With respect to the electrostatic maps, our results suggest that a critical reassessment of the existing approaches for the construction of electrostatic maps is necessary. To this end, we suggest two complementary lines of research. First, it might be warranted to reinvestigate the functional form underlying electrostatic maps, and possibly go beyond a linear dependence on the local electric field and field gradient, and to assess the dependence of the electrostatic shifts on local mode parameters in more details.