The "inverse hydration" of neutral complexes of Pt(II) by an axial water molecule, whose one OH-bond is oriented toward Pt, has been the subject of recent works, theoretical as well as experimental. To study the influence of the ligands on this non-conventional H-bond, we extend here our previous energy calculations, using the second-order Moeller-Plesset perturbation theory (MP2) method together with the Dolg-Pélissier pseudopotential for platinum, to various neutral complexes including the well-known chemotherapeutic agent "cisplatin". The stabilization energy, depending on the nature and the configuration of platinum ligands, is dominated by the same important dispersive component, for all the investigated complexes. For a further characterization of this particular H-bond, we used the atoms in molecules theory (AIM) and the topological analysis of the electron localization function (ELF). The charge transfer occurring from the complex to the water molecule and the Laplacian of the density at the bond critical point between water and Pt are identified as interesting AIM descriptors of this non-conventional H-bond. Beyond this AIM analysis, we show that the polarization of the ELF bonding O-H basin involved in the non-conventional H-bond is enhanced during the approach of the water molecule to the Pt complexes. When the water medium, treated in an implicit solvation model, is taken into account, the interaction energies become independent on the nature and configuration of platinum ligands. However, the topological descriptors remain qualitatively unchanged.