Using density functional theory (DFT) with dispersion correction and ab initio post Hartree-Fock methods, we treat the bonding, the structure, the stability, and the spectroscopy of the complexes between Znq+ and imidazole (Im), Zn(q+)Im(n) (where q = 0, 1 and 2; n = 1-4). These entities are subunits of zeolitic imidazolate frameworks (ZIFs) and Zn-enzymes, which possess relevant roles in industrial and biological domains, respectively. We also investigate the Im(n) (n = 2-4) clusters for comparison. For each species, we determine several new structures that were not found previously. Our calculations show a competition between atomic metal solvation, by either sigma-type interactions or pi-stacking type interaction, and proton transfer through hydrogen bonding (H-bonding) in charged species. This results in several geometrical environments around the metal. These are connected with structural properties and the functional role of Zn cation within ZIFs and Zn-enzymes. Moreover, we show that the Zn(2+)Im(n) subunits do not absorb in the visible domain, winch may be related to the photostability of ZIFs. Our findings are important for the development of new applications of ZIFs and metalloenzymes.