Editing Octet rule

{{Short description|Chemical rule of thumb}}
{{More citations needed|date=October 2023}}
[[File:Carbon-dioxide-octet-Lewis-2D.png|thumb|The bonding in [[carbon dioxide]] (CO<sub>2</sub>): all atoms are surrounded by 8 electrons, fulfilling the '''octet rule'''.]]
The '''octet rule''' is a [[chemistry|chemical]] [[rule of thumb]] that reflects the theory that [[main-group element]]s tend to [[chemical bond|bond]] in such a way that each [[atom]] has eight [[electrons]] in its [[valence shell]], giving it the same [[electron configuration|electronic configuration]] as a [[noble gas]]. The rule is especially applicable to [[carbon]], [[nitrogen]], [[oxygen]], and the [[halogens]]; although more generally the rule is applicable for the [[s-block]] and [[p-block]] of the [[periodic table]]. Other rules exist for other elements, such as the [[duplet rule]] for [[hydrogen]] and [[helium]], and the [[18-electron rule]] for [[transition metal]]s.

The valence electrons in molecules like carbon dioxide (CO₂) can be visualized using a [[Lewis structure|Lewis electron dot diagram]]. In [[Covalent bond|covalent bonds]], electrons shared between two atoms are counted toward the octet of both atoms. In carbon dioxide each oxygen shares four electrons with the central carbon, two (shown in red) from the oxygen itself and two (shown in black) from the carbon. All four of these electrons are counted in both the carbon octet and the oxygen octet, so that both atoms are considered to obey the octet rule.

== Example: sodium chloride (NaCl) ==
[[File:Ionic bonding animation.gif|right]]

The octet rule is simplest in the case of [[ionic bonding]] between two atoms, one a [[metal]] of low [[electronegativity]] and the other a [[Nonmetal (chemistry)|nonmetal]] of high electronegativity.  For example, [[sodium metal]] and [[chlorine gas]] combine to form [[sodium chloride]], a [[crystal lattice]] composed of alternating sodium and chlorine [[atomic nucleus|nuclei]].  Electron density inside this lattice forms clumps at the atomic scale, as follows.  

An isolated chlorine atom (Cl) has two and eight electrons in its [[principal quantum number|first and second]] electron shells, located near the nucleus.  However, it has only seven electrons in the third and [[valence shell|outermost electron shell]].  One additional electron would completely fill the outer electron shell with eight electrons, a situation the octet rule commends.  Indeed, adding an electron to the produce the [[chloride ion]] (Cl<sup>&minus;</sup>) [[electron affinity|releases]] 3.62&nbsp;[[electron-volt|eV]] of energy.<ref>{{cite book |last1=Housecroft |first1=Catherine E. |last2=Sharpe |first2=Alan G. |title=Inorganic Chemistry |date=2005 |publisher=Pearson Education Limited |isbn=0130-39913-2 |page=883 |edition=2nd}}  Per source, the enthalpy change for
:Cl&nbsp;+ {{e-}}&nbsp;→ Cl<sup>-</sup>
is -349&nbsp;kJ/mol.  Unit conversion performed using [[WolframAlpha|Wolfram{{!}}Alpha]] database, 13 April 2025.</ref>  Conversely, another surplus electron cannot fit in the same shell, instead beginning the fourth electron shell around the nucleus.  Thus the octet rule proscribes formation of a hypothetical Cl<sup>2&minus;</sup> [[ion]], and indeed the latter has only been observed as a [[plasma (physics)|plasma]] under extreme conditions.  

A sodium atom (Na) has a single electron in its outermost electron shell, the first and second shells again being full with two and eight electrons respectively. The octet rule favors removal of this outermost electron to form the Na<sup>+</sup> ion, which [[isoelectronic series|has the exact same electron configuration]] as Cl<sup>&minus;</sup>.  Indeed, sodium is observed to transfer one electron to chlorine during the formation of sodium chloride, such that the resulting lattice is best considered as a periodic array of Na<sup>+</sup> and Cl<sup>&minus;</sup> ions.  

