Editing Lone pair

{{Short description|Pair of valence electrons which are not shared with another atom in a covalent bond}}
[[File:Hydroxide lone pairs-2D.svg|thumb|right|200px|Lone pairs (shown as pairs of dots) in the [[Lewis structure]] of [[hydroxide]]]]

In chemistry, a '''lone pair''' refers to a pair of [[valence electron]]s that are not shared with another atom in a [[covalent bond]]<ref name=goldbookoxstate>[[IUPAC]] ''[[Gold Book]]'' definition: [https://goldbook.iupac.org/terms/view/L03618 ''lone (electron) pair'']</ref> and is sometimes called an '''unshared pair''' or '''non-bonding pair'''. Lone pairs are found in the outermost [[electron shell]] of atoms. They can be identified by using a [[Lewis structure]]. [[Electron pair|Electron pairs]] are therefore considered lone pairs if two electrons are paired but are not used in [[chemical bonding]]. Thus, the number of [[electron]]s in lone pairs plus the number of electrons in bonds equals the number of valence electrons around an atom.

Lone pair is a concept used in [[valence shell electron pair repulsion theory]] (VSEPR theory) which explains the [[Molecular geometry|shapes of molecules]]. They are also referred to in the chemistry of [[Lewis acids and bases]]. However, not all non-bonding pairs of electrons are considered by chemists to be lone pairs. Examples are the transition metals where the non-bonding pairs do not influence molecular geometry and are said to be stereochemically inactive. In [[molecular orbital theory]] (fully [[delocalized]] canonical [[Molecular orbital|orbitals]] or localized in some form), the concept of a lone pair is less distinct, as the correspondence between an orbital and components of a Lewis structure is often not straightforward.  Nevertheless, occupied [[non-bonding orbital]]s (or orbitals of mostly nonbonding character) are frequently identified as lone pairs.

[[File:ParSolitario.png|thumb|right|300px|Lone pairs in [[ammonia]] (A), [[water]] (B), and [[hydrogen chloride]] (C)]]

A ''single'' lone pair can be found with atoms in the [[nitrogen group]], such as nitrogen in [[ammonia]]. ''Two'' lone pairs can be found with atoms in the [[chalcogen]] group, such as oxygen in water. The [[halogen]]s can carry ''three'' lone pairs, such as in [[hydrogen chloride]].

In VSEPR theory the electron pairs on the oxygen atom in water form the vertices of a tetrahedron with the lone pairs on two of the four vertices. The H–O–H [[bond angle]] is 104.5°, less than the 109° predicted for a [[tetrahedral angle]], and this can be explained by a repulsive interaction between the lone pairs.<ref name="FoxWhitesell2004">{{cite book |last1=Fox |first1=M.A. |last2=Whitesell |first2=J.K. |title=Organic Chemistry |publisher=Jones and Bartlett Publishers |year=2004 |isbn=978-0-7637-2197-8 |url=https://books.google.com/books?id=xx_uIP5LgO8C |access-date=5 May 2021 |page=}}</ref><ref name="McMurry2000">{{cite book |last=McMurry |first=J. |title=Organic Chemistry 5th Ed. |publisher=Ceneage Learning India Pvt Limited |year=2000 |isbn=978-81-315-0039-2 |url=https://books.google.com/books?id=1i84SwAACAAJ |access-date=5 May 2021}}</ref><ref name="Lee">{{cite book |last=Lee |first=J.D. |title=Concise Inorganic Chemistry |publisher=Van Nostrand |series=Student's paperback edition |year=1968 |url=https://books.google.com/books?id=THcfnwEACAAJ |access-date=5 May 2021 |page=}}</ref>

Various computational criteria for the presence of lone pairs have been proposed.  While electron density ρ('''r''') itself generally does not provide useful guidance in this regard, the [[Laplace operator|Laplacian]] of the electron density is revealing, and one criterion for the location of the lone pair is where  ''L''('''r''') ''= –''∇<sup>2</sup>ρ('''r''') is a local maximum.  The minima of the electrostatic potential ''V''('''r''') is another proposed criterion.  Yet another considers the [[electron localization function]] (ELF).<ref name=":0">{{cite journal |last1=Kumar |first1=Anmol |last2=Gadre |first2=Shridhar R. |last3=Mohan |first3=Neetha |last4=Suresh |first4=Cherumuttathu H. |date=2014-01-06 |title=Lone Pairs: An Electrostatic Viewpoint |journal=The Journal of Physical Chemistry A |language=en |volume=118 |issue=2 |pages=526–532 |doi=10.1021/jp4117003 |pmid=24372481 |issn=1089-5639 |bibcode=2014JPCA..118..526K}}</ref>

