  A first-principles study of the adsorption of a single water molecule on a
layer of graphitic carbon nitride employing an embedding approach is presented.
The embedding approach involves an algorithm to obtain localized Wannier
orbitals of various types expanded in a plane-wave basis and intrinsic atomic
orbital projectors. The localized occupied orbitals are employed in combination
with unoccupied natural orbitals to perform many-electron perturbation theory
calculations of local fragments. The fragments are comprised of a set of
localized orbitals close to the adsorbed water molecule. Although the surface
model contains more than 100 atoms in the simulation cell, the employed
fragments are small enough to allow for calculations using high-level theories
up to the coupled cluster ansatz with single, double and perturbative triple
particle-hole excitation operators (CCSD(T)). To correct for the missing
long-range correlation energy contributions to the adsorption energy, we embed
CCSD(T) theory into the direct random phase approximation, yielding rapidly
convergent adsorption energies with respect to the fragment size. Convergence
of computed binding energies with respect to the virtual orbital basis set is
achieved employing a number of recently developed techniques. Moreover, we
discuss fragment size convergence for a range of approximate many-electron
perturbation theories. The obtained benchmark results are compared to a number
of density functional calculations.
