View source for Flippin–Lodge angle


{{multiple image
 | width = 250
 | footer = 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 (here '''plane I''', the plane containing the [[carbonyl]] and its '''R''' and '''R'''' substituents, likewise with other electrophiles). ''Hence, in both cases, the problem can be addressed using two angles, an altitude-type angle and an azimuth-type angle.'' (A third component of description is [[stereochemistry|stereochemical]], i.e., indicating whether approach is from above or below the electrophile plane, see following.)

The nucelophile (atom or group) is represented here as ''':Nu'''. The substituents,  '''R''' and '''R'''', attached to the carbon atom of the [[carbonyl]] group may be an atom such as hydrogen (H), [[alkyl group]]s such as [[methyl]], [[Ethyl group|ethyl]], etc. (including far more complex ones), or other [[functional group]]s such as the O- and N-containing groups of [[ester]]s and [[amide]]s. In both panels, a second plane, '''plane II''' (red), is defined that is [[orthogonal]] (perpendicular) to the first, containing the carbon and oxygen atoms of the [[carbonyl]], C=O, and [[bisection|bisecting]] the '''R<big>—•—</big>R'''' angle (where the "•" is the carbon atom). A third plane, mutually orthogonal to the first two, '''plane III''' (green), contains only the carbon atom of the carbonyl; it corresponds to the plane of the page in the Newman projection at right. In that projection, the '''vector''' (arrow) pointing from :Nu to the carbon of the carbonyl is mirrored across plane I to make clear that the nucleophile can approach from either above or below this plane (with resulting differences in the stereochemistry of reaction products, see text). The dotted line from :Nu to plane I indicates the computational process of [[Projection (mathematics)|mathematically projecting]] the geometric point representing :Nu onto plane I, which is sometimes a necessary maths operation (see text).

Note, for sake of clarity of presentation in the image at left, the nucleophile and azimuthal angle, <math>\alpha_{FL}</math>, are shown as displaced toward the R substituent, while in the Newman projection, the opposite is the case. In this article, the R substituent is arbitrarily being assigned to the more [[steric bulk|sterically bulky]] group, and so the displacement shown at right is most representative of the phenomena described throughout. Note also, 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).
 | image1 = BurgiDunitzFlippinLodgeCelestCoordAnalogyBoxedCorr.jpg
 | alt1 = To be supplied
 | caption1 = Flippin–Lodge and [[Bürgi–Dunitz angle|Bürgi–Dunitz]] nucleophile approach trajectory angles, <math>\alpha_{FL}</math> and <math>\alpha_{BD}</math>, analogized to azimuth and altitude parameters in the [[Horizontal coordinate system|celestial (horizontal) coordinate system]].
 | image2 = FlippinLodgeHeatchcockNewmanCorrectPlanesBoxed.jpg
 | alt2 =To be supplied
 | caption2 = Flippin–Lodge angle, <math>\alpha_{FL}</math>, for a nucleophilic "attack" (addition) at a [[carbonyl]]-containing [[electrophile]], in [[Newman projection]], with electrophile plane I viewed edge-on.<ref name=Heathcock1990>C.H. Heathcock (1990) Understanding and controlling diastereofacial selectivity in carbon-carbon bond-forming reactions, Aldrichimica Acta 23(4):94-111, esp. p. 101, see {{cite web |url=http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf |title=Archived copy |access-date=2014-01-06 |archive-url=https://web.archive.org/web/20140106112716/http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf |archive-date=2014-01-06 }}, accessed 9 June 2014.</ref>
}}

The '''Flippin–Lodge angle''' is one of two angles used by [[organic chemistry|organic]] and [[biochemistry|biological chemist]]s studying the relationship between a molecule's [[chemical structure]] and ways that it [[chemical reactivity|reacts]], for reactions involving "attack" of an electron-rich reacting species, the [[nucleophile]], on an electron-poor reacting species, the [[electrophile]]. Specifically, the angles—the [[Bürgi–Dunitz angle|Bürgi–Dunitz]], <math>\alpha_{BD}</math>, and the Flippin–Lodge, <math>\alpha_{FL}</math>—describe the "trajectory" or "angle of attack" of the nucleophile as it approaches the electrophile, in particular when the latter is [[Trigonal planar molecular geometry|planar]] in shape. This is called a [[nucleophilic addition]] reaction and it plays a central role in the [[biochemistry|biological chemistry]] taking place in many [[biosynthesis|biosyntheses]] in nature, and is a central "tool" in the reaction toolkit of modern organic chemistry, e.g., to construct new molecules such as [[pharmaceuticals]]. Theory and use of these angles falls into the areas of [[synthetic chemistry|synthetic]] and [[physical organic chemistry]], which deals with [[chemical structure]] and [[reaction mechanism]], and within a sub-specialty called ''structure correlation''.