==Angle changes==
[[File:Tetrahedral Structure of Water.png|thumb|Tetrahedral structure of water]]
The pairs often exhibit a negative [[chemical polarity|polar character]] with their high charge density and are located closer to the [[atomic nucleus]] on average compared to the bonding pair of electrons. The presence of a lone pair decreases the bond angle between the bonding pair of electrons, due to their high electric charge, which causes great repulsion between the electrons. They are also involved in the formation of a [[dative bond]]. For example, the creation of the [[hydronium]] (H<sub>3</sub>O<sup>+</sup>) ion occurs when acids are dissolved in water and is due to the [[oxygen]] atom donating a lone pair to the [[hydrogen]] ion.

This can be seen more clearly when looked at it in two more common [[molecule]]s. For example, in [[carbon dioxide]] (CO<sub>2</sub>), which does not have a lone pair, the oxygen atoms are on opposite sides of the carbon atom ([[linear molecular geometry]]), whereas in [[water]] (H<sub>2</sub>O) which has two lone pairs, the angle between the hydrogen atoms is 104.5° ([[bent molecular geometry]]). This is caused by the repulsive force of the oxygen atom's two lone pairs pushing the hydrogen atoms further apart, until the forces of all electrons on the hydrogen atom are in [[mechanical equilibrium|equilibrium]]. This is an illustration of the [[VSEPR theory]].

==Dipole moments==
Lone pairs can contribute to a molecule's [[molecular dipole moment|dipole moment]]. [[Ammonia|NH<sub>3</sub>]] has a dipole moment of 1.42 D. As the [[electronegativity]] of nitrogen (3.04) is greater than that of hydrogen (2.2) the result is that the N-H bonds are polar with a net negative charge on the nitrogen atom and a smaller net positive charge on the hydrogen atoms. There is also a dipole associated with the lone pair and this reinforces the contribution made by the polar covalent N-H bonds to ammonia's [[molecular dipole moment|dipole moment]]. In contrast to NH<sub>3</sub>, [[nitrogen trifluoride|NF<sub>3</sub>]] has a much lower dipole moment of 0.234 D. Fluorine is more [[electronegativity|electronegative]] than nitrogen and the [[bond dipole moment|polarity]] of the N-F bonds is opposite to that of the N-H bonds in ammonia, so that the dipole due to the lone pair opposes the N-F bond dipoles, resulting in a low molecular dipole moment.<ref>{{Housecroft2nd|page=40}}</ref>

==Stereogenic lone pairs==
{| align=right valign=center width="272px" style="margin-left:2em; margin-bottom:1ex"
| colspan=3 align=right |
|-
|[[File:Amine R-N.svg|56px]]
| style="font-size:200%" |⇌&nbsp;
|[[File:Amine N-R.svg|56px]]
|-
| colspan=3 |Inversion of a generic organic amine molecule at nitrogen
|}

A lone pair can contribute to the existence of chirality in a molecule, when three other groups attached to an atom all differ. The effect is seen in certain [[amine]]s, [[phosphine]]s,<ref>Quin, L. D. (2000). ''A Guide to Organophosphorus Chemistry,'' LOCATION: John Wiley & Sons. {{ISBN|0471318248}}.</ref> [[sulfonium]] and [[oxonium ion]]s, [[sulfoxide]]s, and even [[carbanion]]s.

The [[chiral resolution|resolution]] of enantiomers where the stereogenic center is an amine is usually precluded because the [[activation energy|energy barrier]] for [[nitrogen inversion]] at the stereo center is low, which allow the two stereoisomers to rapidly interconvert at room temperature. As a result, such chiral amines cannot be resolved, unless the amine's groups are constrained in a cyclic structure (such as in [[Tröger's base]]).
{{Clear}}

