The diatomic neutral oxides and their ions, MO0,+/-, M = Sc, Ti. Cr, and Mn, have been studied through multireference configuration interaction and coupled-cluster methods With the purpose to paint a more comprehensive and detailed picture on these not so easily tamed systems, we have constructed complete potential energy curves for a large number of states of all Mo-0,Mo-+/-'s reporting structural and spectroscopic properties. Our overall results are in very good agreement with the, in general limited, experimental data The always difficult to be pinpointed "nature of the chemical bond" becomes more recondite for these highly open ionic-covalent species. We have tried to give some answers as to the bonding interactions using simple valence-bond-Lewis diagrams in conjunction with Mulliken populations and the symmetry of the in situ atoms. It is our belief that, particularly for this kind of molecule, molecular orbital concepts are of limited help for a consistent rationalization of the bond formation