The interlayer pi-pi interaction between finite-size models of graphene sheets was investigated by using a density functional theory method, augmented with an empirical R(-6) term for the description of long-range dispersive interaction; these were calibrated by studying the pi-pi interaction between various benzene dimer configurations and comparing the results with previous calculations. For stacked bilayers (dimers) and multilayers of polyaromatic hydrocarbons, which serve as molecular models of graphene sheets, we found that binding energies and energy gaps are strongly dependent on their sizes, while the stacking order and the number of stacked layers have a minor influence. The remarkably broad variation of the energy gap, ranging from 1.0 to 2.5 eV, due mainly to variation of the model size, suggests the potential of broadband luminescence in the visible range for carbon-based nanomaterials that have pi-pi interacting.
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