Bürgi–Dunitz angle
The Bürgi–Dunitz angle (BD angle) is one of two angles that fully define the geometry of "attack" (approach via collision) of a nucleophile on a trigonal 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 (olefins) as well. Precisely, in the case of nucleophilic attack at a carbonyl, it is defined as the Nu-C-O bond angle, where Nu is the atom of the nucleophile forming the bond with the carbon atom. The angle was named after crystallographers Hans-Beat Bürgi and Jack D. Dunitz, its first senior investigators. The second angle defining the geometry 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 H. Heathcock after his contributing collaborators Lee A. Flippin and Eric P. Lodge. These angles are generally best construed to mean the angle observed or measured 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 to formaldehyde, image at left). I.e., the BD and FL angles of the hydride-formadehyde system have one pair of values, while the angles observed for other systems are expected to vary.
The BD angle adopted during an approach by a nucleophile to a trigonal unsaturated electrophile depends primarily on the molecular orbital (MO) shapes and occupancies of the unsaturated center (e.g., carbonyl center), and only secondarily on the molecular orbitals of the nucleophile. Original measurements for a series of intramolecular amine-carbonyl ketone interactions observed in crystals of compounds bearing both functionalities—e.g., methadone and protopine, images at left and right, below—gave a narrow range of BD angle values (105 ± 5°). Corresponding computational estimates (SCF-LCAO-MO calculations) on the approach of the s-orbital of the hydride anion (H−) to the pi-system of the simplest aldehyde, formaldehyde (H2C=O), gave a BD angle value of 107°. Both the crystallographic measurement for aminoketones and the computational estimated for this simplest system are quite close to the theoretical ideal of a tetrahedral angle (internal angles of a tetrahedron, 109.5°), consistent with the importance of this geometry in developing transition states in nucleophilic attacks at trigonal centers.
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