To remove the outermost Na electron and return to an "octet-approved" state [[ionization energy|requires]] a small amount of energy: 5.14&nbsp;eV.<ref>{{harvnb|Housecroft|Sharpe|2005}}, p.&nbsp;880.  Source gives ionization energy of +495.8&nbsp;kJ/mol.  Unit conversion performed using [[WolframAlpha|Wolfram{{!}}Alpha]] database, 13 April 2025.</ref>  This energy is provided from the 3.62&nbsp;eV released during chloride formation, and the [[electrostatic attraction]] between positively-charged Na<sup>+</sup> and negatively-charged Cl<sup>&minus;</sup> ions, which releases a 8.12&nbsp;eV [[lattice energy]].<ref>{{harvnb|Housecroft|Sharpe|2005}}, p.&nbsp;156.  Source gives lattice energy of 783&nbsp;kJ/mol.  Unit conversion performed using [[WolframAlpha|Wolfram{{!}}Alpha]] database, 13 April 2025.</ref>  By contrast, any further electrons removed from Na would reside in the deeper second electron shell, and produce an octet-violating Na<sup>2+</sup> ion.  Consequently, the second ionization energy required for the next removal is much larger&nbsp;&mdash; 47.28&nbsp;eV<ref>{{harvnb|Housecroft|Sharpe|2005}}, p.&nbsp;880.  Source gives ionization energy of +4562&nbsp;kJ/mol.  Unit conversion performed using [[WolframAlpha|Wolfram{{!}}Alpha]] database, 13 April 2025.</ref>&nbsp;&mdash; and the corresponding ion is only observed under extreme conditions.

== History ==
[[File:Newlands periodiska system 1866.png|thumb|upright=1.8|[[John Newlands (chemist)|Newlands]]' law of octaves]]

In 1864, the English chemist [[John Alexander Reina Newlands|John Newlands]] classified the sixty-two known elements into eight groups, based on their physical properties.<ref>See:
*{{cite journal|last1=Newlands|first1=John A. R.|title=On relations among the equivalents|journal=The Chemical News|date=7 February 1863|volume=7|pages=70–72|url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433062748920;view=1up;seq=78}}
*{{cite journal|last1=Newlands|first1=John A. R.|title=On relations among the equivalents|journal=The Chemical News|date=20 August 1864|volume=10|pages=94–95|url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433062749290;view=1up;seq=108}}
*{{cite journal|last1=Newlands|first1=John A. R.|title=On the law of octaves|journal=The Chemical News|date=18 August 1865|volume=12|page=83|url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433062749274;view=1up;seq=97}}
*{{cite journal|last1=(Editorial staff)|title=Proceedings of Societies: Chemical Society: Thursday, March 1.|journal=The Chemical News|date=9 March 1866|volume=13|pages=113–114|url=https://babel.hathitrust.org/cgi/pt?id=nyp.33433062749266;view=1up;seq=121}}
*{{cite book|last1=Newlands|first1=John A.R.|title=On the Discovery of the Periodic Law and on Relations among the Atomic Weights|date=1884|publisher=London, England|location=E. & F.N. Spon|url=https://archive.org/stream/ondiscoveryperi02newlgoog#page/n4/mode/2up}}</ref><ref>in a letter published in ''Chemistry News'' in February 1863, according to the [http://www.nndb.com/people/480/000103171/ Notable Names Data Base]</ref><ref>[http://web.lemoyne.edu/~giunta/EA/NEWLANDSann.HTML Newlands on classification of elements]
</ref><ref>{{cite journal |last1=Ley |first1=Willy |title=For Your Information: The Delayed Discovery |journal=Galaxy Science Fiction |date=October 1966 |volume=25 |issue=1 |pages=116–127 |url=https://archive.org/stream/Galaxy_v25n01_1966-10#page/n115/mode/2up}}</ref>

