 Solution

The relevant chelate rings contain four atoms for dppm, five for dppe, and six for dppp, counting the nickel and both phosphorus atoms. The one-carbon bridge in dppm forces a compact ring and the small bite angle $75.62^{\circ }$. A two-carbon tether accommodates a five-membered chelate closer to the preferred square-planar cis angle, giving $86.99^{\circ }$. The more flexible three-carbon tether can open slightly beyond $90^{\circ }$, giving $91.77^{\circ }$.

For a simplified symmetric chelate with Ni–P distance $r$ and P–P donor separation $d$,Increasing the accessible donor separation therefore increases the bite angle $\beta$. The ligand is a three-dimensional tether, so ring puckering and substituent crowding matter as well as the number of methylene groups. This geometrical explanation does not require different formal oxidation states or electron counts for the three complexes.