Quadrant diagrams

A generic model for steric biasing of chiral metal-ligand adducts has been advanced to facilitate the prediction of the facial stereoselectivity in catalyst-substrate complexes and transition states. In this model, the environment around the metal is divided into quadrants in which tlie horizontal dividing line is congment with a plane or pseudo-plane in 

Quadrant diagrams for a Cj-symmetric catalyst. B. Unfavorable binding and C. favorable binding of an olefin in diastereomeric oiefin complexes. 

The means by which metal complexes of chiral ligands block quadrants depends on the nature of the ligand and the metal-ligand adduct. In some cases, the stereogenic centers of the ligands exist in close proximity to the metal. In other cases, the stereogenic centers are located so far from the metal that it is not obvious how the effect of these distant stereocenters can be transmitted to the site of reaction. 

PyBox and Chiraphos, illustrating the positioning of key substituents contributing to the chiral environment of the catalyst bearing these ligands. 

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The difference between the structures and reactivity of the diastereomers can be visualized using Knowles quadrant diagrams. Overlaying the structures of the two diastereomers on the quadrant diagram for DuPHOS (Figure 3) clearly reveals that displacement of the (3-carbon of Pro-/ into the plane lessens steric interactions of the (3-methylene with the hindered quadrant (Figure 10). 

Figure 10. Orientations of substrate in catalyst-enamide diastereomers overlaid onto quadrant diagram representing DuPHOS ligand (see Figure 3). The phosphorus atoms and bridging carbons of the DuPHOS ligand are still shown, but some hydrogens have been removed for clarity.

In developing some of the relationships, it is helpful to use a four-quadrant diagram in which each quadrant represents a species in a lipid or water phase. The diagram below shows a typical distribution of an acid, AH, between two phases where ion partitioning is assumed to be negligible. The partition coefficent, P, is the ratio of the concentration of AH in the octanol to the concentration of AH in the aqueous phase. The distribution coefficient, D, is the ratio of the concentration in the octanol to that of all forms in the water. This is also called the apparent partition coefficient. 

When the ion-pair partitioning is indicated in the quadrant diagram (below) it becomes obvious that a circle of equilibria is present. Knowing the octanol pKa, the log P and the aqueous pKa should allow one to calculate the partition coefficient of the ion pair. From these equilibria one can write that the difference in log P between the acid and its salt is the same as the difference between the pKa s (Equation 9). The closer the pKa s, the more lipid soluble the ion pair will be, relative to the acid. Internal hydrogen bonding or chelation that stabilizes an ion pair will affect the octanol stability more than the aqueous stability, where it is less needed, and so will decrease the delta pKa. Chelation should therefore favor biolipid solubility of ion pairs. Ultimate examples are available in some ionophores. This is one of the properties of some of the herbicides I pointed out earlier. 

Sometimes the log P from a two-phase titration using Equations 18 or 19 is low, compared with shake-flask values. We attribute this to ion-pair partitioning. The quadrant diagram. Figure 8, is helpful for developing the pertinent equations. The amount of each species in each phase is shown in the appropriate sector. 

Figure 8. A quadrant diagram to aid derivation of equation 20. V is the volume of octanol or water phase [X] is the concentration of AH in the aqueous phase P is the partition coefficient of AH P is the partition coefficient of the ion pair A"Na+ pKa is the aqueous single-phase pKa pK is the two-phase pKa.

Figure 1.20 Models built with using the X-ray structure of the cyclooctadienyl-rhodium complex of the diphosphine 17 (a) X-ray structure without the cod ligand (b) structure obtained by rotation around P-C bonds of the tetrahydronaphtalenyl substituent and (c) quadrant diagram corresponding to the upper structure— hindered quadrants are made by axial phenyls. (Reprinted with permission from Gridnev, 1. D. and imamoto, T., Acc. Chem. Res., 37, 633-644. Copyright 2004 American Chemical Society.)...

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