In the late 19th century, it was known that coordination compounds (formerly called "molecular compounds") were formed by the combination of atoms or molecules in such a manner that the valencies of the atoms involved apparently became satisfied. In 1893, [[Alfred Werner]] showed that the number of atoms or groups associated with a central atom (the "[[coordination number]]") is often 4 or 6; other coordination numbers up to a maximum of 8 were known, but less frequent.<ref>See:
*  {{cite journal |last1=Werner |first1=Alfred |title=Beitrag zur Konstitution anorganischer Verbindungen |journal=Zeitschrift für anorganische und allgemeine Chemie |date=1893 |volume=3 |pages=267–330 |doi=10.1002/zaac.18930030136 |url=https://babel.hathitrust.org/cgi/pt?id=mdp.39015072644209&view=1up&seq=271 |trans-title=Contribution to the constitution of inorganic compounds |language=de}}
*  English translation:  {{cite book |editor-last1=Werner |editor-first1=Alfred |editor-last2=Kauffman |editor-first2=G.B. |title=Classics in Coordination Chemistry, Part I: The selected papers of Alfred Werner |date=1968 |publisher=Dover Publications |location=New York City, New York, USA |pages=5–88}}</ref> In 1904, [[Richard Abegg]] was one of the first to extend the concept of [[coordination number]] to a concept of [[valence (chemistry)|valence]] in which he distinguished atoms as electron donors or acceptors, leading to positive and negative valence states that greatly resemble the modern concept of [[oxidation states]]. Abegg noted that the difference between the maximum positive and negative [[valence (chemistry)|valences]] of an [[chemical element|element]] under his model is frequently eight.<ref>{{cite journal
| doi = 10.1002/zaac.19040390125
| volume = 39
| issue = 1
| pages = 330–380
| last = Abegg
| first = R.
| title = Die Valenz und das periodische System. Versuch einer Theorie der Molekularverbindungen 
| trans-title = Valency and the periodic system. Attempt at a theory of molecular compounds
| journal = Zeitschrift für Anorganische Chemie
| year = 1904
| url = https://zenodo.org/record/1428102
}}</ref> In 1916, [[Gilbert N. Lewis]] referred to this insight as [[Abegg's rule]] and used it to help formulate his [[cubical atom]] model and the "rule of eight", which began to distinguish between [[valence (chemistry)|valence]] and [[valence electron]]s.<ref>{{cite journal
| doi = 10.1021/ja02261a002
| volume = 38
| issue = 4
| pages = 762–785
| last = Lewis
| first = Gilbert N.
| title = The Atom and the Molecule
| journal = Journal of the American Chemical Society
| year = 1916
| s2cid = 95865413
| url = https://zenodo.org/record/1429068
}}</ref>  In 1919, [[Irving Langmuir]] refined these concepts further and renamed them the "cubical octet atom" and "octet theory".<ref>{{cite journal
| doi = 10.1021/ja02227a002
| volume = 41
| issue = 6
| pages = 868–934
| last = Langmuir
| first = Irving
| title = The Arrangement of Electrons in Atoms and Molecules
| journal = Journal of the American Chemical Society
| year = 1919
| url = https://zenodo.org/record/1429026
}}</ref>  The "octet theory" evolved into what is now known as the "octet rule".

[[Walther Kossel]]<ref>{{cite journal |last1=Kossel |first1=W. |title=Über Molekülbildung als Frage des Atombaus |journal=Annalen der Physik |date=1916 |volume=354 |issue=3 |pages=229–362 |doi=10.1002/andp.19163540302 |bibcode=1916AnP...354..229K |url=https://babel.hathitrust.org/cgi/pt?id=uiug.30112053562358&view=1up&seq=245 |trans-title=On the formation of molecules as a question of atomic structure |language=de}}</ref> and [[Gilbert N. Lewis]] saw that noble gases did not have the tendency of taking part in chemical reactions under ordinary conditions. On the basis of this observation, they concluded that [[atom]]s of [[noble gas]]es are stable and on the basis of this conclusion they proposed a theory of [[valence (chemistry)|valency]] known as "electronic theory of valency" in 1916:

