An alternative synthesis for M(κ2-bipy)4 (M = La, Ce) and [Li(thf)4][M(κ2-bipy)4] (M = Tb, Dy) and the crystal structures for M = La, Ce, and Tb are described. The isomorphous and isostructural neutral molecules, M = La and Ce, are polymeric in the solid-state, as are those of M = Sm and Eu, which were reported in earlier work. The polymeric network is built from eight coordinate units whose geometry in all four cases is that of a square prism. The known molecules, M = Yb and Lu, are also polymeric, but the eight coordinate units have dodecahedral geometries. The structure of the anions in the separated ion pair, [Li(thf)4][M(κ2-bipy)4], in which Tb is reported in this work and Lu is known, are monomeric with geometries that are between that of a square antiprism and a dodecahdron. The electronic structure, from CASSCF multireference quantum mechanical calculations, shows that the electronic ground states for M = La and Lu are multiconfigurational spin doublets and those for the M = Ce and Yb are multiconfigurational spin triplets. This is confirmed by magnetic susceptibility studies as a function of temperature that are consistent with the metals (La, Ce, Sm, Tb, Dy, Yb, and Lu) being trivalent, as are the LIII-edge XANES spectra (Ce, Yb), and divalent for Eu. The multiconfigurational nature of the ground states, developed from CASSCF molecular orbital calculations, renders a single Lewis structure and a single reference molecular orbital representation misleading. The results from the multireference calculations are extended to the other lanthanide molecules and are the genesis of a new model for understanding the magnetic properties of these molecules.