  Molecular adsorption on surfaces plays an important part in catalysis,
corrosion, desalination, and various other processes that are relevant to
industry and in nature. As a complement to experiments, accurate adsorption
energies can be obtained using various sophisticated electronic structure
methods that can now be applied to periodic systems. The adsorption energy of
water on boron nitride substrates, going from zero to 2-dimensional
periodicity, is particularly interesting as it calls for an accurate treatment
of polarizable electrostatics and dispersion interactions, as well as posing a
practical challenge to experiments and electronic structure methods. Here, we
present reference adsorption energies, static polarizabilities, and dynamic
polarizabilities, for water on BN substrates of varying size and dimension.
Adsorption energies are computed with coupled cluster theory, fixed-node
quantum Monte Carlo (FNQMC), the random phase approximation (RPA), and second
order M{\o}ller-Plesset (MP2) theory. These explicitly correlated methods are
found to agree in molecular as well as periodic systems. The best estimate of
the water/h-BN adsorption energy is $-107\pm7$ meV from FNQMC. In addition, the
water adsorption energy on the BN substrates could be expected to grow
monotonically with the size of the substrate due to increased dispersion
interactions but interestingly, this is not the case here. This peculiar
finding is explained using the static polarizabilities and molecular dispersion
coefficients of the systems, as computed from time-dependent density functional
theory (DFT). Dynamic as well as static polarizabilities are found to be highly
anisotropic in these systems. In addition, the many-body dispersion method in
DFT emerges as a particularly useful estimation of finite size effects for
other expensive, many-body wavefunction based methods.
