View source for Bürgi–Dunitz angle

[[File:BurgiDunitzFlippinLodgeCelestCoordAnalogy.jpg|thumb|Bürgi–Dunitz and [[Flippin–Lodge angle|Flippin–Lodge]] nucleophile approach trajectory angles, <math>\alpha_{BD}</math> and <math>\alpha_{FL}</math>, analogized to altitude- and azimuth-types of parameters in the [[Horizontal coordinate system|celestial (horizontal) coordinate system]]. Both in this celestial coordinate system, and in the system to describe a nucleophile approaching a planar electrophile, the problem is to uniquely describe the location of a point off of a plane, relative to specific point on the plane. Hence, in both cases, the problem can be addressed using two angles, an altitude-type angle and an azimuth-type angle. Note, while elevation in celestial applications is most easily measured as the specific altitude shown, the elevation of the nucleophile, <math>\alpha_{BD}</math>, is most easily measured as the [[Angle#Combining angle pairs|supplementary]] angle, Nu-C-O, hence its values are most often >90° (see text and next image).]]

The '''Bürgi–Dunitz angle''' (BD angle) is one of two angles that fully define the geometry of "attack" (approach via collision) of a [[nucleophile]] on a [[trigonal planar molecular geometry|trigonal]] [[Saturated and unsaturated compounds|unsaturated]] center in a [[molecule]], originally the [[carbonyl]] center in an [[Organic compound|organic]] [[ketone]], but now extending to [[aldehyde]], [[ester]], and [[amide]] carbonyls, and to [[alkene]]s (olefins) as well.<ref name=Fleming10_214f>Fleming, I. (2010) ''Molecular Orbitals and Organic Chemical Reactions: Reference Edition'', John Wiley & Sons, pp. 214–215.</ref><ref name=BurgiDunitzTet74>{{cite journal |author1=Bürgi, H.-B.  |author2=Dunitz, J. D. |author3=Lehn. J.-M. |author4=Wipff, G. | title= Stereochemistry of reaction paths at carbonyl centres | journal= [[Tetrahedron (journal)|Tetrahedron]] | year=1974 | volume=30 | issue=12 | pages=1563–1572 | doi = 10.1016/S0040-4020(01)90678-7 }}</ref><ref name="A.S. Cieplak 2008 pp. 205 - 302">Cieplak, A.S. (2008) Organic addition and elimination reactions: Transformation paths of carbonyl derivatives ''In'' Structure Correlation, Vol. 1 (H.-B. Bürgi & J. D. Dunitz, eds.), New York:John Wiley & Sons, pp. 205–302, esp. 216-218. [doi:10.1002/9783527616091.ch06; {{ISBN|9783527616091}} ]</ref>  The angle was named after crystallographers [[Hans-Beat Bürgi]] and [[Jack D. Dunitz]], its first senior investigators.

Practically speaking, the Bürgi–Dunitz and Flippin–Lodge angles were central to the development of understanding of [[chiral synthesis|chiral chemical synthesis]], and specifically of the phenomenon of [[asymmetric induction]] during nucleophilic attack at hindered carbonyl centers (see the [[Cram–Felkin–Anh]] and Nguyen{{huh|date=July 2023}} models).<ref name=Heathcock1990/><ref>Gawley, R.E. & Aube, J. 1996, Principles of Asymmetric Synthesis (Tetrahedron Organic Chemistry Series, Vo. 14), pp. 121-130, esp. pp. 127f.</ref>

