Bürgi–Dunitz angle

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 (see the Cram–Felkin–Anh and Nguyen[clarification needed] models).

[1][3][9] 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.

[2][non-primary source 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, the tetrahedral angle (internal angles of a tetrahedron, 109.5°), and so consistent with a geometry understood to be important to developing transition states in nucleophilic attacks at trigonal centers.

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 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 (see graphic above).

Bürgi–Dunitz and Flippin–Lodge nucleophile approach trajectory angles, and , analogized to altitude- and azimuth-types of parameters in the celestial (horizontal) coordinate system . Both in this celestial coordinate system, and in the system to describe a nucleophile approaching a planar electrophile, the problem is to uniquely describe the location of a point off of a plane, relative to specific point on the plane. Hence, in both cases, the problem can be addressed using two angles, an altitude-type angle and an azimuth-type angle. Note, while elevation in celestial applications is most easily measured as the specific altitude shown, the elevation of the nucleophile, , is most easily measured as the supplementary angle, Nu-C-O, hence its values are most often >90° (see text and next image).