Due to their current and future technological applications, including realisation of water filters and desalination membranes, water adsorption on graphitic sp$^{2}$-bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and non-covalent interactions in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed textbf{WaC18}), which includes a single water molecule interacting with a broad range of carbon structures, and various bulk (3D) and two dimensional (2D) ice polymorphs. The performance of 28 approaches, including semi-local exchange-correlation functionals, non-local (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, are tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depends crucially on the DFT approach, ranging from 135 meV for LDA to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of: generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.
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