Three-point rule

Figure A-2 Trapezoidal rule illustration. Figure A-3 Simpson s three-point rule...

Simpson s three-point rule is used to evaluate the integral ... 

To facilitate the understanding of chiral recognition at the molecular level, a number of attempts have been made to define minimum criteria in terms of the required intermolecular SO-SA interactions [67-74]. The currently most widely accepted concept is known as the three-point rule [67]. This rule states that for chiral recognition to occur a minimum of three simultaneous interactions between SO and at least one of the enantiomers is required, with at least one of these interactions being stereochemicaUy dependent. This concept is graphically illustrated in Fig. 7.3. 

Confusion often arises due to misinterpretation of the term interaction within the conceptional framework of the three-point rule. It is important to understand that in this particular context interaction refers to intermolecular physical forces and their steric implication rather than to specific spatial relationships between substructure elements in the SO and SA entities. This distinction is crucial as intermolecular forces, depending on their physical nature, may be of single-point or of multi-point quality. For example, forces acting exclusively between specific... 

General discussions of enantioselective recognition are given in a number of reviews.A prevalent concept is the "three-point rule. formulated by Pirkle. as Chiral recognition requires a minimum of three simultaneous interactions between the CSP(/receptor) and at least one of the enantiomers, with one of these interactions being stereochemically dependent. Schematically ... 

Recent experimental results have confirmed the principle of chiral interaction (three-point rule) postulated as early as 19S2 by Dalgliesh (56). Additionally, the results prove that the separation models developed for ligand exchange by high-performance liquid chromatography (16,156,157) are also valid for T1.C the diastereomeric complexes formed with the metal ion (e.g., Cu ) and the chiral adsorbent have different stabilities for the different antipodes, and thus chromatographic separation is achieved. 

For example, the lowest order rule in one dimension, the three point rule reads... 

Thus, in both the cases (Figures 15.2 and 15.3), H-bond plays a role in the overall stability of the diastereomeric complex except that the site of FI-bond is different. The three-point rule [29] proposed for resolution of enantiomers considers H-bond as one of the important factors along with jv-tt interactions and steric repulsions between the CSP and one of the enantiomeric forms to distinguish between the two enantiomeric forms. In the application of MR the stationary phase is achiral, but the MR being chiral is responsible for diastereomeric formation and the differential interaction of the diastereomers with the ODS causes separation. 

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