclophanes, Elucidated by QTAIM Dual Functional Analysis with QC Calculations

Bader's Topological Bond Path Does Not Necessarily Indicate Stabilizing Interaction-Proof Studies Based on the Ng@[3n]cyclophane Endohedral Complexes

According to Bader's quantum theory of atoms in molecules (QTAIM), the simultaneous presence of a bond path and the corresponding bond critical point between any two atoms is both a necessary and sufficient condition for the atoms to be bonded to one another. In principle, this means that this pair of atoms should make a stabilizing contribution to the molecular system. However, the multitude of so-called counterintuitive bond paths strongly suggests that this statement is not necessarily true. Particularly 'troublesome' are endohedral complexes, in which encapsulation-enforced proximity between the trapped guest (e.g., an atom) and the host's cage system usually 'produces' many counterintuitive bond paths. In the author's opinion, the best evidence to demonstrate the repulsive nature of the intra-cage guest⋯host interaction is the use of some trapping systems containing small escape channels and then showing that the initially trapped entity spontaneously escapes outside the host's cage during geometry optimization of the initially built guest@host endohedral complex. For this purpose, a group of 24 Ng@[3n]cyclophane (3≤n≤6) endohedral complexes is used. As a result, arguments are presented showing that Bader's topological bond path does not necessarily indicate a stabilizing interaction.

Intrinsic Dynamic and Static Nature of π···π Interactions in Fused Benzene-Type Helicenes and Dimers, Elucidated with QTAIM Dual Functional Analysis

The intrinsic dynamic and static nature of the π···π interactions between the phenyl groups in proximity of helicenes 3-12 are elucidated with the quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA). The π···π interactions appear in C-∗-C, H-∗-H, and C-∗-H, with the asterisks indicating the existence of bond critical points (BCPs) on the interactions. The interactions of 3-12 are all predicted to have a p-CS/vdW nature (vdW nature of the pure closed-shell interaction), except for 2Cbay-∗-7Cbay of 10, which has a p-CS/t-HBnc nature (typical-HBs with no covalency). (See the text for definition of the numbers of C and the bay and cape areas). The natures of the interactions are similarly elucidated between the components of helicene dimers 6:6 and 7:7 with QTAIM-DFA, which have a p-CS/vdW nature. The characteristic electronic structures of helicenes are clarified through the natures predicted with QTAIM-DFA. Some bond paths (BPs) in helicenes appeared or disappeared, depending on the calculation methods. The static nature of Ccape-∗-Ccape is very similar to that of Cbay-∗-Cbay in 9-12, whereas the dynamic nature of Ccape-∗-Ccape appears to be very different from that of Cbay-∗-Cbay. The results will be a guide to design the helicene-containing materials of high functionality.