Additionally, the stereoelectronic principles that underlie nucleophiles adopting a proscribed range of Bürgi–Dunitz angles may contribute to the conformational stability of proteins<ref>{{cite journal |author1=Bartlett, G.J. |author2=Choudhary, A. |author3=Raines, R.T.  |author4=Woolfson, D.N. | title= ''n''→''π''* interactions in proteins | journal= Nat. Chem. Biol. | year=2010 | volume=6 | issue=8 | pmid= 20622857 | pmc= 2921280 | pages=615–620 | doi = 10.1038/nchembio.406}}</ref><ref>{{cite journal | author = Fufezan, C. | title = The role of Buergi‐Dunitz interactions in the structural stability of proteins | journal = Proteins | year = 2010 | volume = 78 | issue = 13 | pmid = 20635415 | pages = 2831–2838 | doi = 10.1002/prot.22800 | s2cid = 41838636 }}</ref> and are invoked to explain the stability of particular conformations of molecules in one hypothesis of a [[Abiogenesis|chemical origin of life]].<ref>{{cite journal |author1=Choudhary, A. |author2=Kamer, K.J. |author3=Powner, M.W. |author4=Sutherland, J.D. |author5=Raines, R.T. | title= A stereoelectronic effect in prebiotic nucleotide synthesis | journal= ACS Chem. Biol. | year=2010 | volume=5 | pmid= 20499895 | issue=7 | pages=655–657 | pmc= 2912435 | doi = 10.1021/cb100093g}}</ref>

== Definition ==
In the addition of a nucleophile (Nu) attack to a carbonyl, the BD angle is defined as the Nu-C-O bond angle. The BD angle adopted during an approach by a [[nucleophile]] to a trigonal unsaturated [[electrophile]] depends primarily on the [[molecular orbital]] (MO) shapes and occupancies of the unsaturated carbon center (e.g., carbonyl center), and only secondarily on the molecular orbitals of the nucleophile.<ref name=Fleming10_214f/>

Of the two angles which define the geometry of nucleophilic "attack", the second describes the "offset" of the nucleophile's approach toward one of the two substituents attached to the carbonyl carbon or other electrophilic center, and was named the [[Flippin–Lodge angle]] (FL angle) by [[Clayton Heathcock]] after his contributing collaborators Lee A. Flippin and Eric P. Lodge.<ref name="Heathcock1990">Heathcock, C.H. (1990) Understanding and controlling diastereofacial selectivity in carbon-carbon bond-forming reactions, ''Aldrichimica Acta'' '''23'''(4):94-111, esp. p. 101, see [http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf] {{Webarchive|url=https://web.archive.org/web/20140106112716/http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf |date=2014-01-06 }}, accessed 9 June 2014.</ref>

These angles are generally construed to mean the angle measured or calculated for a given system, and not the historically observed value range for the original Bürgi–Dunitz aminoketones, or an idealized value computed for a particular system (such as hydride addition to [[formaldehyde]], image at left). That is, the BD and FL angles of the hydride-formaldehyde system produce a given pair of values, while the angles observed for other systems may vary relative to this simplest of chemical systems.<ref name=Fleming10_214f/><ref name="A.S. Cieplak 2008 pp. 205 - 302"/><ref name="RadiskyKoshlandGutter02">Radisky, E.S. & Koshland, D.E. (2002), A clogged gutter mechanism for protease inhibitors, ''Proc. Natl. Acad. Sci. U.S.A.'', '''99'''(16):10316-10321, see [http://www.pnas.org/content/99/16/10316.full.pdf+html?sid=e2adc3d6-5c97-4f82-a493-e1a6d9bdf674], accessed 28 November 2014.</ref>

== Measurement ==
{{refimprove section|date = February 2025}}
The original Bürgi-Dunitz measurements were of a series of intramolecular [[amine]]-[[ketone]] carbonyl interactions, in crystals of compounds bearing both functionalities—e.g., [[methadone]] and [[protopine]]. These gave a narrow range of BD angle values (105 ± 5°); corresponding computations—[[Molecular orbital theory|molecular orbital calculations]] of the [[LCAO|SCF-LCAO-type]]—describing the approach of the s-orbital of a hydride anion (H<sup>−</sup>) to the pi-system of the simplest aldehyde, formaldehyde (H<sub>2</sub>C=O), gave a BD angle value of 107°.<ref name=BurgiDunitzTet74/>{{primary source inline|date=September 2020}}

In the structure of {{small|L}}-methadone (below, left), note the [[tertiary amine]] projecting to the lower right, and the [[carbonyl]] (C{{=}}O) group at the center, which engage in an intramolecular interaction in the crystal structure (after rotation around the single bonds connecting them, during the [[crystallization]] process).{{cn|date = February 2025}} Similarly, in the structure of protopine (below, right), note the [[tertiary amine]] at the center of the molecule, part of a ten-membered ring, and the C{{=}}O group diagonally opposite it on the ring; these engage in an intramolecular interaction allowed by changes in the [[torsion angle]]s of the atoms of the ring.{{cn|date = February 2025}}

