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I know that optimising the bite angle of a diphosphine ligand to its metal increases catalytic efficiency, and for cross-coupling reactions larger bite angles are favoured, but how does this have an impact on the effectiveness of a catalyst?

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The bite angle of a bidentate ligand often has a pronounced effect on reactivity, but it can be difficult to predict a priori whether a given reaction will be enhanced by increasing or decreasing bite angle - you can see this if you ever read a paper where new ligands / catalysts have been developed, which are often accompanied with large tables of screening in order to find an optimised set of reactions.

In general however, bite angle does correlate with the rates of oxidative addition and reductive elimination.

Reductive elimination

The rate of reductive elimination is often correlated to the bite angle of a bidentate ligand. Upon reductive elimination, the two coordinate Pd0 complex would preferentially adopt a linear geometry however with the bidentate ligand coordinating (and the chelate effect preventing it from 'falling off') this is not possible.

Larger bite angles therefore favour reductive elimination as the L-Pd-L (P-Pd-P) bond angle is closer to the desired 180o. The classic example of this was an experiment carried out by Brown in which the rate at which PhMe was eliminated from a variety of complexes was measured.

Pd(dppf)PhMe with a bite angle of 99.1o underwent rapid reductive elimination, even at low temperatures, while Pd(dppe)PhMe with a bite angle of 90.6o was stable at low temperatures, with elimination needing elevated temperatures.

Oxidative addition

The effect of bite angle on oxidative addition is less straightforward, as it depends largely on the mechanism by which the oxidative addition takes place. In general however, complexes with larger bite angles undergo faster rates of oxidation despite the fact that a smaller bite angle increases the rate of the C-X bond cleavage.

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