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°. 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. In the structure of -methadone (above, left), note the tertiary amine projecting to the lower right, and the carbonyl (CO) group at the center, which engage in an intramolecular interaction in the crystal structure (after rotation around the single bonds connecting them, during the crystallization process). Similarly, in the structure of protopine (above, center), note the tertiary amine at the center of the molecule, part of a ten-membered ring, and the CO group opposite it on the ring; these engage in an intramolecular interaction allowed by changes in the torsion angles of the atoms of the ring. Theory 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. (See, in comparison, the related inorganic chemistry concept of the angular overlap model.) In the case of addition to a carbonyl, the HOMO is often a p-type orbital (e.g., on an amine nitrogen or halide anion), 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 (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 new molecular 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). 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