Diagram of allene with interatomic distances marked

If $d_1$ and $d_2$ are the interatomic distances between the pairs of hydrogens shown above, what is the relation between $d_1$ and $d_2$?

I think that $d_1$ and $d_2$ might be equal since the terminal hydrogen atoms are perpendicular to each other.


Propadiene is an allene which has $D_\mathrm{2d}$ symmetry. This dictates that the distances between the hydrogen atoms at the opposite terminal carbons are the same. In mathematical terms:

$$d(\ce{H^a-H^c}) = d(\ce{H^a-H^d}) = d(\ce{H^b-H^c}) = d(\ce{H^b-H^d})$$

Below shows the resymmetrised ($R\gg0.99$) geometry on the GFN2-xTB semi-empirical level of theory. In faint colours the $C_2$ axis are displayed.

geometry of propadiene with highlighted H-H distances

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