Hence, Bürgi, Dunitz, and thereafter many others noted that the crystallographic measurements of the aminoketones and the computational estimate for the simplest nucleophile-electrophile system were quite close to a theoretical ideal, the [[tetrahedral angle]] (internal angles of a [[tetrahedron]], 109.5°), and so consistent with a geometry understood to be important to developing transition states in nucleophilic attacks at trigonal centers.{{citation needed|date=September 2020}}

{{gallery
| align = center
| mode = packed
|File:Levomethadone.svg
|Structure of {{small|L}}-[[methadone]], a key molecule whose crystals were [[X-ray crystallography|studied]] in the development of the BD angle concept.

|File:Protopine structure.svg
|Structure of [[protopine]], an [[alkaloid]], whose crystals were also [[X-ray crystallography|studied]] in the development of the BD angle concept.
<!--
|File:Protopine-from-xtal-Bürgi-Dunitz-Mercury-3D-stick-bs.png
|The amine-to-carbonyl n→&pi;* interaction in protopine with an unusually short N···C distance of 2.555 Å and a Bürgi–Dunitz angle of 102°.<ref name = HallAhmedACSBprototropinXtal>{{ cite journal | first1 = S. R. | last1 = Hall | first2 = F. R. | last2 = Ahmed | title = The crystal structure of protopine, C<sub>20</sub>H<sub>19</sub>O<sub>5</sub>N | journal = [[Acta Crystallographica Section B|Acta Crystallogr. B]] | year = 1968 | volume = 24 | issue = 3 | pages=337–346 | doi = 10.1107/S0567740868002347 }}</ref>-->
}}

== Theory ==
{{multiple image| align = right | direction = horizontal | header = '''Hydride addition to formaldehyde''' | header_align = left/right/center | footer = '''(Left)''' Shown is nucleophilic attack by the charged nucleophile (Nu), hydride anion, on the unsaturated trigonal center of the aldehyde electrophile, formaldehyde (R,R'=H). The value computed as optimal for this system, 107°, is indicated, and is representative of the [[obtuse angle|obtuse]] values observed in most experimental chemical systems.<br/>'''(Right)''' Cartoon of the approach of a p-type highest occupied molecular orbital (HOMO) of a nucleophile such as chloride ion (green sphere), and the lowest unoccupied molecular orbital (LUMO) of the trigonal center of an electrophilic carbonyl of formaldehyde (black sphere carbon, red sphere oxygen, white spheres hydrogen). View is nearly side on, and the developing out-of-plane distortion of the carbonyl carbon atom is omitted for simplicity. | footer_align = left | image1 = Burgi-Dunitz-angle-2D.png | width1 = 124 | caption1 = Estimated Bürgi–Dunitz (<math>\alpha_{BD}</math>) angle for this simplest H<sup>(–)</sup> → H<sub>2</sub>C=O nucleo-philic [[nucleophilic addition|addition]]. | image2 = Nucleophile-HOMO-carbonyl-LUMO-overlap-3D-balls.png | width2 = 100 | caption2  = HOMO-LUMO interaction underlying <math>\alpha_{BD}</math> angle in simple systems.}}

The convergence of observed BD angles can be viewed as arising from the need to maximize overlap between the highest occupied molecular orbital ([[HOMO]]) of the nucleophile, and the lowest unoccupied molecular orbital ([[LUMO]]) of the unsaturated, trigonal center of the electrophile.<ref name=Fleming10_214f/> (See, in comparison, the related inorganic chemistry concept of the angular overlap model.<ref>Hoggard, P.E. (2004) Angular overlap model parameters, ''Struct. Bond.'' '''106''', 37.</ref><ref>Burdett, J.K. (1978) A new look at structure and bonding in transition metal complexes, ''Adv. Inorg. Chem.'' '''21''', 113.</ref><ref>Purcell, K.F. & Kotz, J.C. (1979) ''Inorganic Chemistry'', Philadelphia, PA:Saunders Company.{{page needed|date=November 2014}}</ref>{{page needed|date=November 2014}})

