Editing Energy level (section)

==== Electron–electron interactions in atoms ====
If there is more than one electron around the atom, electron–electron interactions raise the energy level. These interactions are often neglected if the spatial overlap of the electron wavefunctions is low.

For multi-electron atoms, interactions between electrons cause the preceding equation to be no longer accurate as stated simply with {{mvar|Z}} as the [[atomic number]]. A simple (though not complete<!--
**Note** what is hinted at here is that screening is only a mean-field effect. Electron-electron interactions also lead to dynamic correlation-exchange energy shifts. If strong enough, correlation-exchange can prevent us from being able to look at the atom in terms of orbitals at all, leaving only the consideration of many-body states. However, in the case of atoms the correlation-exchange seems to be a small perturbation (usually).
-->) way to understand this is as a [[shielding effect]], where the outer electrons see an effective nucleus of reduced charge, since the inner electrons are bound tightly to the nucleus and partially cancel its charge. This leads to an approximate correction where {{mvar|Z}} is substituted with an [[effective nuclear charge]] symbolized as {{math|''Z''<sub>eff</sub>}} that depends strongly on the principal quantum number.
<math display="block">E_{n,\ell} = - h c R_{\infty} \frac{{Z_{\rm eff}}^2}{n^2}</math>

In such cases, the orbital types (determined by the [[azimuthal quantum number]] {{mvar|ℓ}}) as well as their levels within the molecule affect {{math|''Z''<sub>eff</sub>}} and therefore also affect the various atomic electron energy levels. The [[Aufbau principle]] of filling an atom with electrons for an [[electron configuration]] takes these differing energy levels into account. For filling an atom with electrons in the ground state, the lowest energy levels are filled first and consistent with the [[Pauli exclusion principle]], the [[Aufbau principle]], and [[Hund's rule]].