Editing Sulfate (section)

==Bonding==
[[File:Sulfate covalent-ionic.svg|thumb|Two models of the sulfate ion.<br />'''1''' with [[Chemical polarity#polar molecules|polar covalent]] bonds only; '''2''' with an [[ionic bond]]]][[Image:Sulfate-resonance-2D.png|thumb|Six resonances]]
The first description of the bonding in modern terms was by [[Gilbert N. Lewis|Gilbert Lewis]] in his groundbreaking paper of 1916, where he described the bonding in terms of electron octets around each atom. There are two double bonds, and there is a [[formal charge]] of +2 on the sulfur atom and -1 on each oxygen atom.<ref>{{cite journal|title=The Atom and the Molecule|first=Gilbert N.|last=Lewis|author-link=Gilbert N. Lewis|journal=[[J. Am. Chem. Soc.]]|volume=38|date=1916|issue=4|pages=762–785|url=http://osulibrary.oregonstate.edu/specialcollections/coll/pauling/bond/papers/corr216.3-lewispub-19160400-18-large.html|doi=10.1021/ja02261a002|s2cid=95865413 }} (See page 778.)</ref>{{efn|Lewis assigned to sulfur a negative charge of two, starting from six own valence electrons and ending up with eight electrons shared with the oxygen atoms. In fact, sulfur donates two electrons to the oxygen atoms.|name=formal charge}}

Later, [[Linus Pauling]] used [[valence bond theory]] to propose that the most significant [[Resonance (chemistry)|resonance canonicals]] had two [[pi bond]]s involving d orbitals. His reasoning was that the charge on sulfur was thus reduced, in accordance with his [[Pauling's principle of electroneutrality|principle of electroneutrality]].<ref>{{cite journal|title=The modern theory of valency|first=Linus|last=Pauling|author-link=Linus Pauling|journal=[[J. Chem. Soc.]]|date=1948|volume=17|pages=1461–1467|doi=10.1039/JR9480001461|pmid=18893624|url=https://authors.library.caltech.edu/59671/}}</ref> The S−O bond length of 149&nbsp;pm is shorter than the bond lengths in [[sulfuric acid]] of 157&nbsp;pm for S−OH. The double bonding was taken by Pauling to account for the shortness of the S−O bond.

Pauling's use of d orbitals provoked a debate on the relative importance of [[pi bond]]ing and bond polarity ([[electrostatic attraction]]) in causing the shortening of the S−O bond. The outcome was a broad consensus that d orbitals play a role, but are not as significant as Pauling had believed.<ref>{{cite journal|first=C.&nbsp;A.|last=Coulson|title=d Electrons and Molecular Bonding|journal=[[Nature (journal)|Nature]]|volume=221|page=1106|date=1969|issue=5186|doi=10.1038/2211106a0|bibcode=1969Natur.221.1106C|s2cid=4162835}}</ref><ref>{{cite journal|first=K.&nbsp;A.&nbsp;R.|last=Mitchell|title=Use of outer d orbitals in bonding|journal=[[Chem. Rev.]] |volume=69|page=157|date=1969|issue=2|doi=10.1021/cr60258a001}}</ref>

A widely accepted description involving pπ&nbsp;–&nbsp;dπ bonding was initially proposed by [[Durward William John Cruickshank]]. In this model, fully occupied p orbitals on oxygen overlap with empty sulfur d orbitals (principally the d<sub>''z''<sup>2</sup></sub> and d<sub>''x''<sup>2</sup>–''y''<sup>2</sup></sub>).<ref name="cotton" /> However, in this description, despite there being some π character to the S−O bonds, the bond has significant ionic character. For sulfuric acid, computational analysis (with [[natural bond orbital]]s) confirms a clear positive charge on sulfur (theoretically +2.45) and a low 3d occupancy. Therefore, the representation with four single bonds is the optimal Lewis structure rather than the one with two double bonds (thus the Lewis model, not the Pauling model).<ref name="Stefan">{{cite journal|first1=Thorsten|last1=Stefan|first2=Rudolf|last2=Janoschek|title=How relevant are S=O and P=O Double Bonds for the Description of the Acid Molecules H<sub>2</sub>SO<sub>3</sub>, H<sub>2</sub>SO<sub>4</sub>, and H<sub>3</sub>PO<sub>4</sub>, respectively?|journal=J. Mol. Modeling|volume=6|issue=2|date=Feb 2000|pages=282–288|doi=10.1007/PL00010730|s2cid=96291857}}</ref> 

In this model, the structure obeys the [[octet rule]] and the charge distribution is in agreement with the [[electronegativity]] of the atoms. The discrepancy between the S−O bond length in the sulfate ion and the S−OH bond length in sulfuric acid is explained by donation of p-orbital electrons from the terminal S=O bonds in sulfuric acid into the antibonding S−OH orbitals, weakening them resulting in the longer bond length of the latter.

However, Pauling's representation for sulfate and other main group compounds with oxygen is still a common way of representing the bonding in many textbooks.<ref name="cotton">{{cite book|author1-link=F. Albert Cotton|last1=Cotton|first1=F. Albert|author2-link=Geoffrey Wilkinson|last2=Wilkinson|first2=Geoffrey|date=1966|title=Advanced Inorganic Chemistry|edition=2nd|location=New York, NY|publisher=Wiley}}</ref><ref name="greenwood" /> The apparent contradiction can be clarified if one realizes that the [[covalent bond|covalent]] double bonds in the Lewis structure actually represent bonds that are strongly polarized by more than 90% towards the oxygen atom. On the other hand, in the structure with a [[dipolar bond]], the charge is localized as a [[lone pair]] on the oxygen.<ref name="Stefan" />