Stereochemistry of Cumulenes | Stereochemistry | Organic Chemistry

Cumulenes are the compounds having a cumulated system or adjacent double bonds, and the simplest cumulene is Allene, which is having only two cumulated double bonds.
In allenes, the terminal carbon atoms are sp2 hybridized whereas the middle carbon atom is sp hybridized. The middle carbon has two p orbitals which are perpendicular to each other. Hence they form two pi-bonds by overlapping laterally with the 'p' orbitals on the adjacent carbon atoms. Hence the two double bonds are in two perpendicular planes. Because of this, the substituents on the terminal carbon are also perpendicular to each other.
Hence in Allene, if the substituents on the terminal carbon atom are same, there’ll be a plane of symmetry passing from the central axis.
But if the substituents on the terminal carbon atom are different then there will note any element of symmetry present in the molecule. Under this condition, the molecule will not be superimposable on its mirror image. Thus it possesses molecular chirality and hence it should be optically active.
In case, if there are more than two double bonds (Cumulene) substituents in the terminal carbon atoms are now in the same plane. Therefore there will be a plane of symmetry always present. Thus they are non-chiral molecules and do not show optical activity.
Therefore we can say that the cumulenes having an even number of double bonds exhibit optical isomerism (Dextro and levo) while cumulenes having an odd number of double bonds exhibits geometrical isomerism (cis and trans). Please note that there should be different groups on terminal carbon atoms.
2, 3, 4 Hexa-triene (shows geometrical isomerism)
2, 3, 4, 5 Hepta-tetra-ene (shows optical isomerism)
Thus it is clear that the non-planarity of the molecule causes molecular chirality and hence the optical activity.

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