{{quote|''During the formation of a chemical bond, atoms combine together by gaining, losing or sharing electrons in such a way that they acquire nearest noble gas configuration.''<ref>{{cite web|url=http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/papers/corr216.3-lewispub-19160400.html |title=The Atom and the Molecule. April 1916. - Published Papers and Official Documents - Linus Pauling and The Nature of the Chemical Bond: A Documentary History |publisher=Osulibrary.oregonstate.edu |access-date=2014-01-03 |url-status=dead |archive-url=https://web.archive.org/web/20131125222947/http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/papers/corr216.3-lewispub-19160400.html |archive-date=November 25, 2013 }}</ref>}}

== Explanation in quantum theory ==

The quantum theory of the atom explains the eight electrons as a [[closed shell]] with an s<sup>2</sup>p<sup>6</sup> electron configuration. A closed-shell configuration is one in which low-lying energy levels are full and higher energy levels are empty. For example, the [[neon]] atom ground state has a full {{nowrap|1=''n'' = 2}} shell (2s<sup>2</sup>2p<sup>6</sup>) and an empty {{nowrap|1=''n'' = 3}} shell. According to the octet rule, the atoms immediately before and after neon in the periodic table (i.e. C, N, O, F, Na, Mg and Al), tend to attain a similar configuration by gaining, losing, or sharing electrons.

The [[argon]] atom has an analogous 3s<sup>2</sup>3p<sup>6</sup> configuration. There is also an empty 3d level, but it is at considerably higher energy than 3s and 3p (unlike in the hydrogen atom), so that 3s<sup>2</sup>3p<sup>6</sup> is still considered a closed shell for chemical purposes. The atoms immediately before and after argon tend to attain this configuration in compounds. There are, however, some [[hypervalent molecule]]s in which the 3d level may play a part in the bonding, although this is controversial (see below).

For [[helium]] there is no 1p level according to the quantum theory, so that 1s<sup>2</sup> is a closed shell with no p electrons. The atoms before and after helium (H and Li) follow a duet rule and tend to have the same 1s<sup>2</sup> configuration as helium.

== Exceptions ==
Many [[reactive intermediate]]s do not obey the octet rule.  Most are unstable, although some can be isolated.  

Typically, octet rule violations occur in either low-dimensional [[coordination geometry|coordination geometries]] or in [[radical (chemistry)|radical species]].  Although hypervalent molecules are commonly taught to violate the octet rule, [[Ab initio quantum chemistry methods|''ab initio'' calculations]] show that almost all known examples obey the octet rule.  The compounds form many [[bond order|fractional bonds]] through [[chemical resonance|resonance]] (see {{slink||Hypervalent molecules}} below).

===Low-dimensional geometries===
In the [[trigonal planar]] coordination geometry, one [[p orbital|''p'' orbital]] points out of the bonding plane, and can only [[orbital overlap|overlap]] with nearby atomic orbitals in a [[π bond]].  If that ''p'' orbital would be empty in an isolated atom, it may be filled through an intramolecular [[dative bond]], as with [[aminoboranes]].  However, in some cases (e.g. [[boron trichloride]] and various [[borane]]s, [[triphenylcarbenium|triphenylmethanium]]), no nearby filled orbital can profitably overlap with the empty ''p'' orbital.  In such cases, the orbital remains empty, and the compound obeys a "sextet rule".  Likewise, linear compounds, such as [[dimethylzinc]], have two ''p'' orbitals perpendicular to the bonding axis, and may obey a "quartet rule".<ref>{{cite book|pp=298-299|year=1985|publisher=Wiley|lccn=84-15310|isbn=0-471-87393-4|last1=Albright|first1=T.&nbsp;A.|last2=Burdett|first2=Jeremy&nbsp;K.|last3=Whangbo|first3=Myung-Hwan|title=Orbital Interactions in Chemistry}}</ref>  In either case, the empty unshielded orbitals tend to attract adducts.  

===Radicals===
Radicals satisfy the octet rule in one [[quantum spin|spin orientation]], with four spin-up electrons in the valence shell, and almost satisfy it in the opposite spin orientation. Thus, for example, the [[methyl radical]] (CH<sub>3</sub>), which has an unpaired electron in a [[non-bonding orbital]] on the carbon atom and no electron of opposite spin in the same orbital. Another example is the radical [[chlorine monoxide]] (ClO<sup>•</sup>) which is involved in [[ozone depletion]].  

