Sigma-pi and equivalent-orbital models

<h2 id="multiple-bonds">Multiple bonds</h2>
Further information: <a href="/facts/Bent_bond/NQ7odhFQ">Bent bond</a>
Two different explanations for the nature of double and triple <a href="/facts/Covalent_bond/EzMLf3Pz">covalent bonds</a> in <a href="/facts/Organic_compound/gqCNaN45">organic</a> molecules were proposed in the 1930s. <a href="/facts/Linus_Pauling/cBNBzs5c">Linus Pauling</a> proposed that the double bond in ethylene results from two equivalent tetrahedral orbitals from each atom,<a class="footnote-ref" id="fnref:5" href="#fn:5">5</a> which later came to be called banana bonds or tau bonds.<a class="footnote-ref" id="fnref:6" href="#fn:6">6</a> <a href="/facts/Erich_H%25C3%25BCckel/EmM42Vtp">Erich Hückel</a> proposed a representation of the double bond as a combination of a <a href="/facts/Sigma_bond/CSyEe5CY">sigma bond</a> plus a <a href="/facts/Pi_bond/3Q6LAGYK">pi bond</a>.<a class="footnote-ref" id="fnref:7" href="#fn:7">7</a><a class="footnote-ref" id="fnref:8" href="#fn:8">8</a><a class="footnote-ref" id="fnref:9" href="#fn:9">9</a> The σ-π representation is the better-known one, and it is the one found in most textbooks since the late-20th century.

<h2 id="multiple-lone-pairs">Multiple lone pairs</h2>
Further information: <a href="/facts/Lone_pair/Q6kEAC4g">Lone pair</a>

Initially, Linus Pauling's scheme of water as presented in his hallmark paper on valence bond theory consists of two inequivalent lone pairs of σ and π symmetry.<a class="footnote-ref" id="fnref:10" href="#fn:10">10</a> As a result of later developments resulting partially from the introduction of VSEPR, an alternative view arose which considers the two lone pairs to be equivalent, colloquially called rabbit ears.<a class="footnote-ref" id="fnref:11" href="#fn:11">11</a>
Weinhold and Landis describe the symmetry adapted use of the orbital hybridization concept within the context of <a href="/facts/Natural_bond_orbital/fmU1d69B">natural bond orbitals</a>, a localized orbital theory containing modernized analogs of classical (valence bond/Lewis structure) bonding pairs and lone pairs.<a class="footnote-ref" id="fnref:12" href="#fn:12">12</a> For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals of π symmetry, while the other is an spx hydrid orbital of σ symmetry. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an spx hybrid orbital).
The question of whether it is conceptually useful to derive equivalent orbitals from symmetry-adapted ones, from the standpoint of bonding theory and pedagogy, is still a controversial one, with recent (2014 and 2015) articles opposing<a class="footnote-ref" id="fnref:13" href="#fn:13">13</a> and supporting<a class="footnote-ref" id="fnref:14" href="#fn:14">14</a> the practice.

<h2 id="references">References</h2>

<ol>
<li id="fn:1">Peter B. Karadakov; Joseph Gerratt; David L. Cooper; Mario Raimondi (1993), "Bent versus .sigma.-.pi. bonds in ethene and ethyne: the spin-coupled point of view", J. Am. Chem. Soc., 115 (15): 6863–6869, doi:10.1021/ja00068a050. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></li>
<li id="fn:2">Wiberg, Kenneth B. (1996), "Bent Bonds in Organic Compounds", Acc. Chem. Res., 29 (5): 229–34, doi:10.1021/ar950207a. <a href="/wiki/Kenneth_B._Wiberg" target="_blank">/wiki/Kenneth_B._Wiberg</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></li>
<li id="fn:3">Fleming, Ian (2010), Molecular Orbitals and Organic Chemical Reactions (reference ed.), London: Wiley, p. 61, ISBN 978-0-470-74658-5. <a href="978-0-470-74658-5" target="_blank">978-0-470-74658-5</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></li>
<li id="fn:4">A., Carroll, Felix (2010). Perspectives on structure and mechanism in organic chemistry (2nd ed.). Hoboken, N.J.: John Wiley. ISBN 9780470276105. OCLC 286483846.{{cite book}}: CS1 maint: multiple names: authors list (link) <a href="9780470276105" target="_blank">9780470276105</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></li>
<li id="fn:5">Pauling, Linus (1931), "The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules", J. Am. Chem. Soc., 53 (4): 1367–1400, doi:10.1021/ja01355a027. <a href="/wiki/Linus_Pauling" target="_blank">/wiki/Linus_Pauling</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></li>
<li id="fn:6">Wintner, Claude E. (1987), "Stereoelectronic effects, tau bonds, and Cram's rule", J. Chem. Educ., 64 (7): 587, Bibcode:1987JChEd..64..587W, doi:10.1021/ed064p587. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></li>
<li id="fn:7">Hückel, E. (1930), "Zur Quantentheorie der Doppelbindung", Z. Phys., 60 (7–8): 423–456, Bibcode:1930ZPhy...60..423H, doi:10.1007/BF01341254 <a href="/wiki/Erich_H%C3%BCckel" target="_blank">/wiki/Erich_H%C3%BCckel</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></li>
<li id="fn:8">Penney, W. G. (1934), "The Theory of the Structure of Ethylene and a Note on the Structure of Ethane", Proceedings of the Royal Society, A144 (851): 166–187, Bibcode:1934RSPSA.144..166P, doi:10.1098/rspa.1934.0041 <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></li>
<li id="fn:9">Penney, W. G. (1934), "The Theory of the Stability of the Benzene Ring and Related Compounds", Proceedings of the Royal Society, A146 (856): 223–238, Bibcode:1934RSPSA.146..223P, doi:10.1098/rspa.1934.0151. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></li>
<li id="fn:10">Pauling, Linus (1931), "The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules", J. Am. Chem. Soc., 53 (4): 1367–1400, doi:10.1021/ja01355a027. <a href="/wiki/Linus_Pauling" target="_blank">/wiki/Linus_Pauling</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></li>
<li id="fn:11">Laing, Michael (1987). "No rabbit ears on water. The structure of the water molecule: What should we tell the students?". J. Chem. Educ. 64 (2): 124–128. Bibcode:1987JChEd..64..124L. doi:10.1021/ed064p124. <a href="/wiki/Bibcode_(identifier)" target="_blank">/wiki/Bibcode_(identifier)</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></li>
<li id="fn:12">Weinhold, Frank; Landis, Clark R. (2012). Discovering Chemistry with Natural Bond Orbitals. Hoboken, N.J.: Wiley. pp. 67–68. ISBN 978-1-118-11996-9. <a href="978-1-118-11996-9" target="_blank">978-1-118-11996-9</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></li>
<li id="fn:13">Clauss, Allen D.; Nelsen, Stephen F.; Ayoub, Mohamed; Moore, John W.; Landis, Clark R.; Weinhold, Frank (2014-10-08). "Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms". Chemistry Education Research and Practice. 15 (4): 417–434. doi:10.1039/C4RP00057A. ISSN 1756-1108. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></li>
<li id="fn:14">Hiberty, Philippe C.; Danovich, David; Shaik, Sason (2015-07-07). "Comment on "Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms". A reply to a criticism". Chemistry Education Research and Practice. 16 (3): 689–693. doi:10.1039/C4RP00245H. S2CID 143730926. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></li>
</ol>

Sigma-pi and equivalent-orbital models open-in-new

Sigma-pi and equivalent-orbital models