Flippin–Lodge angle

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 ${\displaystyle {\alpha }_{BD}}$ range of the original Bürgi–Dunitz aminoketones), or an idealized value computed for a particular system (such as the ${\displaystyle {\alpha }_{FL}}$ = 0° for hydride addition to formaldehyde). That is, the ${\displaystyle {\alpha }_{BD}}$ and ${\displaystyle {\alpha }_{FL}}$ 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.

A stated convention for ${\displaystyle {\alpha }_{FL}}$ is that it is positive (>0°) when it deviates in 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);

hence, as noted, ${\displaystyle {\alpha }_{FL}}$ 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^–) to formaldehyde (H₂C=O).

Steric and orbital contributions to its value

In contrast to the Bürgi–Dunitz angle, ${\displaystyle {\alpha }_{BD}}$, and using the case of carbonyl additions as example: the ${\displaystyle {\alpha }_{FL}}$ 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 ${\displaystyle {\alpha }_{FL}}$ ≈ 7° for hydride attack on pivaldehyde (see image), where 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 ${\displaystyle {\alpha }_{FL}}$ ≈ 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 ${\displaystyle {\alpha }_{BD}}$ 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 (AOM)—which leads in many cases to a convergence of ${\displaystyle {\alpha }_{BD}}$ values (but not all, see below); however, the ${\displaystyle {\alpha }_{FL}}$ 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, while most chemistry takes place via collisions of molecules tumbling in solution; remarkably, the theories of the ${\displaystyle {\alpha }_{FL}}$, with the complexity they reflect, evolved not from crystallographic work, but 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 Bürgi-Dunitz angle, ${\displaystyle {\alpha }_{DB}}$, is modified to include further complex, electrophile-specific attractive and repulsive electrostatic and van der Waals interactions that can alter ${\displaystyle {\alpha }_{DB}}$ and bias ${\displaystyle {\alpha }_{FL}}$ toward one substituent or the other (see above). As well, dynamics are at play in each system (e.g., changing torsional angles) and are implicitly included in studies of reaction outcomes in solution, as in the early studies of ${\displaystyle {\alpha }_{FL}}$,—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. For instance, while a simple amide addition study with relatively small substituents gave an ${\displaystyle {\alpha }_{FL}}$ of ≈50° in solution, the crystallographic value determined for an enzymatic cleavage of an amide by the serine protease subtilisin gave an ${\displaystyle {\alpha }_{FL}}$ of 8°, and a compilation of literature crystallographic ${\displaystyle {\alpha }_{FL}}$ 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). At the same time, the subtilisin ${\displaystyle {\alpha }_{BD}}$ was 88° (quite distinct from the hydride-formaldehyde ${\displaystyle {\alpha }_{BD}}$ value of 107°, see the Bürgi–Dunitz article), and ${\displaystyle {\alpha }_{BD}}$ 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

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 ${\displaystyle {\alpha }_{FL}}$ was first defined by Heathcock, and has been primarily used. 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.

Given a reaction system of a given nucleophile with a carbonyl having the two substituents R and R', where substituent R' is sterically small relative to substituent R (e.g., R' = hydrogen atom, R = phenyl), the ${\displaystyle {\alpha }_{FL}}$ values that are inferred from the reaction outcomes and theoretical studies tend to be larger; alternatively, if the hydrocarbon substituents are nearer or equal in steric size, the inferred ${\displaystyle {\alpha }_{FL}}$values diminish and may approach zero (e.g., R' = tert-butyl, R = phenyl). 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; while the patterns become more complex when factors other than steric bulk come into play (see section above on orbital contributions), Flippin, Lodge, and Heathcock were able to show that generalizations could be made that were useful to reaction design.

A surpassing area of application has been 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 the steric and orbital description above, the aldol reaction article, and David Evans' related Harvard teaching materials on the aldol). 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 ${\displaystyle {\alpha }_{FL}}$ 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.