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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electron configuration | 5/6 | https://en.wikipedia.org/wiki/Electron_configuration | reference | science, encyclopedia | 2026-05-05T10:52:21.981173+00:00 | kb-cron |
=== Other exceptions to Madelung's rule === There are several more exceptions to Madelung's rule among the heavier elements, and as atomic number increases it becomes more and more difficult to find simple explanations such as the stability of half-filled subshells. It is possible to predict most of the exceptions by Hartree–Fock calculations, which are an approximate method for taking account of the effect of the other electrons on orbital energies. Qualitatively, for example, the 4d elements have the greatest concentration of Madelung anomalies, because the 4d–5s gap is larger than the 3d–4s and 5d–6s gaps. For the heavier elements, it is also necessary to take account of the effects of special relativity on the energies of the atomic orbitals, as the inner-shell electrons are moving at speeds approaching the speed of light. In general, these relativistic effects tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals. This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p1/2 orbital as well and cause its occupancy in the ground state), as relativity intervenes to make the 7s orbitals lower in energy than the 6d ones. The table below shows the configurations of the f-block (green) and d-block (blue) atoms. It shows the ground state configuration in terms of orbital occupancy, but it does not show the ground state in terms of the sequence of orbital energies as determined spectroscopically. For example, in the transition metals, the 4s orbital is of a higher energy than the 3d orbitals; and in the lanthanides, the 6s is higher than the 4f and 5d. The ground states can be seen in the Electron configurations of the elements (data page). However this also depends on the charge: a calcium atom has 4s lower in energy than 3d, but a Ca2+ cation has 3d lower in energy than 4s. In practice the configurations predicted by the Madelung rule are at least close to the ground state even in these anomalous cases. The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding, as do the empty p orbitals in transition metals. Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done, to emphasise the filling order and to clarify that even orbitals unoccupied in the ground state (e.g. lanthanum 4f or palladium 5s) may be occupied and bonding in chemical compounds. (The same is also true for the p-orbitals, which are not explicitly shown because they are only actually occupied for lawrencium in gas-phase ground states.)
The various anomalies describe the free atoms and do not necessarily predict chemical behavior. Thus for example neodymium typically forms the +3 oxidation state, despite its configuration [Xe] 4f4 5d0 6s2 that if interpreted naïvely would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as [Rn] 5f3 6d1 7s2 is not very stable in the +3 oxidation state either, preferring +4 and +6. The electron-shell configuration of elements beyond hassium has not yet been empirically verified, but they are expected to follow Madelung's rule without exceptions until element 120. Element 121 should have the anomalous configuration [Og] 8s2 5g0 6f0 7d0 8p1, having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models, but Madelung's rule is expected to break down due to the closeness in energy of the 5g, 6f, 7d, and 8p1/2 orbitals. That said, the filling sequence 8s, 5g, 6f, 7d, 8p is predicted to hold approximately, with perturbations due to the huge spin-orbit splitting of the 8p and 9p shells, and the huge relativistic stabilisation of the 9s shell.
== Open and closed shells ==
In the context of atomic orbitals, an open shell is a valence shell which is not completely filled with electrons or that has not given all of its valence electrons through chemical bonds with other atoms or molecules during a chemical reaction. Conversely a closed shell is obtained with a completely filled valence shell. This configuration is very stable. For molecules, "open shell" signifies that there are unpaired electrons. In molecular orbital theory, this leads to molecular orbitals that are singly occupied. In computational chemistry implementations of molecular orbital theory, open-shell molecules have to be handled by either the restricted open-shell Hartree–Fock method or the unrestricted Hartree–Fock method. Conversely a closed-shell configuration corresponds to a state where all molecular orbitals are either doubly occupied or empty (a singlet state). Open shell molecules are more difficult to study computationally.
== Noble gas configuration ==
Noble gas configuration is the electron configuration of noble gases. The basis of all chemical reactions is the tendency of chemical elements to acquire stability. Main-group atoms generally obey the octet rule, while transition metals generally obey the 18-electron rule. The noble gases (He, Ne, Ar, Kr, Xe, Rn) are less reactive than other elements because they already have a noble gas configuration. Oganesson is predicted to be more reactive due to relativistic effects for heavy atoms.