Because chemical reactions take place in [[three dimensional|three dimensions]], their quantitative description is, in part, a [[Euclidean geometry|geometry]] problem. Two angles, first the Bürgi–Dunitz angle, <math>\alpha_{BD}</math>, and later the Flippin–Lodge angle, <math>\alpha_{FL}</math>, were developed to describe the approach of the reactive [[atom]] of a nucleophile (a point off of a plane) to the reactive atom of an electrophile (a point on a plane). The <math>\alpha_{FL}</math> is an angle that estimates the displacement of the nucleophile, at its elevation, toward or away from the particular R and R' [[substituent]]s attached to the electrophilic atom (see image). The <math>\alpha_{BD}</math> is the angle between the approach vector connecting these two atoms and the plane containing the electrophile (see the [[Bürgi–Dunitz angle|Bürgi–Dunitz]] article). Reactions addressed using these angle concepts use nucleophiles ranging from single atoms (e.g., chloride [[anion]], [[chloride|Cl<sup>–</sup>]]) and polar organic [[functional group]]s (e.g., [[primary amine]]s, R"-NH<sub>2</sub>), to complex [[chiral catalyst]] reaction systems and [[enzyme]] [[active site]]s. These nucleophiles can be paired with an array of planar electrophiles: [[aldehyde]]s and [[ketone]]s, [[Carboxylic Acid Derivatives#Carbonyl compounds|carboxylic acid-derivatives]], and the carbon-carbon double bonds of [[alkene]]s. Studies of <math>\alpha_{BD}</math> and <math>\alpha_{FL}</math> can be theoretical, based on [[Molecular orbital|calculations]], or experimental (either quantitative, based on [[X-ray crystallography]], or inferred and semiquantitative, rationalizing results of particular chemical reactions), or a combination of these.

The most prominent application and impact of the Flippin–Lodge angle has been in the area of chemistry where it was originally defined: in practical [[organic synthesis|synthetic]] studies of the outcome of carbon-carbon bond-forming reactions in solution.  An important example is the [[aldol reaction]], e.g., addition of ketone-derived nucleophiles ([[enol]]s, [[enolate]]s), to electrophilic [[aldehyde]]s that have attached groups varying in size and polarity. Of particular interest, given the [[three-dimensional]] nature of the concept, is understanding how the combined features on the nucleophile and electrophile impact the [[stereochemistry]] of reaction outcomes (i.e., the "handedness" of new  [[chiral]] centers created by a reaction). Studies invoking Flippin–Lodge angles in synthetic chemistry have improved the ability of chemists to predict outcomes of known reactions, and to design better reactions to produce particular stereoisomers ([[enantiomer]]s and [[diastereomer]]s) needed in the construction of complex natural products and drugs.

== Technical introduction ==
The Flippin–Lodge (FL) angle, <math>\alpha_{FL}</math> is the latter-derived of two angles that fully define the geometry of "attack" (approach via collision) of a [[nucleophile]] on a [[trigonal]] [[Saturated and unsaturated compounds|unsaturated]] center of an [[electrophile|electrophilic]] [[molecule]] (the second being the Bürgi–Dunitz angle, <math>\alpha_{BD}</math>, see below).<ref name=Fleming2010>Ian Fleming (2010) Molecular Orbitals and Organic Chemical Reactions: Student Edition, John Wiley and Sons, pp. 158–160; see also Ian Fleming (2010) Molecular Orbitals and Organic Chemical Reactions: Reference Edition, John Wiley and Sons, pp.&nbsp;214–215, {{ISBN|0-470-74658-0}}, [https://www.amazon.com/Molecular-Orbitals-Organic-Chemical-Reactions/dp/0470746599], accessed 5 January 2014.</ref><ref name=GawleyAube1996/> Theory and application of these angles falls into the area of [[synthetic chemistry|synthetic]], and of [[physical organic chemistry]] (in the specializations of [[chemical structure]] and [[reaction mechanism]]), in the latter, within a sub-specialty called ''structure correlation''.<ref name = Cieplak08>{{cite book | author = Cieplak, A.S. | year = 2008 | orig-date = 1994 | chapter = Organic Addition and Elimination Reactions; Transformation Paths of Carbonyl Derivatives [Ch. 6] | title =  Structure Correlation, Vol. 1 | pages = 205–302, esp. 270–274 |editor= Bürgi, Hans-Beat |editor2=Dunitz, Jack D. | location = Weinheim, GER | publisher = VCH | isbn = 978-3-527-61608-4 | chapter-url = https://books.google.com/books?isbn=352761608X | access-date = 1 March 2016 }}</ref> Studies of  <math>\alpha_{FL}</math> and <math>\alpha_{BD}</math> can be theoretical, based on [[Molecular orbital|calculations]], or experimental (either quantitative, based on [[X-ray crystallography]], or inferred and semiquantitative, rationalizing results of particular chemical reactions), or a combination of these.<ref name=Fleming2010/><ref name=GawleyAube1996/><ref name = Cieplak08/>

