Editing Electron configuration (section)

=== Shortcomings of the aufbau principle ===
The aufbau principle rests on a fundamental postulate that the order of orbital energies is fixed, both for a given element and between different elements; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactly{{efn|Electrons are [[identical particle]]s, a fact that is sometimes referred to as "indistinguishability of electrons". A one-electron solution to a many-electron system would imply that the electrons could be distinguished from one another, and there is strong experimental evidence that they can't be. The exact solution of a many-electron system is a [[N-body problem|''n''-body problem]] with ''n''&nbsp;≥&nbsp;3 (the nucleus counts as one of the "bodies"): such problems have evaded [[Mathematical analysis|analytical solution]] since at least the time of [[Leonhard Euler|Euler]].}} (although there are mathematical approximations available, such as the [[Hartree–Fock method]]).

The fact that the aufbau principle is based on an approximation can be seen from the fact that there is an almost-fixed filling order at all, that, within a given shell, the s-orbital is always filled before the p-orbitals. In a [[hydrogen-like atom]], which only has one electron, the s-orbital and the p-orbitals of the same shell have exactly the same energy, to a very good approximation in the absence of external electromagnetic fields. (However, in a real hydrogen atom, the [[energy level]]s are slightly split by the magnetic field of the nucleus, and by the [[quantum electrodynamic]] effects of the [[Lamb shift]].)