==Unusual lone pairs==
A stereochemically active lone pair is also expected for divalent [[lead]] and [[tin]] ions due to their formal electronic configuration of n''s''<sup>2</sup>. In the solid state this results in the distorted metal coordination observed in the [[tetragonal crystal system|tetragonal]] [[litharge]] structure adopted by both PbO and SnO.
The formation of these heavy metal n''s''<sup>2</sup> lone pairs which was previously attributed to intra-atomic [[Orbital hybridisation|hybridization]] of the metal s and p states<ref>''Stereochemistry of Ionic Solids'' J.D.Dunitz and L.E.Orgel, Advan. Inorg. and Radiochem. '''1960''', 2, 1–60</ref> has recently been shown to have a strong anion dependence.<ref>{{cite journal |doi=10.1103/PhysRevLett.96.157403 |volume=96 |title=Electronic Origins of Structural Distortions in Post-Transition Metal Oxides: Experimental and Theoretical Evidence for a Revision of the Lone Pair Model |year=2006 |journal=Physical Review Letters |last1=Payne |first1=D. J. |issue=15 |page=157403 |pmid=16712195 |bibcode=2006PhRvL..96o7403P |url=https://ora.ox.ac.uk/objects/uuid:da90e4c7-566c-4a37-bab0-cd00b17043ff}}</ref> This dependence on the electronic states of the anion can explain why some divalent lead and tin materials such as PbS and SnTe show no stereochemical evidence of the lone pair and adopt the symmetric rocksalt crystal structure.<ref>{{cite journal |doi=10.1016/j.jssc.2005.01.030 |volume=178 |title=The origin of the stereochemically active Pb(II) lone pair: DFT calculations on PbO and PbS |year=2005 |journal=Journal of Solid State Chemistry |pages=1422–1428 |last1=Walsh |first1=Aron |issue=5 |bibcode=2005JSSCh.178.1422W}}</ref><ref>{{cite journal |doi=10.1021/jp051822r |volume=109 |title=Influence of the Anion on Lone Pair Formation in Sn(II) Monochalcogenides: A DFT Study |year=2005 |journal=The Journal of Physical Chemistry B |pages=18868–18875 |last1=Walsh |first1=Aron |issue=40 |pmid=16853428}}</ref>

In molecular systems the lone pair can also result in a distortion in the coordination of ligands around the metal ion. The lone-pair effect of lead can be observed in supramolecular complexes of [[lead(II) nitrate]], and in 2007 a study linked the lone pair to [[lead poisoning]].<ref>{{cite journal |last1=Gourlaouen |first1=Christophe |last2=Parisel |first2=Olivier |title=Is an Electronic Shield at the Molecular Origin of Lead Poisoning? A Computational Modeling Experiment |journal=Angewandte Chemie International Edition |date=15 January 2007 |volume=46 |issue=4 |pages=553–556 |doi=10.1002/anie.200603037 |pmid=17152108}}</ref> Lead ions can replace the native metal ions in several key enzymes, such as zinc cations in the [[ALAD]] enzyme, which is also known as [[porphobilinogen synthase]], and is important in the synthesis of [[heme]], a key component of the oxygen-carrying molecule [[hemoglobin]]. This inhibition of heme synthesis appears to be the molecular basis of lead poisoning (also called "saturnism" or "plumbism").<ref>{{cite journal |last1=Jaffe |first1=E. K. |last2=Martins |first2=J. |last3=Li |first3=J. |last4=Kervinen |first4=J. |last5=Dunbrack |first5=R. L. |display-authors=2 |title=The Molecular Mechanism of Lead Inhibition of Human Porphobilinogen Synthase |journal=Journal of Biological Chemistry |date=13 October 2000 |volume=276 |issue=2 |pages=1531–1537 |doi=10.1074/jbc.M007663200 |pmid=11032836 |doi-access=free}}</ref><ref>{{cite journal |last1=Scinicariello |first1=Franco |last2=Murray |first2=H. Edward |last3=Moffett |first3=Daphne B. |last4=Abadin |first4=Henry G. |last5=Sexton |first5=Mary J. |last6=Fowler |first6=Bruce A.|title=Lead and δ-Aminolevulinic Acid Dehydratase Polymorphism: Where Does It Lead? A Meta-Analysis |journal=Environmental Health Perspectives |date=15 September 2006 |volume=115 |issue=1 |pages=35–41 |doi=10.1289/ehp.9448 |pmid=17366816 |pmc=1797830}}</ref><ref>{{cite web |last1=Chhabra |first1=Namrata |title=Effect of Lead poisoning on heme biosynthetic pathway |url=http://usmle.biochemistryformedics.com/effect-of-lead-poisoning-on-heme-biosynthetic-pathway/ |website=Clinical Cases: Biochemistry For Medics |access-date=30 October 2016 |url-status=dead |archive-url=https://web.archive.org/web/20160403160650/http://usmle.biochemistryformedics.com/effect-of-lead-poisoning-on-heme-biosynthetic-pathway/ |archive-date=3 April 2016 |date=November 15, 2015}}</ref>