Nucleophiles in this [[addition reaction]] may range from single atoms ([[hydride]], [[chloride]]), to polar organic [[functional group]]s ([[amine]]s, [[Alcohol (chemistry)|alcohol]]s), to complex systems (nucleophilic [[enolate]]s with [[chiral catalyst]]s, [[amino acid]] [[side chain]]s in [[enzyme]] [[active site]]s; see below). Planar electrophiles include [[aldehyde]]s and [[ketone]]s, [[carboxylic acid]]-derivatives such as [[ester]]s, and [[amide]]s, and the carbon-carbon double bonds of particular [[alkene]]s ([[olefin]]s).<ref name=Heathcock1990/><ref name=Fleming2010/> In the example of nucleophilic attack at a carbonyl, <math>\alpha_{FL}</math> is a measure of the "offset" of the nucleophile's approach to the electrophile, toward one or the other of the two substituents attached to the carbonyl carbon.<ref name=Heathcock1990/><ref name=Fleming2010/><ref name=GawleyAube1996/> The relative values of angles for pairs of reactions can be inferred and semiquantitative, based on rationalizations of the products of the reactions; alternatively, as noted in the figure, <math>\alpha_{FL}</math> values may be formally derived from crystallographic coordinates by geometric calculations, or graphically, e.g., after projection of Nu onto the carbonyl plane and measuring the angle supplementary to  ''L''Nu'-C-O (where Nu' is the projected atom). This often overlooked angle of the nucleophile's trajectory was named the [[Flippin-Lodge]] angle by [[Clayton H. Heathcock]] after his contributing collaborators Lee A. Flippin and Eric P. Lodge.<ref name=Heathcock1990/><ref name=GawleyAube1996/><ref name=LodgeHeathcock1987>E.P. Lodge & C.H. Heathcock (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><ref name="Flippin1983">L.A. Flippin & C.H. Heathcock (1983) Acyclic stereoselection. 16. High diastereofacial selectivity in Lewis acid mediated additions of enolsilanes to chiral aldehydes, J. Am. Chem. Soc. 105:1667-1668.</ref> The second angle defining the geometry, the more well known [[Bürgi–Dunitz angle|Bürgi–Dunitz]] angle, <math>\alpha_{BD}</math>, describes the Nu-C-O bond angle and was named after crystallographers Hans-Beat Bürgi and [[Jack D. Dunitz]], its first senior investigators (see that [[Bürgi–Dunitz angle|related article]]).<ref name=BurgiDunitzTet74>{{cite journal |author1=H. B. Bürgi |author2=J. D. Dunitz |author3=J. M. Lehn |author4=G. Wipff | 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>

The Flippin–Lodge angle has been abbreviated variously by the symbols φ, ψ, θ<sub>x</sub>, and <math>\alpha</math> or <math>\alpha_{FL}</math>;<ref name=Fleming2010/><ref name=GawleyAube1996>R.E. Gawley & J. Aube (1996) Principles of Asymmetric Synthesis (Tetrahedron Organic Chemistry Series, Vo. 14), New York:Pergamon, pp. 121-130, esp. pp. 127f, {{ISBN|0-08-041875-9}}.</ref><ref name=BurgiDunitzTet74/><ref name=RadiskyKoshland2002>{{cite journal |author1=Radisky, E.S. |author2=Koshland, D.E. | year = 2002 | title = A clogged gutter mechanism for protease inhibitors | journal = Proc. Natl. Acad. Sci. USA | volume = 99 | issue = 16 | pages = 10316–10321 | doi=10.1073/pnas.112332899 | pmid=12142461 | pmc=124911| bibcode = 2002PNAS...9910316R | doi-access = free }}</ref>{{sfnp|Koskinen|2012|pp=3-7f}}{{efn|name=RadKoshExplanNote}} the latter pair to closely associate the Flippin–Lodge angle with its sister angle, the [[Bürgi–Dunitz angle|Bürgi–Dunitz]], which was originally abbreviated as <math>\alpha</math> by its discoverers/formulators (e.g., see Bürgi et al., 1974.<ref name=BurgiDunitzTet74/>). The symbols <math>\alpha_{FL}</math> and <math>\alpha_{BD}</math> are used here, respectively, to refer to the Flippin-Lodge and Bürgi-Dunitz concepts and measured values.

