The circle centers lie on the molecule axis z at the coordinates z 1 = ± z 2 = z. The model assumes that the electrons move with constant speed on circular trajectories of radii ρ 1 = ρ 2 = ρ.

2 displays the Bohr model for a hydrogen molecule, in which two nuclei with charges Z| e| are separated by a fixed distance R (adiabatic approximation), and the two electrons move in the space between them. We next outline Bohr's insightful picture and our extensions.įig. 3, we present a simple continuation of the line of thought that Bohr was following, which is indeed asymmetric and provides a good quantitative picture of H 2 at small and large R. Sommerfeld even sensed that the symmetric configuration was suspect. As with the Bohr atomic picture, it contains valuable insight and can provide a good analytical description of molecular behavior. It is somewhat ironic that the Bohr picture of the molecule never caught on. It will hardly be as symmetrically built as the model exhibited in 22.” His figure 22 is the same as our symmetric configuration in Fig. Sommerfeld, in his seminal book ( 5), provided the following apt assessment: “We shall now describe a little more fully the model that Bohr has suggested for the constitution of the hydrogen molecule H 2, although, nowadays, we can take only a historical interest in it.” After some discussion, he asks, “But is it correct?” To which he answers, “Only a short while ago, even while this book was in its first edition, we were inclined to accept it.” And later he concludes, “Thus the true model of the H 2 molecule is still unknown. Any realistic model must show the ground-state potential energy function dissociating to H + H. 1.Ĭlearly, the Bohr picture of a molecule goes wrong at large R. Please note a similarity between the symmetric configuration 1 and Bohr's sketch of H 2 molecule in Fig. Energy E( R) of H 2 molecule for four electron configurations ( Upper) as a function of internuclear distance R calculated within the Bohr model (solid lines) and the exact ground and first excited state energy (dots).** Unit of energy is 1 atomic unit (a.u.) = 27.21 eV, and unit of distance is the Bohr radius.

Bohr atom model