Figure 1.

Physical organic chemistry concepts regarding the trajectory of the approach of a nucleophile to an electrophilic center. (a) The Bürgi–Dunitz angle (α_BD) describes the trajectory of approach of a nucleophile (the lysine N^∊ atom in the TAL reaction) to an electrophilic center (the substrate carbonyl C atom in TAL). Atoms and groups of a carbonyl R ₁C(O)R ₂ are positioned on a blue-grey plane and an approaching N atom is poised above. The α_BD is estimated as ∠N^∊⋯C=O (arrow). (b) The α_BD originates in HOMO–LUMO overlap. After Bürgi, Lehn et al. (1974 ▶) and Fleming (2010 ▶), a side-on cartoon view of the approach of the two lobes of the p-type highest occupied molecular orbital (HOMO) of nitrogen (green) is shown at three hypothetical positions (α_BD = 135, 90 and 45°). Poses are relative to the four lobes of the antibonding π*-type lowest unoccupied molecular orbital (LUMO) of formaldehyde, H₂C=O, the simplest carbonyl electrophile (standard atom colors). Per current theory, carbinolamine C—N and C—O single bonds result when the nitrogen trajectory follows an obtuse value of α_BD, allowing HOMO–LUMO overlap by wavefunctions (lobes) of like sign (shading) such that this attractive potential overcomes other repulsive potentials (Bürgi, Dunitz et al., 1974 ▶; Fleming, 2010 ▶). An approximate optimum computed for addition to formaldehyde of the simplest nucleophile, hydride anion (H^ψ), is indicated by the orange dashed line (α_BD ≃ 107°, SCF calculations; Bürgi et al., 1973 ▶).