Weak and strong π interactions between two monomers - assessed with local vibrational mode theory

We introduce in this work a unique parameter for the quantitative assessment of the intrinsic strength of the π–interaction between two monomers forming a complex. The new parameter is a local intermonomer stretching force constant, based on the local mode theory, originally developed by Konkoli and Cremer, and derived from the set of nine possible intermonomer normal vibrational modes. The new local force constant was applied to a diverse set of more than 70 molecular complexes, which was divided into four groups. Group 1 includes atoms, ions, and small molecules interacting with benzene substituted substituted benzenes. Group 2 includes transition metal hydrides and oxides interacting with benzene while Group 3 involves ferrocenes, chromocenes, and titanium sandwich compounds. Group 4 presents an extension to oxygen π–hole interactions in comparison with in-plane hydrogen bonding. We found that the strength of the π–interactions in these diverse molecular complexes can vary from weak interactions with predominantly electro-static character, found e.g., for argon-benzene complexes to strong interactions with a substantial covalent nature, found e.g., for ferrocenes; all being seamlessly described and compared with the new intermonomer local mode force constant, which also outperforms other descriptors such as an averaged force constant or a force constant guided by the electron density bond paths. We hope that our ﬁndings will inspire the community to apply the new parameter also to other intermonomer π–interactions, enriching in this way the broad ﬁeld of organometallic chemistry with a new eﬃcient assessment tool.