== As an experimental observable ==
These angles are best construed to mean the angles observed (measured) for a given system, and ''not'' an historically observed range in values (e.g., as in the <math>\alpha_{BD}</math> range of the original Bürgi–Dunitz aminoketones), or an idealized value computed for a particular system (such as the <math>\alpha_{FL}</math> = 0° for hydride addition to formaldehyde).<ref name=BurgiDunitzTet74/> That is, the <math>\alpha_{BD}</math> and <math>\alpha_{FL}</math> angles of the hydride-formadehyde system have one pair of values, while the angles observed for other systems—combinations of nucelophile and electrophile, in combination with catalyst and other variables that define the experimental condition, including whether the reaction is ''in solutio'' or otherwise—are fully ''expected'' (and are reported) to vary, at least somewhat, from the theoretical, symmetric hydride-formaldehyde case.<ref name=Fleming2010/><ref name=RadiskyKoshland2002/>{{efn|name=RadKoshExplanNote}}

A stated ''convention for <math>\alpha_{FL}</math>'' is that it is ''positive (>0°) when it deviates in direction:''
* ''away from the larger substituent'' attached to the electrophilic center, <u>''or''</u>
* ''away from the more electron-rich substituent'' (where these two and other factors can be in a complex competition, see below); 
hence, as noted, <math>\alpha_{FL}</math> for reaction of a simple nucleophile with a symmetrically substituted carbonyl (R = R', or other symmetric planar electrophile) is expected to be 0° ''in vacuo'' or ''in solutio'', e.g., as in the case of the computed and experimental addition of hydride (H<sup>–</sup>) to formaldehyde (H<sub>2</sub>C=O).<ref name=Fleming2010/>

