Electronic Structure of Diatomic Molecules
What makes the solution for the electronic motion in a molecule so much more difficult from that for an atom (which as we have seen is certainly not easy!) is that the problem, in general, is multicentered. In an atom, with a single nucleus, one may use spherical coordinates for the multielectron problem. The angular part of the problem is effectively solved by invoking spherical harmonics for the basis functions for each electron. In a molecule, spherical symmetry is broken, and one cannot even use the same quantum numbers that one could use for an atom. It is little wonder that most texts that do treat the quantum mechanics of molecules ignore the atomic underpinnings. One can hardly blame the authors; the methodology is fundamentally different.