text: Bürgi–Dunitz angle theory was initially developed based on "frozen" interactions in crystals, while most chemistry takes place via collisions of molecules tumbling in solution; remarkably, the theories of the , with the complexity they reflect, evolved not from crystallographic work, but from studying reaction outcomes in such practical reactions as addition of enolates to aldehydes (e.g., in study of diastereoselection in particular aldol reactions). In applying both angles of the nucleophile trajectory to real chemical reactions, the HOMO-LUMO centered view of the Bürgi-Dunitz angle, , is modified to include further complex, electrophile-specific attractive and repulsive  electrostatic and van der Waals interactions that can alter  and bias  toward one substituent or the other (see above). As well, dynamics are at play in each system (e.g., changing torsional angles) and are implicitly included in studies of reaction outcomes in solution, as in the early studies of ,—though not in crystallographic structure correlation approaches as gave birth to the BD concept.
  Finally, in constrained environments (e.g., in enzyme and nanomaterial binding sites), these angles, when characterized, appear to be quite distinct, an observation conjectured to arise because reactivity is not based on random collision, and so the relationship between orbital overlap principles and reactivity is more complex. For instance, while a simple amide addition study with relatively small substituents gave an  of ≈50° in solution, the crystallographic value determined for an enzymatic cleavage of an amide by the serine protease subtilisin gave an  of 8°, and a compilation of literature crystallographic  values for the same reaction in different catalysts clustered at 4 ± 6° (i.e., only slightly offset from directly behind the carbonyl, despite significant dissymmetry of the substrate electrophiles). At the same time, the subtilisin  was 88° (quite distinct from the hydride-formaldehyde  value of 107°, see the Bürgi–Dunitz article), and  angle values from the careful literature compilation clustered at 89 ± 7° (i.e., only slightly offset from directly above or below the carbonyl carbon).