== Steric and orbital contributions to its value ==
[[Image:Pivaldehyde.svg|thumb|right|160px|alt=line-angle representation of an organic aldehyde, (CH3)3C-C(=O)-H|'''Pivaldehyde''' (trimethyl[[acetaldehyde]]).<ref>{{cite web|url=https://pubchem.ncbi.nlm.nih.gov/compound/12417#section=Top|title=Trimethylacetaldehyde|author=Pubchem|work=nih.gov|access-date=2 March 2016}}</ref> Example of an [[aldehyde]] with a [[steric bulk|sterically bulky]] R group attached to the [[carbonyl]], >C=O, the ''tertiary''-[[butyl]] group (with 3 [[methyl]] groups, at lower left). By definition, the other "group", R', is a hydrogen (H) atom, shown here pointing directly upward.]]
In contrast to the Bürgi–Dunitz angle, [[Bürgi–Dunitz angle|<math>\alpha_{BD}</math>]],<ref name=BurgiDunitzTet74/> and using the case of carbonyl additions as example: the <math>\alpha_{FL}</math> angle adopted during an approach by the nucleophile to a trigonal electrophile depends in complex fashion on:
* the relative steric size of the two substituents attached to (alpha to) the electrophilic carbonyl, which give rise to varying degrees of repulsive van der Waals's interactions (e.g., giving <math>\alpha_{FL}</math> ≈ 7° for [[hydride]] attack on [[pivaldehyde]] (see image), where R=''tertiary''-butyl, and R'=H),<ref name=Fleming2010/>
* the electronic characteristics of substituents alpha to the carbonyl, where heteroatom-containing substituents can, through their [[stereoelectronic]] influence, function as overly intrusive steric groups (e.g., giving <math>\alpha_{FL}</math> ≈ 40-50° for esters and amides with small R' groups, since R is an O- and N-substituent, respectively),<ref name=Fleming2010/> and
* the nature of the bonds made by more distant atoms to the atoms alpha to the carbonyl, e.g., where the energy of the σ* molecular orbital (MO) between the alpha- and beta-substituents was seen to compete with the foregoing influences,<ref name=LodgeHeathcock1987/>
as well as on the MO shapes and occupancies of the carbonyl and attacking nucleophile.<ref name=Fleming2010/><ref name=GawleyAube1996/> Hence, the <math>\alpha_{BD}</math> observed for nucleophilic attack appears to be influenced primarily by the energetics of the HOMO-LUMO overlap of the nucleophile-electrophile pair in the systems studied—see the [[Bürgi–Dunitz angle|Bürgi–Dunitz]] article, and the related inorganic chemistry concept of the angular overlap model (AOM){{efn|While the AOM is almost uniformly applied to inorganic cases, per [[International Union of Pure and Applied Chemistry|IUPAC]] definition it applies to main group elements as well, see Minkin, op. cit., and this extension is explicitly covered in the text and other writings of the late Prof. Jeremy Burdett, et. op. cit.}}<ref>{{cite journal | author = Minkin, V. I. and the Working Party of the IUPAC Organic Chemistry Division Commission on Physical Organic Chemistry | year = 1999 | title = Glossary of Terms Used in Theoretical Organic Chemistry (IUPAC Recommendations 1999) | journal = [[Pure and Applied Chemistry|Pure Appl. Chem.]] | format = print, online policy recommendations | volume = 71 | issue = 10 | pages = 1919–1981, esp. 1923 | issn = 0033-4545 | id =  (print); 1365-3075 (online) | doi = 10.1351/pac199971101919 | s2cid = 6475517 | url = http://pac.iupac.org/publications/pac/pdf/1999/pdf/7110x1919.pdf | access-date = 1 March 2016}}</ref>{{efn|name=IUPAC1999Quote}}{{efn|The co-authors (members of the IUPAC Working Party) for the foregoing report, in addition to the author given, were S. Alvarez, Y. Apeloig, A. Balaban, M. Basilevsky, F. Bernardi, J. Bertran, G. Calzaferri, J. Chandrasekhar, M. Chanon, J. Dannenberg, R. Gleiter, K. Houk, Z. Maksic, R. Minyaev, E. Osawa, A. Pross, P. v. R. Schleyer, S. Shalk, H.-U. Siehl, R. Sustmann, J. Tomasi, D. Wales, I. Williams and G. Zhidomirov. IUPAC Project Year 1993, Project Code 320/16/93.}}<ref>{{cite journal | author = Richardson, D. E. | year = 1993 | title = The Angular Overlap Model as a Unified Bonding Model for Main Group and Transition Metal Compounds: A Version Suitable for Undergraduate Inorganic Students | journal = [[Journal of Chemical Education|J. Chem. Educ.]] | volume = 70 | issue = 5| pages = 372ff | doi = 10.1021/ed070p372 | bibcode = 1993JChEd..70..372R }}</ref><ref>{{cite book | author = Burdett, J.K. | year = 1997 | title = Chemical Bonds: A Dialog | chapter = What's the Best Way of Looking at the Interactions of Transition Metals with their Ligands, and What's Behind the Eighteen-electron Rule? [Chapter 7] | edition = en anglais | location = Chichester, ENG | publisher = John Wiley | series = Inorganic Chemistry: A Textbook Series (Vol. 13) | chapter-url = https://books.google.com/books?isbn=0471971308 | access-date = 29 February 2016 | isbn = 978-0-471-97130-6 | pages = [https://archive.org/details/chemicalbondsdia0000burd/page/53 53–66, esp. 54ff] | url = https://archive.org/details/chemicalbondsdia0000burd/page/53 }}; {{cite book | author = Burdett, J.K. | year = 1980 | title = Molecular Shapes: Theoretical Models of Inorganic Stereochemistry | location = New York, NY, USA | publisher = Wiley Interscience }}{{page needed|date=March 2016}}; {{cite journal | author = Burdett, J.K. | year = 1978 | title = A new look at structure and bonding in transition metal complexes | journal = Adv. Inorg. Chem. | version = print review | volume = 21 | pages = 113ff }}</ref>—which leads in many cases to a convergence of <math>\alpha_{BD}</math> values (but not all, see below); ''however'', the <math>\alpha_{FL}</math> required to provide optimal overlap between HOMO and LUMO reflect the complex interplay of energetic contributions described with examples above.

== Origin and current scope of concept ==
Bürgi–Dunitz angle theory was initially developed based on "frozen" interactions in crystals,<ref name=Fleming2010/><ref name=GawleyAube1996/>{{rp|124ff}}<ref name=BurgiDunitzTet74/> while most chemistry takes place via collisions of molecules tumbling in solution; remarkably, the theories of the <math>\alpha_{FL}</math>, with the complexity they reflect, evolved not from crystallographic work, but from studying reaction outcomes in such practical reactions as addition of [[enolate]]s to aldehydes (e.g., in study of diastereoselection in particular [[aldol]] reactions).<ref name=Heathcock1990/><ref name=GawleyAube1996/> In applying both angles of the nucleophile trajectory to real chemical reactions, the HOMO-LUMO centered view of the Bürgi-Dunitz angle, <math>\alpha_{DB}</math>, is modified to include further complex, electrophile-specific attractive and repulsive  [[electrostatic]] and [[van der Waals interaction]]s that can alter <math>\alpha_{DB}</math> and bias <math>\alpha_{FL}</math> toward one substituent or the other (see above).<ref name=LodgeHeathcock1987/> As well, dynamics are at play in each system (e.g., changing [[torsional angle]]s) and are implicitly included in studies of reaction outcomes in solution, as in the early studies of <math>\alpha_{FL}</math>,<ref name=LodgeHeathcock1987/>—though not in crystallographic structure correlation approaches as gave birth to the BD concept.