[[Stable radical]]s tend to adopt states in which the unpaired electron can [[delocalized electron|delocalize]] through resonance. In such cases, the octet rule can be restored through the formalism of a [[Covalent bond#One- and three-electron bonds|1- or 3-electron bond]].  

Species such as [[carbene]]s can be interpreted two different ways, depending on their spin state. [[Carbene#Singlet-triplet effects|Triplet]] carbenes are best thought of as two radicals localized on the same atom, and obey the octet rule in those radicals' shared spin-up orientation. [[Carbene#Singlet-triplet effects|Singlet]] carbenes tend to adopt a planar configuration, and are best thought of as obeying the planar sextet rule.

== Hypervalent molecules ==
{{Main|Hypervalent molecule}}

Main-group elements in the third and later rows of the periodic table can form hypercoordinate or  [[hypervalent molecule]]s in which the central main-group atom is bonded to more than four other atoms, such as [[phosphorus pentafluoride]], PF<sub>5</sub>, and [[sulfur hexafluoride]], SF<sub>6</sub>. For example, in PF<sub>5</sub>, if it is supposed that there are five true [[covalent bond]]s in which five distinct electron pairs are shared, then the phosphorus would be surrounded by 10 valence electrons in violation of the octet rule. In the early days of quantum mechanics, [[Linus Pauling|Pauling]] proposed that third-row atoms can form five bonds by using one s, three p and one d orbitals, or six bonds by using one s, three p and two d orbitals.<ref>L. Pauling ''The Nature of the Chemical Bond'' (3rd ed., Oxford University Press 1960) p.63. In this source Pauling considers as examples PCl<sub>5</sub> and the [[hexafluorophosphate|PF<sub>6</sub><sup>−</sup>]] ion. {{ISBN|0-8014-0333-2}}</ref> To form five bonds, the one s, three p and one d orbitals combine to form five sp<sup>3</sup>d [[hybrid orbital]]s which each share an electron pair with a halogen atom, for a total of 10 shared electrons, two more than the octet rule predicts. Similarly to form six bonds, the six sp<sup>3</sup>d<sup>2</sup> hybrid orbitals form six bonds with 12 shared electrons.<ref>R.H. Petrucci, W.S. Harwood and F.G. Herring, General Chemistry (8th ed., Prentice-Hall 2002) p.408 and p.445 {{ISBN|0-13-014329-4}}</ref> In this model the availability of empty d orbitals is used to explain the fact that third-row atoms such as phosphorus and sulfur can form more than four covalent bonds, whereas second-row atoms such as nitrogen and oxygen are strictly limited by the octet rule.<ref>Douglas B.E., McDaniel D.H. and Alexander J.J. ''Concepts and Models of Inorganic Chemistry'' (2nd ed., John Wiley 1983) pp.45-47 {{ISBN|0-471-21984-3}}</ref>

[[image:penta phos.svg|thumb|500px | center |5 resonance structures of phosphorus pentafluoride]]
However other models describe the bonding using only s and p orbitals in agreement with the octet rule. A [[Valence bond theory|valence bond]] description of PF<sub>5</sub> uses [[Resonance (chemistry)|resonance]] between different PF<sub>4</sub><sup>+</sup> F<sup>−</sup> structures, so that each F is bonded by a covalent bond in four structures and an ionic bond in one structure. Each resonance structure has eight valence electrons on P.<ref>Housecroft C.E. and Sharpe A.G., ''Inorganic Chemistry'', 2nd ed. (Pearson Education Ltd. 2005), p.390-1</ref> A [[molecular orbital theory]] description considers the [[HOMO/LUMO|highest occupied molecular orbital]] to be a non-bonding orbital localized on the five fluorine atoms, in addition to four occupied bonding orbitals, so again there are only eight valence electrons on the phosphorus.{{citation needed|date=March 2015}} The validity of the octet rule for hypervalent molecules is further supported by [[Hypervalent molecule#Bonding in hypervalent molecules|ab initio molecular orbital calculations]], which show that the contribution of d functions to the bonding orbitals is small.<ref>Miessler D.L. and Tarr G.A., ''Inorganic Chemistry'', 2nd ed. (Prentice-Hall 1999), p.48</ref><ref>Magnusson, E., J.Am.Chem.Soc. (1990), v.112, p.7940-51 ''Hypercoordinate Molecules of Second-Row Elements: d Functions or d Orbitals?''</ref>

