Although it is possible to model the electronic structure of molecules with great accuracy, such numerical methods provide little intuitive insight into electron–electron interactions. In two papers, in Physical Review Letters and Proceedings of the National Academy of Sciences, Anatoly Svidzinsky and colleagues 1,2 have taken a trip down memory lane to uncover an intriguing approach to understanding the chemical bonds within molecules, and at the same time take a fresh perspective on the "old quantum theory" developed by Niels Bohr in 1913.
The famous Bohr model introduced the quantized nature of electron orbits in one-electron atoms, long before wave mechanics was developed. Much later, in the 1980s, the so-called D-scale approach provided a quantitative description of the two electrons surrounding a helium nucleus, by generalizing the Schrödinger equation to D dimensions; the situation relevant to the three-dimensional world is deduced by interpolating between the D = 1 and the D 
limits.
However, neither approach — although each successful in its own realm — has so far yielded satisfactory results for two-centre problems, such as the hydrogen molecule. Svidzinsky et al. have re-examined the D-scale approach and show how a simple modification can fix its shortcomings 1. Whereas the original did not even predict a bound ground state for the hydrogen molecule, their new version provides quantitative values that are remarkably close to those obtained from extensive computer simulations. Furthermore, the authors show that, in the large-D limit, dimensional scaling can reproduce the Bohr model — notably by bringing in quantum mechanical concepts that were completely unknown to Bohr at the time.
Svidzinsky et al. explore further 2 this link between 'new' and 'old', to demonstrate that Bohr's planetary model is indeed able to quantitatively describe the hydrogen molecule and some more complicated molecules such as diatomic lithium — and gives a clear physical picture of how a chemical bond forms.
