Flippin–Lodge angle

The Flippin–Lodge angle (FL angle) is one of two angles used by organic and biological chemists studying the relationship between the structure of molecules and ways that they react, for a particular common type of chemical reaction. The angles—the Bürgi–Dunitz (BD) and the Flippin–Lodge (FL)—describe the "angle of attack" of an electron-rich reactant, the nucleophile, with an electron-poor reactant, an electrophile, in particular when the latter is planar in shape. This is called a nucleophilic addition reaction and it is plays a central role in the biological chemistry taking place in the biosyntheses of metabolism, and is a central reaction "tool" in the toolkit of modern organic chemistry for constructing new molecules such as pharmaceuticals. Theory and use of these angles falls into the specialty of physical organic chemistry, which deals with chemical structure and reaction mechanism, in particular, the area called structure correlation.

Cartoon of a hypothetical Flippin-Lodge (FL) angle. Shown is attack by a charged nucleophile (Nu) such as hydride (H^–) or chloride (Cl^–) anion on the trigonal planar center of a carbonyl (C=O) of a ketone (R and R' are not hydrogen, H) or an aldehyde (generally, R or R' are H). The optimal FL value for hydride attack on formaldehyde (R = R' = H) is 0°, because of the electrophile's symmetry. The FL angle is measured in the plane of the carbonyl and its substituents (plane of the page); however, Nu always lies above or below this plane. To determine the angle, one projects the Nu onto the carbonyl plane to give point Nu^†. The FL, then, is the angle in the C=O plane between Nu^† and the line of the C=O bond (dashed line). It can be measured graphically as Ψ = 180° – (LNu^†-C-O), or using crystallographic coordinates and line-plane formulae (e.g., vector/matrix algebra). The FL angle has been represented variously by the symbols φ, ψ, θ_x, and α_FL (to connect it to α or α_BD, the Bürgi–Dunitz angle).

Because reactions take place in three dimensions, their quantitative description is a geometry problem; two angles, first the BD, later the FL, 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 the plane). The BD is the angle between the line connecting these two atoms and a reference line that it intersects on the plane (see related article). The FL angle describes the extent to which the distinct plane containing both lines is offset from being perfectly perpendicular to the electrophile's plane (see figure). That is, it measures displacement of the nucleophile toward or away from the particular R and R' substituents attached to the electrophilic atom. FL and BD angle studies can be theoretical, based on 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. Addition reactions addressed using FL and BD angle concepts involve nucleophiles ranging from single atoms and polar organic functional groups to sophisticated enzyme active site and chiral catalyst-reactant systems. These nucleophiles can be paired with an array of planar electrophiles: aldehydes and ketones, carboxylic acid-derivatives, and the carbon-carbon double bonds of alkenes (olefins).

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 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 (enols, enolates), to aldehydes with attached groups varying in size and polarity. Of particular interest, given the three-dimensional nature of the concept, is understanding how 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 FL 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 (enantiomers and diastereomers) needed in the construction of complex natural products and drugs.

Technical Introduction

The Flippin–Lodge angle (FL angle) is the latter-derived of two angles that fully define the geometry of "attack" (approach via collision) of a nucleophile on an trigonal unsaturated center of an electrophilic molecule. Nucleophiles in this addition reaction may range from single atoms (hydride, chloride), to polar organic functional groups (amines, alcohols), to complex systems (nucleophilic enolates with chiral catalysts, amino acid side chains in enzyme active sites; see below). Planar electrophiles include aldehydes and ketones, carboxylic acid-derivatives such as esters, and amides, and the carbon-carbon double bonds of particular alkenes (olefins). In the example of nucleophilic attack at a carbonyl, the FL angle 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 (ibid., and ). 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, FL 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 LNu'-C-O (where Nu' is the projected atom). This often overlooked angle of the nucleophile's trajectory was named the Flippin-Lodge (FL) angle by Clayton H. Heathcock after his contributing collaborators Lee A. Flippin and Eric P. Lodge. The second angle defining the geometry, the more well known Bürgi–Dunitz (BD) angle, describes the Nu-C-O bond angle and was named after crystallographers Hans-Beat Bürgi and Jack D. Dunitz, its first senior investigators (see related article).

The angle as an experimental observable, rather than ideal

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., the BD angle range of the original Bürgi–Dunitz aminoketones), or an idealized value computed for a particular system (such as the FL = 0° for hydride addition to formaldehyde, image at right). That is, the BD and FL angles of the hydride-formadehyde system have one pair of values, while the angles observed for other systems are fully expected to vary from this.

