**4. Conclusions**

In this work, the LVM analysis of Konkoli and Cremer was utilized to quantify strength of *π*–hole interactions in terms of a special local force constant *ka*. This is the first work to quantify *π*–hole interactions in terms other than distance parameters *r* and binding/dissociation energies. Given the fact that the aforementioned parameters are not reliable descriptors of bond strength, our results provide a much needed perspective on the matter. In addition to quantification of *π*–hole interaction strength in terms of *ka*, this work confirms an interplay between three key factors which can influence bond strength and can be insightful for the design of materials with specific properties. The three main factors influencing *π*–hole interaction strength in systems **1–14** are as follows: (1) aryl-substituent effects; where F–substituents polarization of aryl C–atoms which will encourage or discourage interactions between acceptor ligands and the aryl ring. Since these effects indirectly influence the *π*–hole interaction by affecting the nature of the aryl ring, aryl substituent effects are the least significant of the three effects; (2) the nature of the atoms which form the aryl ring, where presence of nitrogen can substantially increase strength of the *π*–hole interaction, where the

more N the better; and (3) Presence of HBs and SBIs between *π*–hole acceptor/donor, where strength of the SBI correlates positively with strength of the *π*–hole interaction. HBs can have a substantial effect on strength of the *π*–hole interaction, depending on the directionality; where if the *π*–hole donor is the HB acceptor, strength of the *π*–hole interaction increases. Conversely, if HB donation is in the same direction as *π*–hole donation, the *π*–hole interaction will be weakened substantially. Future goals are to refine computational *ωμ* harmonic scaling factors, and to expand this research on aryl *π*–hole interactions to a large number of systems, including halogen anions, CO, and OCH – 3as acceptors.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2073-4352/10/7/556/s1, Figure S1: Description of the 9 possible local modes between the monomers of a dimeric system; Table S1: Description of the videos showing selected normal mode vibrations for **R2** and system **1**. The videos are uploaded as separate files; Table S2: Cartesian atomic coordinates of optimized equilibrium geometries for all model species.

**Author Contributions:** Conceptualization, S.Y., M.F., and E.K.; methodology, S.Y., M.F., Y.T., W.Z., and E.K.; validation, S.Y., M.F., Y.T., and E.K.; programming, W.Z.; formal analysis, S.Y.; investigation, S.Y.; resources, E.K.; data curation, S.Y.; writing—original draft preparation, S.Y.; writing—review and editing, M.F., and E.K.; visualization, S.Y.; supervision, E.K. and M.F.; funding acquisition, E.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Science Foundation gran<sup>t</sup> number CHE 1464906.

**Acknowledgments:** The authors thank SMU for providing computational resources. We thank Vytor Oliveira for helpful discussions.

**Conflicts of Interest:** The authors declare no conflicts of interest.
