The electronic structure of representative hydrogen bonded systems: hydrogen cyanide, imidazole and malonic acid have been studied at the non-empirical level. The role of the dimensionality on the potential barrier for the proton transfer has been examined. It was shown that it depends on the crystal structure and only in some cases like hydrogen cyanide or imidazole the relevant crystals may be considered as one-dimensional. However, for more complicated crystallographic structures, e.g. malonic acid, the evaluated barrier is strongly dependent on the dimensionality taken into account in our calculations.