We present a density-functional theoretical investigation of the electronic and magnetic properties of octametallic Cr-based molecular antiferromagnetic rings. The presence of the divalent magnetic ion M unbalances the charge and the spin of the parent Cr-8 ring, leading to a finite total spin in the molecules. Results are presented for Cr-8, i.e., [Cr8F8(O2CH)(16)] (1), and for Cr7M rings belonging to two different derivatives, i.e., [Me2NH2][Cr7MF8(O2CH)(16)], with M=Ni, Mn, Fe, and Cu, and Me=CH3 (2, "green" derivative), and [Cr-7 NiF3(C6H10NO5)(O2CH)(15) (H2O)] (3,"purple" derivative). Exchange interaction parameters have been extracted from broken-symmetry calculations and compared with the available experiments; in agreement with them, we find that exchange parameters are rather similar in the two derivatives, although somewhat larger in the "purple" derivative. The analysis of the electronic properties shows some differences depending on M, in particular in the size of the highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) gaps. For all the "green" rings we observe that the HOMOs are localized on the divalent ion site, while the HOMOs for the "purple" Cr7Ni have a more delocalized nature; LUMOs, instead, are, except for "green" Cr7Cu, localized on the Cr atoms opposite to the M site. We discuss how these findings may show up in terms of an asymmetric I-V curve in molecular junctions working in the sequential tunneling regime, or help in discerning the orientation of the molecules with respect to a surface, in scanning tunneling experiments.