Nanoscale π–π stacked molecules are bound by collective charge fluctuations

Non-covalent π−π interactions are central to chemical and biological processes, yet the full understanding of their origin that would unite the simplicity of empirical approaches with the accuracy of quantum calculations is still missing. Here we employ a quantum-mechanical Hamiltonian model for van der Waals interactions, to demonstrate that intermolecular electron correlation in large supramolecular complexes at equilibrium distances is appropriately described by collective charge fluctuations. We visualize these fluctuations and provide connections both to orbital-based approaches to electron correlation, as well as to the simple London pairwise picture. The reported binding energies of ten supramolecular complexes obtained from the quantum-mechanical fluctuation model joined with density functional calculations are within 5% of the reference energies calculated with the diffusion quantum Monte-Carlo method. Our analysis suggests that π−π stacking in supramolecular complexes can be characterized by strong contributions to the binding energy from delocalized, collective charge fluctuations—in contrast to complexes with other types of bonding