Editing Electron configuration (section)

=== Ionization of the transition metals ===
The naïve application of the aufbau principle leads to a well-known [[paradox]] (or apparent paradox) in the basic chemistry of the [[transition metal]]s. [[Potassium]] and [[calcium]] appear in the periodic table before the transition metals, and have electron configurations [Ar]&nbsp;4s{{sup|1}} and [Ar]&nbsp;4s{{sup|2}} respectively, i.e. the 4s-orbital is filled before the 3d-orbital. This is in line with Madelung's rule, as the 4s-orbital has ''n''&nbsp;+&nbsp;{{mvar|l}}&nbsp;=&nbsp;4 (''n''&nbsp;=&nbsp;4, {{mvar|l}}&nbsp;=&nbsp;0) while the 3d-orbital has ''n''&nbsp;+&nbsp;{{mvar|l}}&nbsp;=&nbsp;5 (''n''&nbsp;=&nbsp;3, {{mvar|l}}&nbsp;=&nbsp;2). After calcium, most neutral atoms in the first series of transition metals ([[scandium]] through [[zinc]]) have configurations with two 4s electrons, but there are two exceptions. [[Chromium]] and [[copper]] have electron configurations [Ar]&nbsp;3d{{sup|5}}&nbsp;4s{{sup|1}} and [Ar]&nbsp;3d{{sup|10}}&nbsp;4s{{sup|1}} respectively, i.e. one electron has passed from the 4s-orbital to a 3d-orbital to generate a half-filled or filled subshell. In this case, the usual explanation is that "half-filled or completely filled subshells are particularly stable arrangements of electrons". However, this is not supported by the facts, as [[tungsten]] (W) has a Madelung-following d{{sup|4}}&nbsp;s{{sup|2}} configuration and not d{{sup|5}}&nbsp;s{{sup|1}}, and [[niobium]] (Nb) has an anomalous d{{sup|4}}&nbsp;s{{sup|1}} configuration that does not give it a half-filled or completely filled subshell.<ref name=mustdie>{{cite journal |last1=Scerri |first1=Eric |date=2019 |title=Five ideas in chemical education that must die |journal=Foundations of Chemistry |volume=21 |pages=61–69 |doi=10.1007/s10698-018-09327-y|s2cid=104311030 }}</ref>

The apparent paradox arises when electrons are ''removed'' from the transition metal atoms to form [[ion]]s. The first electrons to be ionized come not from the 3d-orbital, as one would expect if it were "higher in energy", but from the 4s-orbital. This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals.{{efn|There are some cases in the second and third series where the electron remains in an s-orbital.}} The configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of ionization of a given atom (such as Fe<sup>4+</sup>, Fe<sup>3+</sup>, Fe<sup>2+</sup>, Fe<sup>+</sup>, Fe) usually follow the order 1s, 2s, 2p, 3s, 3p, 3d, 4s, ...

This phenomenon is only paradoxical if it is assumed that the energy order of atomic orbitals is fixed and unaffected by the nuclear charge or by the presence of electrons in other orbitals. If that were the case, the 3d-orbital would have the same energy as the 3p-orbital, as it does in hydrogen, yet it clearly does not. There is no special reason why the Fe{{sup|2+}} ion should have the same electron configuration as the chromium atom, given that [[iron]] has two more protons in its nucleus than chromium, and that the chemistry of the two species is very different. Melrose and [[Eric Scerri]] have analyzed the changes of orbital energy with orbital occupations in terms of the two-electron repulsion integrals of the [[Hartree–Fock method]] of atomic structure calculation.<ref>{{cite journal | last = Melrose | first = Melvyn P. |author2=Scerri, Eric R. | title = Why the 4s Orbital is Occupied before the 3d | journal = Journal of Chemical Education | volume = 73 | issue = 6 | pages = 498–503 | year = 1996 | doi = 10.1021/ed073p498|bibcode = 1996JChEd..73..498M }}</ref> More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied.<ref>{{cite magazine |last=Scerri |first=Eric |author-link=Eric Scerri |date=7 November 2013 |title=The trouble with the aufbau principle |url=https://eic.rsc.org/feature/the-trouble-with-the-aufbau-principle/2000133.article |url-status=live |magazine=[[Education in Chemistry]] |volume=50 |issue=6 |pages=24–26 |publisher=[[Royal Society of Chemistry]] |archive-url=https://web.archive.org/web/20180121061346/https://eic.rsc.org/feature/the-trouble-with-the-aufbau-principle/2000133.article |archive-date=21 January 2018 |access-date=12 June 2018}}</ref>

