The adsorption energies and orientation of methanol on graphene are determined from first-principles density functional calculations. We employ the well-tested vdW-DF method that seamlessly includes dispersion interactions with all of the more close-ranged interactions that result in bonds like the covalent and hydrogen bonds. The adsorption of a single methanol molecule and small methanol clusters on graphene are studied at various coverages. Adsorption in clusters or at high coverages (less than a monolayer) is found to be preferable, with the methanol C-O axis approximately parallel to the plane of graphene. The adsorption energies calculated with vdW-DF are compared with previous DFT-D and MP2-based calculations for single methanol adsorption on flakes of graphene (polycyclic aromatic hydrocarbons). For the high coverage adsorption energies we also find reasonably good agreement with previous desorption measurements.
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