Editing Electron configuration (section)

=== Other exceptions to Madelung's rule ===
There are several more exceptions to [[Aufbau principle#Madelung energy ordering rule|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,<ref>{{cite journal | last = Meek | first = Terry L. |author2=Allen, Leland C. | title = Configuration irregularities: deviations from the Madelung rule and inversion of orbital energy levels | journal = [[Chemical Physics Letters]] | volume = 362 | issue = 5–6 | pages = 362–64 | doi=10.1016/S0009-2614(02)00919-3 | year = 2002|bibcode = 2002CPL...362..362M }}</ref> 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.<ref name=primefan>{{cite web |url=http://www.primefan.ru/stuff/personal/ptable.pdf |title=Периодическая система химических элементов Д. И. Менделеева |trans-title=D. I. Mendeleev's periodic system of the chemical elements |last=Kulsha |first=Andrey |date=2004 |website=primefan.ru |access-date=17 May 2020 |language=ru}}</ref>

For the heavier elements, it is also necessary to take account of the [[Relativistic quantum chemistry|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<ref>{{GoldBookRef|file=RT07093|title=relativistic effects}}</ref> tend to decrease the energy of the s-orbitals in relation to the other atomic orbitals.<ref>{{cite journal | first = Pekka | last = Pyykkö | title = Relativistic effects in structural chemistry | journal = [[Chemical Reviews]] |year = 1988 | volume = 88 | pages = 563–94 | doi = 10.1021/cr00085a006 | issue = 3}}</ref> This is the reason why the 6d elements are predicted to have no Madelung anomalies apart from lawrencium (for which relativistic effects stabilise the p<sub>1/2</sub> 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 Ca<sup>2+</sup> 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.<ref>See the [https://physics.nist.gov/PhysRefData/Handbook/periodictable.htm NIST tables]</ref> The empty f orbitals in lanthanum, actinium, and thorium contribute to chemical bonding,<ref name=Glotzel>{{cite journal |last1=Glotzel |first1=D. |date=1978 |title=Ground-state properties of f band metals: lanthanum, cerium and thorium |journal=Journal of Physics F: Metal Physics |volume=8 |issue=7 |pages=L163–L168 |doi=10.1088/0305-4608/8/7/004|bibcode=1978JPhF....8L.163G }}</ref><ref name=LaF3>{{cite journal |last1=Xu |first1=Wei |last2=Ji |first2=Wen-Xin |first3=Yi-Xiang |last3=Qiu |first4=W. H. Eugen |last4=Schwarz |first5=Shu-Guang |last5=Wang |date=2013 |title=On structure and bonding of lanthanoid trifluorides LnF<sub>3</sub> (Ln = La to Lu) |journal=Physical Chemistry Chemical Physics |volume=2013 |issue=15 |pages=7839–47 |doi=10.1039/C3CP50717C|pmid=23598823 |bibcode=2013PCCP...15.7839X }}</ref> as do the empty p orbitals in transition metals.<ref>[https://pubs.rsc.org/en/content/articlehtml/2015/sc/c5sc02776d Example for platinum]</ref>