In chemical environments, configurations can change even more: Th<sup>3+</sup> as a bare ion has a configuration of [Rn]&nbsp;5f<sup>1</sup>, yet in most Th<sup>III</sup> compounds the thorium atom has a 6d<sup>1</sup> configuration instead.<ref>{{cite journal |first1=Ryan R. |last1=Langeslay |first2=Megan E. |last2=Fieser |first3=Joseph W. |last3=Ziller |first4=Philip |last4=Furche |first5=William J. |last5=Evans |title=Synthesis, structure, and reactivity of crystalline molecular complexes of the {[C<sub>5</sub>H<sub>3</sub>(SiMe<sub>3</sub>)<sub>2</sub>]<sub>3</sub>Th}<sup>1−</sup> anion containing thorium in the formal +2 oxidation state |journal=Chem. Sci. |year=2015 |volume=6 |pages=517–521 |doi=10.1039/C4SC03033H|pmc=5811171 |pmid=29560172 |issue=1 }}</ref><ref>{{cite book|last1 = Wickleder|first1 = Mathias S.|first2 = Blandine|last2 = Fourest|first3 = Peter K.|last3 = Dorhout|ref = Wickleder et al.|contribution = Thorium|title = The Chemistry of the Actinide and Transactinide Elements|editor1-first = Lester R.|editor1-last = Morss|editor2-first = Norman M.|editor2-last = Edelstein|editor3-first = Jean|editor3-last = Fuger|edition = 3rd|date = 2006|volume = 3|publisher = Springer|location = Dordrecht, the Netherlands|pages = 52–160|url = http://radchem.nevada.edu/classes/rdch710/files/thorium.pdf|doi = 10.1007/1-4020-3598-5_3| isbn=978-1-4020-3555-5 |url-status = dead|archive-url = https://web.archive.org/web/20160307160941/http://radchem.nevada.edu/classes/rdch710/files/Thorium.pdf|archive-date = 2016-03-07}}</ref> Mostly, what is present is rather a superposition of various configurations.<ref name=mustdie /> For instance, copper metal is poorly described by either an [Ar]&nbsp;3d{{sup|10}}&nbsp;4s{{sup|1}} or an [Ar]&nbsp;3d{{sup|9}}&nbsp;4s{{sup|2}} configuration, but is rather well described as a 90% contribution of the first and a 10% contribution of the second. Indeed, visible light is already enough to excite electrons in most transition metals, and they often continuously "flow" through different configurations when that happens (copper and its group are an exception).<ref>{{Cite journal|doi = 10.26434/chemrxiv.11860941|title = The Chemical Bond Across the Periodic Table: Part 1 – First Row and Simple Metals|last1 = Ferrão|first1 = Luiz|last2 = Machado|first2 = Francisco Bolivar Correto|last3 = Cunha|first3 = Leonardo dos Anjos|last4 = Fernandes|first4 = Gabriel Freire Sanzovo|url = https://figshare.com/articles/The_Chemical_Bond_Across_the_Periodic_Table_Part_1_First_Row_and_Simple_Metals/11860941|journal =[[ChemRxiv]] | s2cid=226121612 |access-date = 23 August 2020|archive-date = 1 December 2020|archive-url = https://web.archive.org/web/20201201001121/https://figshare.com/articles/The_Chemical_Bond_Across_the_Periodic_Table_Part_1_First_Row_and_Simple_Metals/11860941|url-status = dead|url-access = subscription}}</ref>

Similar ion-like 3d{{sup|''x''}}&nbsp;4s{{sup|0}} configurations occur in [[transition metal complex]]es as described by the simple [[crystal field theory]], even if the metal has [[oxidation state]]&nbsp;0. For example, [[chromium hexacarbonyl]] can be described as a chromium atom (not ion) surrounded by six [[carbon monoxide]] [[ligand]]s. The electron configuration of the central chromium atom is described as 3d{{sup|6}} with the six electrons filling the three lower-energy d orbitals between the ligands. The other two d orbitals are at higher energy due to the crystal field of the ligands. This picture is consistent with the experimental fact that the complex is [[diamagnetic]], meaning that it has no unpaired electrons. However, in a more accurate description using [[molecular orbital theory]], the d-like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom.