Proton transfer in hydrogen bond dimers formed by acetate anion plus 4-methyl-imidazole, in both neutral and protonated forms, is studied by means of ab initio correlated calculations at the MP2/6-311++G(d,p) level of theory. These two dimers are selected as systems displaying a short and strong hydrogen bond with possible low barriers to proton transfer, also these systems resemble the dyad formed by histidine aspartate which is present in a variety of enzymes whose catalytic mechanisms involve the formation of short hydrogen bonds in the active site. The purpose of this job is twofold: we focus here on the effect of the polarity of the surrounding medium on the hydrogen bond, and on the other hand we analyse the relevance of the intermonomeric distance for the low barrier to proton transfer between the partners of the dimer. We have carried out an investigation for a number of intermonomeric distances and it was found that polar solvents and short intermonomeric distances lower the barrier, enhancing in that way the proton transfer between neutral imidazole and acetate. However, the binding energy of the dimer does not follow necessarily the same pattern. In the case of protonated imidazole no double well is found at all in the potential energy curve (not even in polar media) and barrierless proton transfer to acetate occurs at the shortest intermonomeric distances.