Computational experiments reveal that although the [[coordination number]] does not change upon substitution in calcium-binding proteins, the introduction of lead distorts the way the ligands organize themselves to accommodate such an emerging lone pair: consequently, these proteins are perturbed. This lone-pair effect becomes dramatic for zinc-binding proteins, such as the above-mentioned porphobilinogen synthase, as the natural substrate cannot bind anymore – in those cases the protein is [[enzyme inhibitor|inhibited]].

In [[Group 14]] elements (the [[carbon group]]), lone pairs can manifest themselves by shortening or lengthening [[single bond]] ([[bond order]] 1) lengths,<ref>{{cite journal |last1=Richards |first1=Anne F. |last2=Brynda |first2=Marcin |last3=Power |first3=Philip P. |title=Effects of the alkali metal counter ions on the germanium–germanium double bond length in a heavier group 14 element ethenide salt |journal=Chem. Commun. |date=2004 |issue=14 |pages=1592–1593 |doi=10.1039/B401507J |pmid=15263933}}</ref> as well as in the effective order of [[triple bond]]s as well.<ref>{{cite journal |last1=Power |first1=Philip P. |title=π-Bonding and the Lone Pair Effect in Multiple Bonds between Heavier Main Group Elements |journal=Chemical Reviews |date=December 1999 |volume=99 |issue=12 |pages=3463–3504 |doi=10.1021/cr9408989 |pmid=11849028}}</ref><ref name="LeeSekiguchi2011">{{cite book |author1=Vladimir Ya. Lee |author2=Akira Sekiguchi |title=Organometallic Compounds of Low-Coordinate Si, Ge, Sn, and Pb: From Phantom Species to Stable Compounds |url=https://books.google.com/books?id=kAS9u4If26wC&pg=PA23 |date=22 July 2011 |publisher=John Wiley & Sons |isbn=978-1-119-95626-6 |page=23}}</ref> The familiar [[alkyne]]s have a carbon-carbon triple bond ([[bond order]] 3) and a linear geometry of 180° bond angles (figure '''A''' in reference <ref name="SpikesDigermyne">{{cite journal |last1=Spikes |first1=Geoffrey H. |last2=Power |first2=Philip P. |title=Lewis base induced tuning of the Ge–Ge bond order in a "digermyne" |journal=Chem. Commun. |date=2007 |issue=1 |pages=85–87 |doi=10.1039/b612202g |pmid=17279269}}</ref>). <!-- I'm assuming this is what the original editor was referring to by "germanium to germanium [..] effective bond order 2" -->However, further down in the group ([[silicon]], [[germanium]], and [[tin]]), formal triple bonds have an effective bond order 2 with one lone pair (figure '''B'''<ref name="SpikesDigermyne"/>) and [[cis-trans isomerism|trans]]-bent geometries. In [[lead]], the effective bond order is reduced even further to a single bond, with two lone pairs for each lead atom (figure ''C''<ref name="SpikesDigermyne"/>). In the [[organogermanium compound]] (''Scheme 1'' in the reference), the effective bond order is also 1, with complexation of the [[Lewis acid|acidic]] [[isonitrile]] (or ''isocyanide'') C-N groups, based on interaction with germanium's empty 4p orbital.<ref name="SpikesDigermyne"/><ref>{{cite journal |last1=Power |first1=Philip P. |title=Silicon, germanium, tin, and lead analogues of acetylenes |journal=Chemical Communications |date=2003 |issue=17 |pages=2091–101 |doi=10.1039/B212224C |pmid=13678155}}</ref>

[[File:Digermina.png|center|600px|Lone pair trends in group 14 triple bonds]]

==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.

==See also==
{{Wiktionary|lone pair}}
{{Commons category|Lone pair}}
*[[Coordination complex]]
*[[HOMO and LUMO]] (highest occupied molecular orbital and lowest unoccupied molecular orbital)
*[[Inert-pair effect]]
*[[Ligand]]
*[[Shared pair]]

==References==
{{Reflist}}

{{Chemical bonding theory}}

[[Category:Chemical bonding]]