Finally, in constrained environments (e.g., in [[enzyme]] and [[nanomaterial]] binding sites), these angles, when characterized, appear to be quite distinct, an observation conjectured to arise because reactivity is not based on random collision, and so the relationship between orbital overlap principles and reactivity is more complex.<ref name=RadiskyKoshland2002/>{{efn|name=RadKoshExplanNote}}<ref name=LightEtal14>S.H. Light, G. Minasov, M.-E. Duban & W.F. Anderson (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], accessed 10 June 2014.</ref> For instance, while a simple amide addition study with relatively small substituents gave an <math>\alpha_{FL}</math> of ≈50° in solution,<ref name=Fleming2010/> the crystallographic value determined for an [[enzymatic]] cleavage of an amide by the [[serine protease]] [[subtilisin]] gave an <math>\alpha_{FL}</math> of 8°, and a compilation of literature crystallographic <math>\alpha_{FL}</math> values for the same reaction in different catalysts clustered at 4 ± 6° (i.e., only slightly offset from directly behind the carbonyl, despite significant dissymmetry of the substrate electrophiles).<ref name=RadiskyKoshland2002/>{{efn|name=RadKoshExplanNote}} At the same time, the subtilisin <math>\alpha_{BD}</math> was 88° (quite distinct from the hydride-formaldehyde <math>\alpha_{BD}</math> value of 107°, see the [[Bürgi–Dunitz angle|Bürgi–Dunitz]] article), and <math>\alpha_{BD}</math> angle values from the careful literature compilation clustered at 89 ± 7° (i.e., only slightly offset from directly above or below the carbonyl carbon).

== Applications ==
[[Image:Mukaiyama Aldol-Übersichtsreaktion2.svg|thumb|right|500px|alt= | '''The [[Mukaiyama aldol addition]] reaction.'''<ref>{{cite journal | author = Mahrwald, Rainer | year = 1999 | title = Diastereoselection in Lewis-Acid-Mediated Aldol Additions | journal = Chem. Rev. | volume = 99 | issue = 5 | pages = 1095–1120, esp. pp. 1099, 1102, 1108 | url = http://isites.harvard.edu/fs/docs/icb.topic93502.files/Lectures_and_Handouts/28-Handouts/Mukaiyama_aldol_Rev.CR99.pdf | access-date = 5 December 2015 | doi=10.1021/cr980415r| pmid = 11749441 }}</ref>]]
The Flippin-Lodge and Bürgi-Dunitz angles were central, practically, to the development of a clearer understanding of [[asymmetric induction]] during nucleophilic attack at hindered carbonyl centers in synthetic organic chemistry. It was in this area that <math>\alpha_{FL}</math> was first defined by Heathcock, and has been primarily used.<ref name=Heathcock1990/><ref name=GawleyAube1996/> Larger substituents around the electrophilic center, such as tert-butyls, lead to higher stereoselectivities in asymmetric induction than smaller substituents like methyls. The trajectory of the nucleophile approaching a center flanked by two large substituents is more limited, i.e. the Flippin–Lodge angle is smaller. For example, in [[Mukaiyama aldol addition]], the bulkier phenyl tert-butyl ketone has a higher selectivity for the ''syn'' isomer than the smaller phenyl methyl ketone. Likewise, if bulky a nucleophile, such as a t-butylmethylsilyl enolate, is used, the selectivity is higher than for a small nucleophile like a lithium enolate.<ref name="Flippin1983"/>

Given a reaction system of a given nucleophile with a carbonyl having the two substituents R and R', where substituent R' is [[steric]]ally small relative to substituent R (e.g., R' = hydrogen atom, R = phenyl), the <math>\alpha_{FL}</math> values that are inferred from the reaction outcomes and theoretical studies tend to be larger;{{citation needed|date=December 2015}} alternatively, if the hydrocarbon substituents are nearer or equal in [[steric]] size, the inferred <math>\alpha_{FL}</math>values diminish and may approach zero (e.g., R' = ''tert''-butyl, R = phenyl).{{citation needed|date=December 2015}} Thus, from the perspective of simpler electrophile systems where only steric bulk come into play, the attack trajectories of the classes of nucleophiles studied makes clear that as the disparity in size between the substituent increase, there is a perturbation in the FL angle that can be used to provide higher stereoselectivities in designed reaction systems;{{citation needed|date=December 2015}} while the patterns become more complex when factors other than steric bulk come into play (see section above on orbital contributions),<ref name=Fleming2010/><ref name=LodgeHeathcock1987/> Flippin, Lodge, and Heathcock were able to show that generalizations could be made that were useful to reaction design.<ref name=Heathcock1990/><ref name=Fleming2010/><ref name=GawleyAube1996/>

