Editing Lone pair (section)

==Different descriptions for multiple lone pairs==
{{Further|Sigma-pi and equivalent-orbital models}}
[[File:H2O lone pairs two descriptions.png|thumb|The symmetry-adapted and hybridized lone pairs of H<sub>2</sub>O]]
In elementary chemistry courses, the lone pairs of water are described as "rabbit ears": two equivalent electron pairs of approximately sp<sup>3</sup> hybridization, while the HOH bond angle is 104.5°, slightly smaller than the ideal tetrahedral angle of arccos(–1/3) ≈ 109.47°. The smaller bond angle is rationalized by [[VSEPR theory]] by ascribing a larger space requirement for the two identical lone pairs compared to the two bonding pairs.  In more advanced courses, an alternative explanation for this phenomenon considers the greater stability of orbitals with excess s character using the theory of [[isovalent hybridization]], in which bonds and lone pairs can be constructed with sp<sup>''x''</sup> hybrids wherein nonintegral values of ''x'' are allowed, so long as the total amount of s and p character is conserved (one s and three p orbitals in the case of second-row p-block elements).

To determine the hybridization of oxygen orbitals used to form the bonding pairs and lone pairs of water in this picture, we use the formula 1 + ''x'' cos θ = 0, which relates bond angle θ with the hybridization index ''x''.  According to this formula, the O–H bonds are considered to be constructed from O bonding orbitals of ~sp<sup>4.0</sup> hybridization (~80% p character, ~20% s character), which leaves behind O lone pairs orbitals of ~sp<sup>2.3</sup> hybridization (~70% p character, ~30% s character).  These deviations from idealized sp<sup>3</sup> hybridization (75% p character, 25% s character) for tetrahedral geometry are consistent with [[Bent's rule]]: lone pairs localize more electron density closer to the central atom compared to bonding pairs; hence, the use of orbitals with excess s character to form lone pairs (and, consequently, those with excess p character to form bonding pairs) is energetically favorable.

However, theoreticians often prefer an alternative description of water that separates the lone pairs of water according to symmetry with respect to the molecular plane.  In this model, there are two energetically and geometrically distinct lone pairs of water possessing different symmetry: one (σ) in-plane and symmetric with respect to the molecular plane and the other (π) perpendicular and anti-symmetric with respect to the molecular plane.  The σ-symmetry lone pair (σ(out)) is formed from a hybrid orbital that mixes 2s and 2p character, while the π-symmetry lone pair (p) is of exclusive 2p orbital parentage. The s character rich O σ(out) lone pair orbital (also notated ''n''<sub>O</sub><sup>(σ)</sup>) is an ~sp<sup>0.7</sup> hybrid (~40% p character, 60% s character), while the p lone pair orbital (also notated ''n''<sub>O</sub><sup>(π)</sup>) consists of 100% p character.

Both models are of value and represent the same total electron density, with the orbitals related by a [[unitary transformation]]. In this case, we can construct the two equivalent lone pair hybrid orbitals ''h'' and ''h''<nowiki/>' by taking linear combinations ''h'' = ''c''<sub>1</sub>σ(out) + ''c''<sub>2</sub>p and ''h''<nowiki/>' = ''c''<sub>1</sub>σ(out) – ''c''<sub>2</sub>p for an appropriate choice of coefficients ''c''<sub>1</sub> and ''c''<sub>2</sub>. For chemical and physical [[properties of water]] that depend on the ''overall'' electron distribution of the molecule, the use of ''h'' and ''h''<nowiki/>' is just as valid as the use of σ(out) and p. In some cases, such a view is intuitively useful.  For example, the stereoelectronic requirement for the [[anomeric effect]] can be rationalized using equivalent lone pairs, since it is the ''overall'' donation of electron density into the antibonding orbital that matters.  An alternative treatment using σ/π separated lone pairs is also valid, but it requires striking a balance between maximizing ''n''<sub>O</sub><sup>(π)</sup>-σ* overlap (maximum at 90° dihedral angle) and ''n''<sub>O</sub><sup>(σ)</sup>-σ* overlap (maximum at 0° dihedral angle), a compromise that leads to the conclusion that a ''gauche'' conformation (60° dihedral angle) is most favorable, the same conclusion that the equivalent lone pairs model rationalizes in a much more straightforward manner.<ref name=":1" />  Similarly, the [[hydrogen bond]]s of water form along the directions of the "rabbit ears" lone pairs, as a reflection of the increased availability of electrons in these regions.  This view is supported computationally.<ref name=":0" />  However, because only the symmetry-adapted canonical orbitals have physically meaningful energies, phenomena that have to do with the energies of ''individual'' orbitals, such as photochemical reactivity or [[photoemission spectroscopy|photoelectron spectroscopy]], are most readily explained using σ and π lone pairs that respect the [[molecular symmetry]].<ref name=":1">{{cite book |title=Orbital interactions in chemistry |last=A. |first=Albright, Thomas |others=Burdett, Jeremy K., 1947-, Whangbo, Myung-Hwan |isbn=9780471080398 |edition= Second |location=Hoboken, New Jersey |oclc=823294395 |date = 2013-04-08}}</ref><ref>While ''n''<sub>O</sub>(π) lone pair is equivalent to the canonical MO with Mulliken label 1''b''<sub>1</sub>, the ''n''<sub>O</sub>(σ) lone pair is ''not quite'' equivalent to the canonical MO of Mulliken label 2''a''<sub>1</sub>, since the fully delocalized orbital includes mixing with the in-phase symmetry-adapted linear combination of hydrogen 1s orbitals, making it slightly bonding in character, rather than strictly nonbonding.</ref>

Because of the popularity of [[VSEPR theory]], the treatment of the water lone pairs as equivalent is prevalent in introductory chemistry courses, and many practicing chemists continue to regard it as a useful model. A similar situation arises when describing the two lone pairs on the carbonyl oxygen atom of a [[ketone]].<ref>{{cite book |title=Modern Physical Organic Chemistry |url=https://archive.org/details/modernphysicalor00ansl |url-access=limited |last1=Ansyln |first1=E. V. |last2=Dougherty |first2=D. A. |publisher=University Science Books |year=2006 |isbn=978-1-891389-31-3 |location=Sausalito, CA |pages=[https://archive.org/details/modernphysicalor00ansl/page/n68 41]}}</ref> However, 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<ref>{{cite journal |last1=Clauss |first1=Allen D. |last2=Nelsen |first2=Stephen F. |last3=Ayoub |first3=Mohamed |last4=Moore |first4=John W. |last5=Landis |first5=Clark R. |last6=Weinhold |first6=Frank |date=2014-10-08 |title=Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms |journal=Chemistry Education Research and Practice |language=en |volume=15 |issue=4 |pages=417–434 |doi=10.1039/C4RP00057A |issn=1756-1108}}</ref> and supporting<ref>{{cite journal |last1=Hiberty |first1=Philippe C. |last2=Danovich |first2=David |last3=Shaik |first3=Sason |date=2015-07-07 |title=Comment on "Rabbit-ears hybrids, VSEPR sterics, and other orbital anachronisms". A reply to a criticism |journal=Chemistry Education Research and Practice |language=en |volume=16 |issue=3 |pages=689–693 |doi=10.1039/C4RP00245H |s2cid=143730926 }}</ref> the practice.