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Since the attached groups are present in different planes, $\ce{ClCH=C=CHCl}$ should not show geometrical isomerism, but my book say that it does. Why?

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  • $\begingroup$ You are right, there is no cis-/trans- isomerism for allenes to speak of. Probably a typo, or the book author considers enantiomeric forms geometrical isomerism too. Feel free to provide an exact quote from your textbook alongside with bibliographical data. $\endgroup$ – andselisk Apr 6 '19 at 7:28
  • $\begingroup$ Enantiomerism is a geometrical isomerism.It is so obvious that I do not check any definition. Just it is that often we intend geometrical isomerism as E/Z isomerism. Even more, isomerism of whatever forms implies a different geometry of stable molecules, though I would never call two chain isomers as geometric, as in this case it would bring more confusion than information. $\endgroup$ – Alchimista Apr 6 '19 at 8:01
  • $\begingroup$ @AbhishekKumar The compound shows axial chirality and hence has two enantiomers. $\endgroup$ – Soumik Das Apr 6 '19 at 8:26
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This is a chiral compound; it has two enantiomers. This source defines "geometrical 8somerism" as isomerism involving different geometrical arrangements, and a pair of nonsuperimposable mirror images would seem to qualify. But in the body they talk about about cis/trans or E/Z isomers, not chiral compounds. The latter, which applies here, should be described by more precise terms like "enantiomers".

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Since the attached groups are present in different planes,

This is exactly why is it has geometrical isomers. Going from one chlorine to the other or hyddrogen to hydrogen involves either a right-handed or left-handed rotation. I think the images below will allow you to see this relation.

enter image description here enter image description here
Left-handed molecule $\qquad ~~~~~\qquad$ Right-handed molecule

Although this does not apply to this case a related concept is atropisomers which uses M or Δ for right-handed rotations and P or Λ for left-handed rotations which would apply to these types of molecules. This convention is also used in coordination chemistry.

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