Vacant s, d, and f orbitals have been shown explicitly, as is occasionally done,<ref>See for example [http://www.primefan.ru/stuff/chem/front2019.png this Russian periodic table poster] by A. V. Kulsha and T. A. Kolevich</ref> 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.)
{| class="wikitable"
|+Electron shells filled in violation of Madelung's rule<ref>{{cite book|first1= G. L.|last1= Miessler |first2= D. A.|last2= Tarr|title=Inorganic Chemistry|edition=2nd |publisher=Prentice-Hall |year=1999|page=38}}</ref> (red)<br />Predictions for elements 109–112<ref name=Haire />
|-
! colspan=3 | Period 4 || &nbsp; || colspan=3 | Period 5 || &nbsp; || colspan=3 | Period 6 || &nbsp; || colspan=3 | Period 7
|-
! Element || Z || Electron Configuration || &nbsp; || Element || Z || Electron Configuration || &nbsp; || Element || Z || Electron Configuration || &nbsp; || Element || Z || Electron Configuration
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Lanthanum]] || 57 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> <span style="color:red;">4f<sup>0</sup> 5d<sup>1</sup></span> || &nbsp; || [[Actinium]] || 89 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>0</sup> 6d<sup>1</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Cerium]] || 58 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> <span style="color:red;">4f<sup>1</sup> 5d<sup>1</sup></span> || &nbsp; || [[Thorium]] || 90 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>0</sup> 6d<sup>2</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Praseodymium]] || 59 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>3</sup> 5d<sup>0</sup> || &nbsp; || [[Protactinium]] || 91 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>2</sup> 6d<sup>1</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Neodymium]] || 60 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>4</sup> 5d<sup>0</sup> || &nbsp; || [[Uranium]] || 92 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>3</sup> 6d<sup>1</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Promethium]] || 61 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>5</sup> 5d<sup>0</sup> || &nbsp; || [[Neptunium]] || 93 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>4</sup> 6d<sup>1</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Samarium]] || 62 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>6</sup> 5d<sup>0</sup> || &nbsp; || [[Plutonium]] || 94 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>6</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Europium]] || 63 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>7</sup> 5d<sup>0</sup> || &nbsp; || [[Americium]] || 95 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>7</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Gadolinium]] || 64 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> <span style="color:red;">4f<sup>7</sup> 5d<sup>1</sup></span> || &nbsp; || [[Curium]] || 96 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> <span style="color:red;">5f<sup>7</sup> 6d<sup>1</sup></span>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Terbium]] || 65 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>9</sup> 5d<sup>0</sup> || &nbsp; || [[Berkelium]] || 97 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>9</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Dysprosium]] || 66 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>10</sup> 5d<sup>0</sup> || &nbsp; || [[Californium]] || 98 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>10</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Holmium]] || 67 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>11</sup> 5d<sup>0</sup> || &nbsp; || [[Einsteinium]] || 99 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>11</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Erbium]] || 68 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>12</sup> 5d<sup>0</sup> || &nbsp; || [[Fermium]] || 100 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>12</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Thulium]] || 69 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>13</sup> 5d<sup>0</sup> || &nbsp; || [[Mendelevium]] || 101 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>13</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|f-block}}"
| colspan=3 | &nbsp; || &nbsp; || colspan=3 | &nbsp; || &nbsp; || [[Ytterbium]] || 70 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>0</sup> || &nbsp; || [[Nobelium]] || 102 || &#91;[[radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>0</sup>
|- bgcolor="{{element color|d-block}}"
| [[Scandium]] || 21 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>1</sup> || &nbsp; || [[Yttrium]] || 39 || &#91;[[krypton|Kr]]&#93; 5s<sup>2</sup> 4d<sup>1</sup> || &nbsp; || [[Lutetium]] || 71 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>1</sup> || &nbsp; || [[Lawrencium]] || 103 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> <span style="color:red;">6d<sup>0</sup> 7p<sup>1</sup></span>
|- bgcolor="{{element color|d-block}}"
| [[Titanium]] || 22 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>2</sup> || &nbsp; || [[Zirconium]] || 40 || &#91;[[krypton|Kr]]&#93; 5s<sup>2</sup> 4d<sup>2</sup> || &nbsp; || [[Hafnium]] || 72 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>2</sup> || &nbsp; || [[Rutherfordium]] || 104 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>2</sup>
|- bgcolor="{{element color|d-block}}"
| [[Vanadium]] || 23 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>3</sup> || &nbsp; || [[Niobium]] || 41 || &#91;[[krypton|Kr]]&#93; <span style="color:red;">5s<sup>1</sup> 4d<sup>4</sup></span> || &nbsp; || [[Tantalum]] || 73 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>3</sup> || &nbsp; || [[Dubnium]] || 105 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>3</sup>
|- bgcolor="{{element color|d-block}}"
| [[Chromium]] || 24 || &#91;[[argon|Ar]]&#93; <span style="color:red;">4s<sup>1</sup> 3d<sup>5</sup></span> || &nbsp; || [[Molybdenum]] || 42 || &#91;[[krypton|Kr]]&#93; <span style="color:red;">5s<sup>1</sup> 4d<sup>5</sup></span> || &nbsp; || [[Tungsten]] || 74 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>4</sup> || &nbsp; || [[Seaborgium]] || 106 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>4</sup>
|- bgcolor="{{element color|d-block}}"
| [[Manganese]] || 25 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>5</sup> || &nbsp; || [[Technetium]] || 43 || &#91;[[krypton|Kr]]&#93; 5s<sup>2</sup> 4d<sup>5</sup> || &nbsp; || [[Rhenium]] || 75 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>5</sup> || &nbsp; || [[Bohrium]] || 107 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>5</sup>
|- bgcolor="{{element color|d-block}}"
| [[Iron]] || 26 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>6</sup> || &nbsp; || [[Ruthenium]] || 44 || &#91;[[krypton|Kr]]&#93; {{red|5s<sup>1</sup> 4d<sup>7</sup>}} || &nbsp; || [[Osmium]] || 76 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>6</sup> || &nbsp; || [[Hassium]] || 108 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>6</sup>
|- bgcolor="{{element color|d-block}}"
| [[Cobalt]] || 27 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>7</sup> || &nbsp; || [[Rhodium]] || 45 || &#91;[[krypton|Kr]]&#93; <span style="color:red;">5s<sup>1</sup> 4d<sup>8</sup></span> || &nbsp; || [[Iridium]] || 77
|| &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>7</sup> || &nbsp; || [[Meitnerium]] || 109
|| &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>7</sup>
|- bgcolor="{{element color|d-block}}"
| [[Nickel]] || 28 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>8</sup> or <br /> &#91;[[argon|Ar]]&#93; <span style="color:red;">4s<sup>1</sup> 3d<sup>9</sup></span> ([[Nickel#Electron configuration dispute|disputed]])<ref>{{cite book |url=https://archive.org/details/periodictableits0000scer |url-access=registration |pages=[https://archive.org/details/periodictableits0000scer/page/239 239]–240 |title=The periodic table: its story and its significance |author=Scerri, Eric R. |publisher=Oxford University Press|year=2007 |isbn=978-0-19-530573-9}}</ref>|| &nbsp; || [[Palladium]] || 46 || &#91;[[krypton|Kr]]&#93; <span style="color:red;">5s<sup>0</sup> 4d<sup>10</sup></span> || &nbsp; || [[Platinum]] || 78 || &#91;[[xenon|Xe]]&#93; <span style="color:red;">6s<sup>1</sup></span> 4f<sup>14</sup> <span style="color:red;">5d<sup>9</sup></span> || &nbsp; || [[Darmstadtium]] || 110
|| &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>8</sup>
|- bgcolor="{{element color|d-block}}"
| [[Copper]] || 29 || &#91;[[argon|Ar]]&#93; <span style="color:red;">4s<sup>1</sup> 3d<sup>10</sup></span> || &nbsp; || [[Silver]] || 47 || &#91;[[krypton|Kr]]&#93; <span style="color:red;">5s<sup>1</sup> 4d<sup>10</sup></span> || &nbsp; || [[Gold]] || 79 || &#91;[[xenon|Xe]]&#93; <span style="color:red;">6s<sup>1</sup></span> 4f<sup>14</sup> <span style="color:red;">5d<sup>10</sup></span> || &nbsp; || [[Roentgenium]] || 111 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>9</sup>
|- bgcolor="{{element color|d-block}}"
| [[Zinc]] || 30 || &#91;[[argon|Ar]]&#93; 4s<sup>2</sup> 3d<sup>10</sup> || &nbsp; || [[Cadmium]] || 48 || &#91;[[krypton|Kr]]&#93; 5s<sup>2</sup> 4d<sup>10</sup> || &nbsp; || [[Mercury (element)|Mercury]] || 80 || &#91;[[xenon|Xe]]&#93; 6s<sup>2</sup> 4f<sup>14</sup> 5d<sup>10</sup> || &nbsp; || [[Copernicium]] || 112 || &#91;[[Radon|Rn]]&#93; 7s<sup>2</sup> 5f<sup>14</sup> 6d<sup>10</sup>
|}

