Hydrogen has been proposed as a long-term non-fossil fuel to be used in a future ideal carbon-neutral energetic economy. However, its low volumetric energy density hinders its storage and transportation. Metal-organic frameworks (MOFs) represent very promising materials for this purpose due to their very extended surface areas. Azolates, in particular tetrazolates, are - together with carboxylate functionalities - very common organic linkers connecting metallic secondary building units in MOFs. This study addresses, from a theoretical perspective, the H-2 adsorptive properties of tetrazolate linkers at the molecular level, following a size-progressive approach. Specifically, we have investigated how the physisorption energies and geometries are affected when changing the environment of the linker by considering the azolates in the gas phase, immersed in a finite cluster, or being part of an infinite extended crystal material. Furthermore, we also study the H-2 adsorptive capacity of these linkers within the cluster model.