I am now inverting the previous question by asking what is the largest angle subtended at a chain of three connected 4-coordinate carbon atoms? Let’s see if further interesting chemistry can be unearthed.
Specifying only angles > 130°, the following distribution is obtained.
It is remarkable how much the standard angle subtended at four-coordinate carbon (109.47°) can be opened. It makes one wonder whether something approaching 180° is achievable, and what the properties of such a molecule might be.
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Roald Hoffmann has sent me the following comment:
"On large angles: Computationally, we found some in hypothetical prismane structures, attached (doi: 10.1021/jo034910l and 10.1021/om960099b) We also did an estimate of the energy to open up that angle in substituted methane, in another paper. The structure your search found are intriguing.