Bürgi–Dunitz angle

The Bürgi–Dunitz angle is one of two angles that fully define the geometry of "attack" of a nucleophile on a trigonal unsaturated compounds|unsaturated] center in a molecule, originally the carbonyl center in an organic ketone, but now extending to aldehyde, ester, and amide carbonyls, and to alkenes as well. 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 chemical synthesis, and specifically of the phenomenon of asymmetric induction during nucleophilic attack at hindered carbonyl centers.
Additionally, the stereoelectronic principles that underlie nucleophiles adopting a proscribed range of Bürgi–Dunitz angles may contribute to the conformational stability of proteins and are invoked to explain the stability of particular conformations of molecules in one hypothesis of a chemical origin of life.

Definition

In the addition of a nucleophile 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 shapes and occupancies of the unsaturated carbon center, and only secondarily on the molecular orbitals of the nucleophile.
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 by Clayton Heathcock after his contributing collaborators Lee A. Flippin and Eric P. Lodge.
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. 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.

Measurement

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 ; corresponding computations—molecular orbital calculations of the SCF-LCAO-type—describing the approach of the s-orbital of a hydride anion to the pi-system of the simplest aldehyde, formaldehyde, gave a BD angle value of 107°.
In the structure of -methadone, note the tertiary amine projecting to the lower right, and the carbonyl group at the center, which engage in an intramolecular interaction in the crystal structure. Similarly, in the structure of protopine, note the tertiary amine at the center of the molecule, part of a ten-membered ring, and the CO group diagonally opposite it on the ring; these engage in an intramolecular interaction allowed by changes in the torsion angles of the atoms of the ring.
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, and so consistent with a geometry understood to be important to developing transition states in nucleophilic attacks at trigonal centers.

Theory

The convergence of observed BD angles can be viewed as arising from the need to maximize overlap between the highest occupied molecular orbital of the nucleophile, and the lowest unoccupied molecular orbital of the unsaturated, trigonal center of the electrophile.
In the case of addition to a carbonyl, the HOMO is often a p-type orbital, 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. The BD angle observed for nucleophilic attack is believed to approach the angle that would produce optimal overlap between HOMO and LUMO. At the same time, the nucleophile avoids overlap with other orbitals of the electrophilic group that are unfavorable for bond formation.

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 interactions that alter the altitudinal BD angle, and bias the azimuthal Flippin-Lodge angle toward one substituent or the other.

Linear and rotational dynamics

BD angle theory was developed based on "frozen" interactions in crystals where the impacts of dynamics at play in the system may be negligible. However, most reaction chemistry of general interest and utility takes place via collisions of molecules rapidly tumbling in solution; accordingly, the dynamics of each situation are sampled effectively, and so are reflected in the outcomes of the reactions.

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.
For instance, the BD value determined for enzymatic cleavage of an amide by a serine protease 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° . At the same time, the subtilisin FL value was 8°, and FL angle values from the careful compilation clustered at 4 ± 6°.