In the case of addition to a carbonyl, the HOMO is often a p-type orbital (e.g., on an [[amine]] nitrogen or [[halide]] [[anion]]), and the LUMO is generally understood to be the [[antibonding]] π* [[molecular orbital]] perpendicular to the plane containing the ketone C=O bond and its substituents (see figure at right above). The BD angle observed for nucleophilic attack is believed to approach the angle that would produce optimal overlap between HOMO and LUMO (based on the principle of the lowering of resulting new [[molecular orbital]] energies after such mixing of orbitals of similar energy and symmetry from the participating reactants). At the same time, the nucleophile avoids overlap with other orbitals of the electrophilic group that are unfavorable for bond formation (not apparent in image at right, above, because of the simplicity of the R=R'=H in formaldehyde).{{citation needed|date=September 2020}}

=== Complications ===

==== Electrostatic and Van der Waals interactions ====
To understand cases of real chemical reactions, the HOMO-LUMO-centered view is modified by understanding of further complex, electrophile-specific repulsive and attractive [[electrostatic]] and [[Van der Waals interaction]]s that alter the altitudinal BD angle, and bias the azimuthal Flippin-Lodge angle toward one substituent or the other (see graphic above).<ref>Lodge, E.P. & Heathcock, C.H. (1987) Steric effects, as well as sigma*-orbital energies, are important in diastereoface differentiation in additions to chiral aldehydes, ''J. Am. Chem. Soc.'', '''109''':3353-3361.</ref>{{primary source inline|date=September 2020}}

====Linear and rotational dynamics ====
BD angle theory was developed based on "frozen" interactions in crystals where the impacts of [[Dynamics (mechanics)|dynamics]] at play in the system (e.g., easily changed [[torsional angle]]s) may be negligible. However, most reaction chemistry of general interest and utility takes place via collisions of molecules rapidly tumbling in [[Solution (chemistry)|solution]]; accordingly, the dynamics of each  situation are sampled effectively, and so are reflected in the outcomes of the reactions.{{citation needed | date = January 2025}}

====Constrained environments in enzymes and nanomaterials ====
Moreover, in constrained reaction environments such as in enzyme and nanomaterial binding sites, early evidence suggests that BD angles for reactivity can be quite distinct, since reactivity concepts assuming orbital overlaps during random collision are not directly applicable.<ref>See for instance, Light, S.H.; Minasov, G.; Duban, M.-E. & Anderson, W.F. (2014) Adherence to Bürgi-Dunitz stereochemical principles requires significant structural rearrangements in Schiff-base formation: Insights from transaldolase complexes, ''Acta Crystallogr. D'' '''70'''(Pt 2):544-52, DOI: 10.1107/S1399004713030666, see [http://journals.iucr.org/d/issues/2014/02/00/dw5075/dw5075.pdf] {{Webarchive|url=https://web.archive.org/web/20140714125624/http://journals.iucr.org/d/issues/2014/02/00/dw5075/dw5075.pdf |date=2014-07-14 }}, accessed 10 June 2014.</ref><ref name=RadiskyKoshlandGutter02/> 

For instance, the BD value determined for [[enzymatic]] cleavage of an amide by a [[serine protease]] ([[subtilisin]]) was 88°, quite distinct from the hydride-formaldehyde value of 107°; moreover, compilation of literature crystallographic BD angle values for the same reaction mediated by different protein catalysts clustered at 89 ± 7°  (i.e., only slightly offset from directly above or below the carbonyl carbon). At the same time, the subtilisin FL value was 8°, and FL angle values from the careful compilation clustered at 4 ± 6° (i.e., only slightly offset from directly behind the carbonyl; see the [[Flippin–Lodge angle]] article).<ref name=RadiskyKoshlandGutter02/>{{primary source inline|date=September 2020}}

== See also ==
* [[Flippin–Lodge angle]]

== References ==
{{reflist|2}}

{{DEFAULTSORT:Burgi-Dunitz Angle}}
[[Category:Physical organic chemistry]]