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{{merge to|Pyramidal inversion|date=January 2021}}

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| colspan=3 align=right |[[Image:Nitrogen-inversion-3D-balls.png|thumb|250px|Nitrogen inversion in ammonia]]

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|[[Image:Amine R-N.svg|96px]]

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|[[Image:Amine N-R.svg|96px]]

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| colspan=3 |'''Inversion of an amine.''' <small>The C₃ axis of the amine is presented as horizontal, and the pair of dots represent the lone pair of the nitrogen atom collinear with that axis. A mirror plane can be imagined to relate the two amine molecules on either side of the arrows. If the three R groups attached to the nitrogen are all unique, then the amine is chiral; whether it can be isolated depends on the [[Gibbs energy|free energy]] required for the molecule's inversion.</small>

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In [[chemistry]], '''nitrogen inversion''' (also '''umbrella inversion''')<ref>{{Cite journal|last1=Ghosh|first1=Dulal C.|last2=Jana|first2=Jibanananda|last3=Biswas|first3=Raka|date=2000|title=Quantum chemical study of the umbrella inversion of the ammonia molecule|url=https://onlinelibrary.wiley.com/doi/abs/10.1002/1097-461X%282000%2980%3A1%3C1%3A%3AAID-QUA1%3E3.0.CO%3B2-D|journal=International Journal of Quantum Chemistry|language=en|volume=80|issue=1|pages=1–26|doi=10.1002/1097-461X(2000)80:1<1::AID-QUA1>3.0.CO;2-D|issn=1097-461X}}</ref> is a [[fluxional molecule|fluxional process]] in [[nitrogen]] and [[amine]]s, whereby the [[molecule]] "turns inside out". It is a [[Molecular vibration|rapid oscillation]] of the nitrogen atom and substituents, the nitrogen "moving" through the plane formed by the substituents (although the substituents also move - in the other direction);<ref>{{Greenwood&Earnshaw2nd|page=423}}</ref> the molecule passing through a [[Trigonal planar molecular geometry|planar]] [[transition state]].<ref>{{ cite journal | author = J. M. Lehn | author-link = Jean-Marie Lehn | title = Nitrogen Inversion: Experiment and Theory | journal = [[Fortschritte der Chemischen Forschung|Fortschr. Chem. Forsch.]] | year = 1970 | volume = 15 | pages = 311–377 | doi = 10.1007/BFb0050820 }}</ref> For a compound that would otherwise be [[Chirality (chemistry)|chiral]] due to a nitrogen [[stereocenter]], nitrogen inversion provides a low energy pathway for [[racemization]], usually making [[chiral resolution]] impossible.<ref>{{March6th|pages=142–145}}</ref>

Nitrogen inversion is one case of the more general phenomenon of [[pyramidal inversion]], which applies to [[carbanion]]s, [[phosphane|phosphines]], [[arsine]]s, [[stibine]]s, and [[sulfoxide]]s.<ref>{{ cite journal |author = Arvi Rauk|author-link2=Leland C. Allen |author2=Leland C. Allen |author3-link=Kurt Mislow |author3=Kurt Mislow | title = Pyramidal Inversion | journal = [[Angewandte Chemie International Edition|Angew. Chem. Int. Ed.]] | year = 1970 | volume = 9 |issue=6 | pages = 400–414 | doi = 10.1002/anie.197004001 }}</ref><ref>{{GoldBookRef|file=P04956|title=Pyramidal inversion}}</ref>

==Energy barrier==

The ammonia interconversion is rapid at room [[temperature]], inverting 30 billion times per second. Two factors contribute to the rapidity of the inversion: a low [[activation energy|energy barrier]] (24.2&nbsp;[[kJ/mol]]; 5.8 kcal/mol) and a narrow width of the barrier itself{{clarify|date=November 2014}}, which allows for frequent [[quantum tunnelling]] (see below). In contrast, [[phosphine]] (PH₃) inverts very slowly at room temperature (energy barrier: 132&nbsp;kJ/mol).<ref>{{cite journal | last1 = Kölmel | first1 = C. | last2 = Ochsenfeld | first2 = C. | last3 = Ahlrichs | first3 = R. | year = 1991 | title = An ab initio investigation of structure and inversion barrier of triisopropylamine and related amines and phosphines | journal = Theor. Chim. Acta | volume = 82 | issue = 3–4| pages = 271–284 | doi = 10.1007/BF01113258 | s2cid = 98837101 }}</ref>

