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structures of alpha- beta- and gamma- cyclodextrin

I am studying the host-guest chemistry of cyclodextrins with achiral aromatic molecules, and I found out that a useful way of studying them is by induced circular dichroism spectroscopy. This technique is used by taking an achiral molecule and placing it in a chiral environment to induce a CD signal. Apparently, the cavity of a cyclodextrin is chiral, but for the life of me I cannot see HOW it is chiral. I know the glucose molecules the ring is made of are D-glucose, but I still see mirror planes in the structure, and I cannot figure out how the cavity is chiral! Help??

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  • $\begingroup$ related chemistry.stackexchange.com/questions/153/… $\endgroup$ – Mithoron Jan 13 '18 at 20:39
  • $\begingroup$ You don't look close enough. From pictures it would seem there's center of symmetry no planes, but rotation is blocked - inside of molecule can't become outside so there's no center and cyclodextrin is chiral. $\endgroup$ – Mithoron Jan 13 '18 at 20:49
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It is because the constituent glucose molecules are chiral.

In the image you can see that all the $\ce{CH2OH}$ groups in the center are out of the plane (towards you). These groups are on the upper side of the cavity. If they were below the plane, the cyclodextrin would have other interactions with the host molecule.

enter image description here

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  • $\begingroup$ Not necessarily because there are more chiral centers, but probably the interactions would have much less chiral nature. That cyclodextrin would serve still for non-chiral purposes like solubilizing hydrophobic molecules. $\endgroup$ – Raoul Kessels Jan 13 '18 at 18:24
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    $\begingroup$ So regardless of the mirror planes in the molecule as a whole, it is still chiral, simply because the glucose molecules provide the chiral information individually? $\endgroup$ – Gabi Jan 13 '18 at 19:10
  • $\begingroup$ Yes, as long as there are chiral centers, the whole is chiral (except if it is a meso form). If you could invert all the chiral centers of glucose and then make a cyclodextrin of them, you would have the specular form; exactly the same properties except for the optical activity. This would be, however, very complicated since cyclodextrin is made from starch, and starch comes from biological sources and there the chiralty is as it is. $\endgroup$ – Raoul Kessels Jan 13 '18 at 19:41
  • $\begingroup$ There's no mirror planes, there could be only one plane making it meso, but half of glucose units would need to be "backwards". $\endgroup$ – Mithoron Jan 13 '18 at 20:52
  • $\begingroup$ @Mithoron I meant it in general. Like in tartaric acid. In the case of glucose I do not think that it is possible to have a meso form since both ends of the molecule are not the same ($\ce{CHO}$ and $\ce{CH2OH}$). $\endgroup$ – Raoul Kessels Jan 13 '18 at 21:05

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