In this study, we present a thorough benchmarking of our direct anharmonic vibrational variation-perturbation approach for adsorbed molecules on surfaces. We then use our method to describe the vibrational structure of a water molecule adsorbed on a Pt(111) surface and compare our results with the available experimental data. By using an explicitly correlated hybrid method to describe the molecule-surface interaction, we improve on the initial periodic PBE/DZP potential energy landscape and obtain vibrational frequencies that are of near-experimental accuracy. We introduce an implementation of anharmonic z-polarized IR intensity calculation and explain the absence of antisymmetric O-H stretch in the experimental data for the adsorbed water molecule, while the symmetric O-H stretch is predicted to be visible.