Question

How can you tell which atoms are in the same plane of cumulene? Why is allene preferentially twisted instead of planar?

Answer 1

Well, you kinda just have to know when it comes to these two types of compounds...

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Cumulene is an entirely planar molecular class, but allene is more stable as a twisted conformer. As a note, a cumulene can have three OR MORE consecutive double bonds.

Here, butatriene has all atoms in the same plane, and in principle, a cumulene is entirely planar. Allene has all planar atoms EXCEPT the left-hand hydrogens.

Even though the entire carbon chain consists of double bonds on both molecules, half of allene is `90^@` rotated, and the left-hand hydrogen atoms are perpendicular to the plane of the screen.

I would think that allene is twisted so that the same `p_(x//y)` atomic orbital is not used in two adjacent `pi` bonds, given that two orthogonal `p` atomic orbitals (`p_x`, `p_y`) are both available, and in such a small system the repulsions could be too unfavorable.