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 {{nowrap|[Xe] 4f<sup>4</sup> 5d<sup>0</sup> 6s<sup>2</sup>}} that if interpreted naïvely would suggest a more stable +2 oxidation state corresponding to losing only the 6s electrons. Contrariwise, uranium as {{nowrap|[Rn] 5f<sup>3</sup> 6d<sup>1</sup> 7s<sup>2</sup>}} is not very stable in the +3 oxidation state either, preferring +4 and +6.<ref name=Jorgensen>{{cite book |last=Jørgensen |first=Christian K. |date=1988 |title=Handbook on the Physics and Chemistry of Rare Earths |volume=11 |chapter=Influence of rare earths on chemical understanding and classification |pages=197–292 |doi=10.1016/S0168-1273(88)11007-6|isbn=978-0-444-87080-3 }}</ref>

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 [[unbinilium|element 120]]. [[Unbiunium|Element 121]] should have the anomalous configuration {{nowrap|<nowiki>[</nowiki>[[Oganesson|Og]]<nowiki>]</nowiki> 8s<sup>2</sup> {{color|red|5g<sup>0</sup>}} 6f<sup>0</sup> 7d<sup>0</sup> {{color|red|8p<sup>1</sup>}}}}, having a p rather than a g electron. Electron configurations beyond this are tentative and predictions differ between models,<ref>{{cite journal |last1=Umemoto |first1=Koichiro |last2=Saito |first2=Susumu |date=1996 |title=Electronic Configurations of Superheavy Elements |url=https://journals.jps.jp/doi/pdf/10.1143/JPSJ.65.3175 |journal=Journal of the Physical Society of Japan |volume=65 |issue=10 |pages=3175–9 |doi=10.1143/JPSJ.65.3175 |bibcode=1996JPSJ...65.3175U |access-date=31 January 2021|url-access=subscription }}</ref> but Madelung's rule is expected to break down due to the closeness in energy of the {{Not a typo|5g}}, 6f, 7d, and 8p<sub>1/2</sub> orbitals.<ref name=Haire>{{cite book| title=The Chemistry of the Actinide and Transactinide Elements| editor1-last=Morss|editor2-first=Norman M.| editor2-last=Edelstein| editor3-last=Fuger|editor3-first=Jean| last1=Hoffman|first1=Darleane C. |last2=Lee |first2=Diana M. |last3=Pershina |first3=Valeria |chapter=Transactinides and the future elements| publisher= [[Springer Science+Business Media]]| year=2006| isbn=978-1-4020-3555-5| location=Dordrecht, The Netherlands| edition=3rd}}</ref> That said, the filling sequence 8s, {{Not a typo|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.<ref>{{cite conference |url=https://www.epj-conferences.org/articles/epjconf/pdf/2016/26/epjconf-NS160-01001.pdf |title=Is the Periodic Table all right ("PT OK")? |last1=Pyykkö |first1=Pekka |date=2016 |conference=Nobel Symposium NS160 – Chemistry and Physics of Heavy and Superheavy Elements}}</ref>