The past decade has seen the first attempts at quantifying a semiclassical description of electrons in molecules. The challenge in this endeavor is to find potentials for electron interactions that adequately capture quantum effects. As has been the case for density functionals, the challenge is particularly great for the effects that follow from the requirement for wave function antisymmetry. Here we extend our empirical inquiry into effective potentials, from prior work on the monatomic atoms and ions of nonmetals, to diatomic molecules and ions formed by these elements. Newly adjusted and trained for the longer distances relevant to diatomics, pairwise potentials are able to fit the bond orders and magnetic properties of homonuclear species. These potentials are then found to do an excellent job of predicting the magnetism of heteronuclear species. In these molecules the predicted distribution of electrons also correctly reflects increasing ionic character with increasing difference in the electronegativities of the participating atoms. The distinctive features of the current potential are discussed, along with issues calling for further improvements.