Nevertheless, for historical reasons, structures implying more than eight electrons around elements like P, S, Se, or I are still common in textbooks and research articles.  In spite of the unimportance of d shell expansion in chemical bonding, this practice allows structures to be shown without using a large number of formal charges or using partial bonds and is recommended by the IUPAC as a convenient formalism in preference to depictions that better reflect the bonding.  On the other hand, showing more than eight electrons around Be, B, C, N, O, or F (or more than two around H, He, or Li) is considered an error by most authorities.

== Other rules ==
The octet rule is only applicable to [[main-group element]]s. Other elements follow other [[electron counting]] rules as their [[valence electron]] configurations are different from main-group elements. These other rules are shown below:
{| class="wikitable"
|-
!Element type||First shell||p-block<br/>([[Main-group element|Main group]])||d-block<br/>([[Transition metal]])
|-
!Electron counting rules
|Duet/Duplet rule
|Octet rule
|18-electron rule
|-
!Full valence configuration
|s<sup>2</sup>
|s<sup>2</sup>p<sup>6</sup>
|d<sup>10</sup>s<sup>2</sup>p<sup>6</sup>
|}
* The '''duet rule''' or '''duplet rule''' of the first shell applies to H, He and Li—the noble gas [[helium]] has two electrons in its outer shell, which is very stable. (Since there is no 1''p'' subshell, 1''s'' is followed immediately by 2''s'', and thus shell 1 can only have at most 2 valence electrons). [[Hydrogen]] only needs one additional electron to attain this stable configuration, while [[lithium]] needs to lose one.
* For [[transition metal]]s, molecules tend to obey the '''[[18-electron rule]]''' which corresponds to the utilization of valence ''d'', ''s'' and ''p'' orbitals to form bonding and non-bonding orbitals. However, unlike the octet rule for main-group elements, transition metals do not strictly obey the 18-electron rule and the valence electron count can vary between 12 and 18.<ref>{{cite book |editor1-last=Frenking |editor1-first=Gernot|editor2-last=Shaik |editor2-first=Sason|title=The Chemical Bond: Chemical Bonding Across the Periodic Table |publisher=Wiley -VCH |date=May 2014 |chapter=Chapter 7: Chemical bonding in Transition Metal Compounds |isbn=978-3-527-33315-8}}</ref><ref>{{cite journal
| title = The Nature of the Bonding in Transition-Metal Compounds
| first1= Gernot |last1=Frenking |first2=Nikolaus |last2=Fröhlich
| journal = [[Chemical Reviews|Chem. Rev.]]
| year = 2000
| volume = 100
| issue = 2
| pages = 717–774
| doi = 10.1021/cr980401l
| pmid= 11749249}}</ref><ref>{{cite journal
| title = Prediction of the Geometries of Simple Transition Metal Polyhydride Complexes by Symmetry Analysis
| first1= Craig |last1=Bayse |first2=Michael |last2=Hall
| journal = [[Journal of the American Chemical Society|J. Am. Chem. Soc.]]
| year = 1999
| volume = 121
| issue = 6
| pages = 1348–1358
| doi = 10.1021/ja981965+
}}</ref><ref>{{cite journal
| title = Structure and bonding in homoleptic transition metal hydride anions
| first= R.B. |last= King 
| journal = Coordination Chemistry Reviews
| year = 2000
| volume = 200–202
| pages = 813–829
| doi = 10.1016/S0010-8545(00)00263-0
}}</ref>

== See also ==
* [[Lewis structure]]
* [[Electron counting]]

== References ==
{{Reflist}}

{{Electron configuration navbox}}

[[Category:Chemical bonding]]
[[Category:Rules of thumb]]