A surpassing area of application has been in studies of various [[aldol reaction]]s, the addition of ketone-derived [[enol]]/[[enolate]] nucleophiles to electrophilic [[aldehyde]]s, each with functional groups varying in size and group polarity;<ref name=GawleyAube1996/> the way that features on the nucleophile and electrophile impact the [[stereochemistry]] seen in reaction products, and in particular, the [[diastereomer|diastereoselection]] exhibited, has been carefully mapped (see the steric and orbital description above,<ref name=Heathcock1990/><ref name=Fleming2010/><ref name=GawleyAube1996/> the [[aldol reaction]] article, and David Evans' related Harvard teaching materials on the aldol<ref>Evans, D.A., et al. (2006) "Carbonyl and Azomethine Electrophiles [Lectures 21, 22]," ''Chemistry 206, Advanced Organic Chemistry,'' packet pp. 91-99, 106-110, and 116, Cambridge, MA, USA: Harvard University Chemistry Department, [http://isites.harvard.edu/fs/docs/icb.topic229995.files/15_27_Lectures.pdf], accessed 5 December 2015.</ref>). These studies have improved the chemists' abilities to design [[Enantioselective synthesis|enantioselective]] and [[Stereoselective|diastereoselective]] reactions needed in the construction of complex molecules, such as the natural product [[wikt:spongistatin|spongistatin]]s<ref>S.B.J. Kan, K.K.-H. Ng & I. Paterson (2013) The Impact of the Mukaiyama Aldol Reaction in Total Synthesis, ''Angew. Chemie Int. Ed.'' '''52'''(35), 9097–9108, see [http://onlinelibrary.wiley.com/doi/10.1002/anie.201303914/abstract], accessed 30 November 2014.</ref> and [[atorvastatin|modern drugs]].<ref>D.A. Evrard & B.L. Harrison (1999) Ann. Rep. Med. Chem. 34, 1.{{page needed|date=November 2014}}</ref>{{page needed|date=November 2014}}<ref>J.-J. Li, D.S. Johnson, D.R. Sliskovic & B.D. Roth (2004) Contemporary Drug Synthesis, Hoboken:Wiley-Interscience, 118.</ref> It remains to be seen whether a particular range of <math>\alpha_{FL}</math> values contributes similarly to the arrangement of functional groups within proteins and so to their conformational stabilities (as has been reported in relation to the BD trajectory),<ref>{{cite journal |author1=G. J. Bartlett |author2=A. Choudhary |author3=R. T. Raines |author4=D. N. Woolfson | 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 = C. Fufezan | 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> or to other BD-correlated stabilizations of conformation important to structure and reactivity.{{sfnp|Choudhary|Kamer|Powner|Sutherland|2010|pp=655-657}}

== See also ==
* [[Bürgi–Dunitz angle]]

== Notes ==
{{noteslist|refs=
{{efn|name=RadKoshExplanNote|While Radisky & Koshland, op. cit., explicitly mention the rootedness of their protein crystallography analysis in the work of [[Bürgi–Dunitz angle|Bürgi and Dunitz]] (citing three of their reports), and while they clearly report an azimuthal angle in their data (their θ<sub>x</sub>), they do not cite the relevant earlier work of Heathcock, Flippin and Lodge (1983–1990), the connection to which, in the context of their Bürgi-Dunitz acknowledgments, and the text and review material of Fleming (2010) and Gawley & Aubé (1996), is viewed as obvious to WP editors. <!--The preceding is a defense against an accusation of WP:OR in including the Radisky & Koshland citation; I am in touch with Radisky, and am in hopes of an upcoming citation which will make this clear connection even clearer, post hoc. [[User:Leprof 7272]] -->}}
{{efn|name=IUPAC1999Quote|[Quoting:] Angular Overlap Model (AOM)—A method of description of transition metal-ligand interactions and main-group element stereochemistry, whose basic assumption is in that the strength of a bond formed using ''atomic orbitals'' on two atoms is related to the magnitude of overlap of the two orbitals. The interactions between the central-atom and ligand orbitals are usually divided into the σ-, π- and δ-types and parametric equations of the type[:] ε<sub>stab,σ</sub> {{=}} F<sup>2</sup>ε<sub>σ</sub> – (F<sup>2</sup>)<sup>2</sup>ƒ<sub>σ</sub> [and] ε<sub>destab,σ</sub> {{=}} – [F<sup>2</sup>ε<sub>σ</sub> – (F<sup>2</sup>)<sup>2</sup>ƒ<sub>σ</sub>] are used, where F is angle-dependent contribution to the ''overlap integral S''<sub>ab</sub> between the two interacting orbitals, whereas parameters ε<sub>σ</sub> and ƒ<sub>σ</sub> are proportional to ''S''<sup>2</sup> and ''S''<sup>4</sup> respectively and depend on the identity of atoms A and B as well the A–B distance. Similar equations are derived for the π- and δ-type interactions. Neither orbital mixing nor nuclear repulsions are accounted for by the model. Its advantage is in that for simple systems a molecular orbital diagram is easily constructed on the basis of two-orbital interactions and clearly reveals trends in orbital energies on distortion ([citing] 5 [Burdett (1980), ''Molecular Shapes,''], 6 [Richardson (1993)]).}}
}}

