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Molecular adsorption on surfaces plays a central role in catalysis,corrosion, desalination, and many other processes of relevance to industry andthe natural world. Few adsorption systems are more ubiquitous or of morewidespread importance than those involving water and carbon, and for amolecular level understanding of such interfaces water monomer adsorption ongraphene is a fundamental and representative system. This system isparticularly interesting as it calls for an accurate treatment of electroncorrelation effects, as well as posing a practical challenge to experiments.Here, we employ many-body electronic structure methodologies that can berigorously converged and thus provide faithful references for themolecule-surface interaction. In particular, we use diffusion Monte-Carlo(DMC), coupled cluster (CCSD(T)), as well as the random phase approximation(RPA) to calculate the strength of the interaction between water and anextended graphene surface. We establish excellent, sub-chemical, agreementbetween the complementary high-level methodologies, and an adsorption energyestimate in the most stable configuration of approximately -100\,meV isobtained. We also find that the adsorption energy is rather insensitive to theorientation of the water molecule on the surface, despite different bindingmotifs involving qualitatively different interfacial charge reorganisation. Inproducing the first demonstrably accurate adsorption energies for water ongraphene this work also resolves discrepancies amongst previously reportedvalues for this widely studied system. It also paves the way for more accurateand reliable studies of liquid water at carbon interfaces with cheapercomputational methods, such as density functional theory and classicalpotentials.

On the physisorption of water on graphene: Sub-chemical accuracy from many-body electronic structure methods