# How are these two molecules identical?

I can see that these compounds are identical as we have basically just done a 180 degree rotation of the molecules.

But if we go by the concepts of chirality, the carbons 2 and 4 are chiral centers and since they have inverted configurations at both chiral centers, they should be enantiomers. Or is it just that I cannot assume the hydrogens not shown to be out of plane?

• Have you heard of meso compounds? – Mithoron Apr 5 '19 at 18:58
• No, you just said that they're identical. Why would you then say that they are enantiomers? The concepts of chirality don't say that. They have to be nonsuperimoposable mirror images, and they are clearly superimposable. – Zhe Apr 5 '19 at 18:59
• An enantiomer is a non-superimposable mirror image. The definition does not say anything about configurations. True, having opposite configurations at all chiral centres often makes two things enantiomers, but not always. – orthocresol Apr 5 '19 at 19:05
• The basic question: Yes the molecules are identical. Optically activity None, this is a meso compound. The two chiral centers cancel each other out so the molecule as a whole is not optically active. – MaxW Apr 5 '19 at 19:13
• On a mildly related note, the general relativity books I'm reading keep saying don't use coordinates, just use coordinate-free descriptions because that will be true in every coordinate system. This is exactly like that. The definition of chirality is fully independent of identifying the configurations of centers. Does this molecule have an improper axis of rotation? If yes, it's not chiral, and you don't need to assign stereochemistry to any center. This is the equivalent coordinate-free language. – Zhe Apr 5 '19 at 19:21

This molecule has a plane of symmetry. Imagine a vertical plane go through $$\ce{C}$$-3 atom of pentane chain. One side of that plane is the mirror image of other side. Hence, this is not optically active molecule by definition. It is called meso-isomer. If you look at (R,S)-configuration and number the chains as they are drown, first compound is (2R,4S)-2,4-dichloropentane and second compound is (2S,4R)-2,4-dichloropentane. But, since each have plane of symmetry, you may number second compound from opposite direction. Then it is (2R,4S)-2,4-dichloropentane. Therefore, they are identical.