Influence of Pancake Bonding and of PAH Radicals on the Stacking Properties of Carbon Nanomaterials: Metadynamics Simulations with Quantum Chemical Methods

Pancake bonding represents an interesting intermolecular bonding type involving radical and diradical polycyclic aromatic hydrocarbons (PAHs) in stacked arrangements. It includes covalent contributions leading to stronger interactions in comparison to conventional noncovalent π–π stacking. The structure of PAH radical clusters capable of pancake bonding and their interaction with the surrounding nonreactive PAH environment are of great relevance for the understanding of carbon nanomaterials. In this work, the properties of pancake bonding in PAH ensembles are investigated by means of metadynamics (MTD) simulations using the Conformer–Rotamer Ensemble Sampling Tool and the quantum chemical tight-binding GFN2-xTB method. The obtained structures were then validated with a more accurate density functional theory. Structural ensembles of pure clusters of seven prototypical open-shell PAHs (the radicals phenalenyl, olympicenyl, and fluorenyl, the biradicals triangulene and heptazethrene, and the biradicaloids pentacene and nonacene) and mixed clusters including closed-shell pyrene were investigated. Low-spin and high-spin aggregates were considered. Stacking motifs were found to include pancake bonding up to dimers and trimers and general PAH aggregation up to pentamers. Additionally, σ-bond formation was found to be common in the low-spin state and generally reduced aggregation generally. Importantly, pyrene was also found to contribute significantly to PAH aggregation with the above open-shell PAHs but was almost entirely excluded from pancake-bonding interactions. The potential magnetic character of the high-spin PAH clusters was analyzed by using the number-weighted fractional occupation density method. The corresponding integrated NFOD values were found to generally increase with the increasing spin multiplicity and molecular size. However, the singlet–triplet (S–T) energy gap between high-spin and low-spin states was found to be relatively large due to antiferromagnetic pancake bonding and due to σ-bond formation. A possible way to reduce the S–T energy gap could be found in the addition of bulkier substituents to the individual PAHs that would reduce pancake bonding and create weakly interacting PAH radicals with low S–T gaps.