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

== Bibliography ==
{{refbegin|2}}
* {{cite journal |last1=Choudhary |first1=A. |last2=Kamer |first2=K.J. |last3=Powner |first3=M.W. |last4=Sutherland |first4=J.D. |last5=Raines |first5=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}}
* {{cite book | author = Cieplak, A.S. | year = 2008 | orig-date = 1994 | chapter = Organic Addition and Elimination Reactions; Transformation Paths of Carbonyl Derivatives [Ch. 6] | title =  Structure Correlation |volume=1 | pages = 205–302, esp. 270–274 |editor= Bürgi, Hans-Beat |editor2=Dunitz, Jack D. | location = Weinheim, GER | publisher = VCH | isbn = 978-3-527-61608-4 | chapter-url = https://books.google.com/books?isbn=352761608X | access-date = 1 March 2016 }} <!-- ''Bürgi and Dunitz-edited volume on structure correlation, including coverage of Flippin-Lodge (<math>\alpha_{FL}</math>) and Bürgi-Dunitz (<math>\alpha_{BD}</math>) concepts.'' -->
* {{citation |last1=Evans |first1=D.A. |year=2006 |title=Carbonyl and Azomethine Electrophiles [Lectures 21, 22] |series=Chemistry 206, Advanced Organic Chemistry |pages=91–99, 106-110, 116 |location=Cambridge, MA, USA |publisher=Harvard University Chemistry Department |url=http://isites.harvard.edu/fs/docs/icb.topic229995.files/15_27_Lectures.pdf |access-date=5 December 2015 }}{{dead url|date=August 2021}} <!-- ''Carefully refined undergraduate teaching notes of David Evans, et al., at Harvard Chemistry, that include the <math>\alpha_{FL}</math> and <math>\alpha_{BD}</math> concepts.'' -->
* {{cite book |last1=Fleming |first1=Ian |year=2010 |title=Molecular Orbitals and Organic Chemical Reactions |edition=Reference |publisher=John Wiley and Sons |pages=214–215 |isbn=978-0-470-74658-5}} <!-- ''Seminal intermediate MO-based text on organic mechanisms, wherein <math>\alpha_{FL}</math> and <math>\alpha_{BD}</math> results are summarized.'' -->
* {{cite journal |last1=Heathcock |first1=C.H. |year=1990 |title=Understanding and controlling diastereofacial selectivity in carbon-carbon bond-forming reactions |journal=Aldrichimica Acta |volume=23 |issue=4 |pages=94–111 |url=http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf |archive-url=https://web.archive.org/web/20140106112716/http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf |access-date=5 January 2014|archive-date=2014-01-06 }} <!-- ''Clayton Heathcock's review of the <math>\alpha_{FL}</math> concept, and the article in which it is named.'' -->
* {{cite book |last1=Koskinen |first1=A.M.P. |year=2012 |title=Asymmetric Synthesis of Natural Products |location=Chichester, UK |publisher=John Wiley and Sons |pages=3–7f}}
* {{cite journal | author = Mahrwald, Rainer | year = 1999 | title = Diastereoselection in Lewis-Acid-Mediated Aldol Additions | journal = Chem. Rev. | volume = 99 | issue = 5 | pages = 1095–1120, esp. pp. 1099, 1102, 1108 | url = http://isites.harvard.edu/fs/docs/icb.topic93502.files/Lectures_and_Handouts/28-Handouts/Mukaiyama_aldol_Rev.CR99.pdf | access-date = 5 December 2015 | doi=10.1021/cr980415r| pmid = 11749441 }} <!-- ''A comprehensive review of the Mukaiyama diastereoselection research area (now 15 years old).'' -->
{{refend}}

{{DEFAULTSORT:Flippin-Lodge angle}}
[[Category:Physical organic chemistry]]
[[Category:Organic chemistry]]
[[Category:Biochemistry]]