== Quantum effects ==

Ammonia exhibits a [[quantum tunnelling]] due to a narrow tunneling barrier,<ref>{{cite book | last = Feynman | first = Richard P. | author-link = Richard Feynman |author2=Robert Leighton |author3=Matthew Sands | title = The Feynman Lectures on Physics |volume=Volume&nbsp;III |chapter=The Hamiltonian matrix | publisher = Addison-Wesley | year = 1965 | location = Massachusetts, USA | isbn = 0-201-02118-8| title-link = The Feynman Lectures on Physics }}</ref> and not due to thermal excitation. Superposition of two states leads to [[energy level splitting]], which is used in ammonia [[maser]]s.

== Examples ==

The inversion of ammonia was first detected by [[microwave spectroscopy]] in 1934.<ref name="Cleeton">{{cite journal|last=Cleeton|first=C.E.|author2=Williams, N.H. |title=Electromagnetic waves of 1.1 cm wave-length and the absorption spectrum of ammonia|journal=Physical Review|year=1934|volume=45|pages=234–237|doi=10.1103/PhysRev.45.234|bibcode = 1934PhRv...45..234C|issue=4 }}</ref>

In one study the inversion in an [[aziridine]] was slowed by a factor of 50 by placing the nitrogen atom in the vicinity of a [[phenol]]ic alcohol group compared to the oxidized [[hydroquinone]].<ref>''Control of Pyramidal Inversion Rates by Redox Switching'' Mark W. Davies, Michael Shipman, James H. R. Tucker, and Tiffany R. Walsh [[J. Am. Chem. Soc.]]; '''2006'''; 128(44) pp.&nbsp;14260–14261; (Communication) {{DOI|10.1021/ja065325f}}</ref>

[[Image:Nitrogeninversionexample.png|400px|center|Nitrogen inversion Davies 2006]]

The system interconverts by oxidation by [[oxygen]] and reduction by [[sodium dithionite]].

== Exceptions ==

Conformational strain and structural rigidity can effectively prevent the inversion of amine groups. [[Tröger's base]] analogs<ref>{{Cite journal|last=MRostami |display-authors=etal |date=2017|title=Design and synthesis of Ʌ-shaped photoswitchable compounds employing Tröger's base scaffold|journal=Synthesis|volume=49|issue=6 |pages=1214–1222|doi=10.1055/s-0036-1588913 }}</ref> (including the Hünlich's base<ref>{{Cite journal|last=MKazem |display-authors=etal |date=2017|title=Facile preparation of Λ-shaped building blocks: Hünlich base derivatization|journal=Synlett|volume=28|issue=13 |pages=1641–1645|doi=10.1055/s-0036-1588180 |s2cid=99294625 |url=https://semanticscholar.org/paper/bfc9c874c3cde0d61f6bb27e9fcedfd49924dfe8 }}</ref>) are examples of compounds whose nitrogen atoms are chirally stable [[stereocenter]]s and therefore have significant [[Optical rotation|optical activity]].<ref name=":0">{{Cite journal|last=MRostami|first=MKazem|title=Optically active and photoswitchable Tröger's base analogs|doi=10.1039/C9NJ01372E|journal=New Journal of Chemistry|volume=43|issue=20|pages=7751–7755|via=The Royal Society of Chemistry|year=2019}}</ref>

[[File:Tröger's base.svg|thumb|272x272px|rigid Tröger's base scaffold prevents nitrogen inversion <ref name=":0" />]]

==References==

{{Reflist|2}}