Anatoly Svidzinsky, Marlan Scully, and Dudley Herschbach have illustrated well how the molecular theory might have looked had quantum mechanics not been invented. It’s worth noting that Niels Bohr was not alone in his attempts to extend semiclassical mechanics to systems more complex than the hydrogen atom. From 1913 to 1925, many semiclassical models of two-electron systems were proposed.
As we see from the authors’ figure 3a, Bohr assumed that electrons in hydrogen molecules move around the molecular axis out of phase. It is a remarkable fact that Werner Heisenberg put forward in 1922 a two-electron atomic model that had electrons moving similarly out of phase and that ascribed a fractional quantum number (½) to the bending mode of the configuration.1 Although Heisenberg’s model predicted the ground-state helium level, which was in excellent agreement with the spectroscopic data, Bohr opposed the model, since a noninteger quantum number was considered sacrilege. For the same reason, Bohr never published his own results. However, the asynchronous two-electron atomic model turned out to be the fertile one, though the corresponding classical configurations can have very complex structure.2