A stated convention for the FL angle is that it is positive when deviating in the direction away from the larger substituent attached to the electrophilic center, or away from the more electron-rich substituent (where these two and other factors can be in a complex competition, see below); the FL angle of a symmetrically substituted carbonyl (R = R') with a simple nucleophile is expected to be 0° in vacuo / in solutio, e.g., as in the case of hydride addition to formaldehyde, H₂C=O (see figure).

Steric and orbital contributions contributing to its value

In contrast to the BD angle (using the case of carbonyl additions as example): the FL 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 FL angle ≈ 7° for pivaldehyde, R=tertiary-butyl, and R'=H),
• 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 FL angle ≈ 40-50° for esters and amides with small R' groups, since R is an O- and N-substituent, respectively), 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,

as well as on the MO shapes and occupancies of the carbonyl and attacking nucleophile. Hence, the BD angle 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 article, and the related inorganic chemistry concept of the angular overlap model—which leads in many cases to a convergence of BD angle values (but not all, see below); however, the FL angle required to provide optimal overlap between HOMO and LUMO may reflect a more complex interplay of energetic contributions.

Origin and current scope of concept

BD angle theory was initially developed based on "frozen" interactions in crystals, while most chemistry takes place via collisions of molecules tumbling in solution; remarkably, the theories of the FL angle, with the complexity they reflect, evolved from studying reaction outcomes in such practical reactions as addition of enolates to aldehydes (e.g., in study of diastereoselection in particular aldol reactions). In applying both angles of the nucleophile trajectory to real chemical reactions, the HOMO-LUMO centered view of the BD angle is modified to include further complex, electrophile-specific attractive and repulsive electrostatic and van der Waals interactions that can alter the BD angle and bias the FL angle toward one substituent or the other (see above). As well, dynamics at play in each system (changing torsional angles) are implicitly included in studies of reaction outcomes in solution as in the early studies of FL angles (ibid.), 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) observed angles 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. For instance, while a simple amide addition study with relatively small substituents gave an FL angle of ≈50° in solution, the crystallographic value determined for an enzymatic cleavage of an amide by the serine protease subtilisin gave a FL value of 8°, and a compilation of literature crystallographic FL angle values for the same reaction in different catalysts clustered at 4 ± 6° (i.e., only slightly offset from directly behind the carbonyl). At the same time, the subtilisin BD value was 88° (quite distinct from the BD hydride-formaldehyde value of 107°, see the Bürgi–Dunitz article), and BD angle values from the careful compilation clustered at 89 ± 7° (i.e., only slightly offset from directly above or below the carbonyl carbon).

Applications

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 the FL angle was first defined by Heathcock, and has been primarily used. Given a carbonyl with two substituents R and R', substituents R' that are small relative to the other substituent R (e.g. R' = hydrogen vs. R = phenyl) tend to have higher FL angle, whereas if of equal size, the FL angle is small (e.g. R' = tert-butyl vs. R = phenyl). Thus, the attack trajectory of a nucleophile is more restricted with larger R', and leading higher stereoselectivities.

A surpassing area of application has in studies of various aldol reactions, the addition of ketone-derived enol/enolate nucleophiles to electrophilic aldehydes, each with functional groups varying in size and group polarity; the way that features on the nucleophile and electrophile impact the stereochemistry seen in reaction products, and in particular, the diastereoselection exhibited, has been carefully mapped (see above, the aldol reaction article, and Evans). These studies have improved the chemists' abilities to design enantioselective and diastereoselective reactions needed in the construction of complex molecules, such as the natural product spongistatins and modern drugs. It remains to be seen whether a particular range of FL angle 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), or to other BD-correlated stabilizations of conformation important to structure and reactivity.

See also

• Heathcock, C.H. (1990) Understanding and controlling diastereofacial selectivity in carbon-carbon bond-forming reactions, Aldrichimica Acta 23(4):94-111, esp. p. 101. [ http://www.sigmaaldrich.com/content/dam/sigma-aldrich/docs/Aldrich/Acta/al_acta_23_04.pdf, accessed 5 January 2014]
• Fleming, Ian (2010) Molecular Orbitals and Organic Chemical Reactions: Reference Edition, John Wiley and Sons, pp. 214–215. [ISBN 0470746580, http://www.amazon.com/Molecular-Orbitals-Organic-Chemical-Reactions/dp/0470746599, accessed 5 January 2014]
• Bürgi–Dunitz angle