Abstract
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.
Highlights
Academic Editor: Fabien SillyHelicenes, which are ortho-fused polycyclic aromatic or heteroaromatic compounds with all rings angularly arranged to form helically shaped molecules, are of current and continuing interest
The π···π interactions in the helicenes were analyzed with quantum theory of atoms-in-molecules (QTAIM) dual functional analysis (QTAIM-DFA [30,31,32,33,34,35]), which we proposed based on the QTAIM approach inThe π···π interactions the helicenes were analyzed with QTAIM
Data from both the perturbed and fully optimized structures are expressed by (θ p, κ p ), where θ p corresponds to the tangent line and κ p is the curvature of the plot. θ and θ p are measured from the y-axis and the y-direction, respectively. (See Figure SA1 of the Appendix S1 of the Supporting Information for the definition of the QTAIM-DFA parameters of (R, θ) and (θ p, κ p ), along with Equations (SA3)–(SA6) and the footnotes of Table 1)
Summary
Helicenes, which are ortho-fused polycyclic aromatic or heteroaromatic compounds with all rings angularly arranged to form helically shaped molecules, are of current and continuing interest. It is crucial to clarify the nature of π···π interactions for future high-functioning material developments based on helicenes. The discussion in this paper will be limited to π···π interactions between the aromatic rings, the nature of which needs to be clarified, since helicenes of the fused benzene type were chosen as the target. Data from the fully optimized structures in the plots were analyzed using polar coordinate (R, θ) representation, which corresponds to the static nature of the interactions [30,31,32,33,34,35]. The perturbed structures necessary for QTAIM-DFA were generated by CIV [38], with the coordinates Ci corresponding to the compliance constants Cii for the internal vibrations [39,40,41,42,43,44]. The structural features and the energy profile are discussed to provide a solid basis for the discussion
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