TheBürgi–Dunitz angle (BD angle) is one of two angles that fully define the geometry of "attack" (approach via collision) of anucleophile on atrigonalunsaturated center in amolecule, originally thecarbonyl center in anorganicketone, but now extending toaldehyde,ester, andamide carbonyls, and toalkenes (olefins) as well.[1][2][3] The angle was named after crystallographersHans-Beat Bürgi andJack D. Dunitz, its first senior investigators.
Practically speaking, the Bürgi–Dunitz and Flippin–Lodge angles were central to the development of understanding ofchiral chemical synthesis, and specifically of the phenomenon ofasymmetric induction during nucleophilic attack at hindered carbonyl centers (see theCram–Felkin–Anh and Nguyen[clarification needed] models).[4][5]
Additionally, the stereoelectronic principles that underlie nucleophiles adopting a proscribed range of Bürgi–Dunitz angles may contribute to the conformational stability of proteins[6][7] and are invoked to explain the stability of particular conformations of molecules in one hypothesis of achemical origin of life.[8]
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 anucleophile to a trigonal unsaturatedelectrophile depends primarily on themolecular orbital (MO) shapes and occupancies of the unsaturated carbon center (e.g., carbonyl center), and only secondarily on the molecular orbitals of the nucleophile.[1]
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 theFlippin–Lodge angle (FL angle) byClayton Heathcock after his contributing collaborators Lee A. Flippin and Eric P. Lodge.[4]
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 toformaldehyde, 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.[1][3][9]
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The original Bürgi-Dunitz measurements were of a series of intramolecularamine-ketone carbonyl interactions, in crystals of compounds bearing both functionalities—e.g.,methadone andprotopine. These gave a narrow range of BD angle values (105 ± 5°); corresponding computations—molecular orbital calculations of theSCF-LCAO-type—describing the approach of the s-orbital of a hydride anion (H−) to the pi-system of the simplest aldehyde, formaldehyde (H2C=O), gave a BD angle value of 107°.[2][non-primary source needed]
In the structure ofL-methadone (below, left), note thetertiary amine projecting to the lower right, and thecarbonyl (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 thecrystallization process).[citation needed] Similarly, in the structure of protopine (below, right), note thetertiary 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 thetorsion angles of the atoms of the ring.[citation needed]
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, thetetrahedral angle (internal angles of atetrahedron, 109.5°), and so consistent with a geometry understood to be important to developing transition states in nucleophilic attacks at trigonal centers.[citation needed]
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.[1] (See, in comparison, the related inorganic chemistry concept of the angular overlap model.[11][12][13][page needed])
In the case of addition to a carbonyl, the HOMO is often a p-type orbital (e.g., on anamine nitrogen orhalideanion), and the LUMO is generally understood to be theantibonding 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 newmolecular 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]
To understand cases of real chemical reactions, the HOMO-LUMO-centered view is modified by understanding of further complex, electrophile-specific repulsive and attractiveelectrostatic andVan der Waals interactions that alter the altitudinal BD angle, and bias the azimuthal Flippin-Lodge angle toward one substituent or the other (see graphic above).[14][non-primary source needed]
BD angle theory was developed based on "frozen" interactions in crystals where the impacts ofdynamics at play in the system (e.g., easily changedtorsional angles) may be negligible. However, most reaction chemistry of general interest and utility takes place via collisions of molecules rapidly tumbling insolution; accordingly, the dynamics of each situation are sampled effectively, and so are reflected in the outcomes of the reactions.[citation needed]
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.[15][9]
For instance, the BD value determined forenzymatic cleavage of an amide by aserine 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 theFlippin–Lodge angle article).[9][non-primary source needed]