This is rather cranking the handle, but taking my previous post and altering the search definition of the crystal structure database from 4- to 5-coordinate metals, one gets the following.
Fe …
Co …
Ni …
Cu …
Trigonal bipyramidal coordination has angles of 90, 120 and 180°. Square pyramidal has no 120° angles, and the 180° angles might be somewhat reduced. Thus the Fe and Co series have plenty of 120, whereas the Ni and Cu series hardly any. The Ni series has many 160° values. It is clearly a serious issue that attempting any correlation with the spin states is going to be a lot of really hard work (I might next do another simple search where bond lengths can be shown to very closely correlate with low/medium/high spin states). I will not be trying a more finely grained analysis of the above plots; I just wanted to point out how very simple and quick they are to generate.
This post has been cross-posted in PDF format at Authorea.
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This is by way of adding 7- and 8-coordination to the 4- and 5- previously covered. Since these higher co-ordinations are rarer, I have specified the central atom as any transition metal, and not a specific column of the periodic table.
First, 7-coordination. Note the hotspots at ~70, 110, 140, 160 and 180°.
And this is the 8-coordination, with hotspots at ~70° and its doubling, 140°.
In the other direction, 3-coordinate. Note the hotspot at trigonal, 120°, but prominent features at ~90/180° which are the T-shaped systems.
And finally, if you are wondering, comes 2-coordinate. With the expected hotspot at 180°, but with quite a tail, down to about 90°.