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I understand that if you rotate a molecule and it has the same configuration as its enantiomer, then it is indeed the same compound as the enantiomer (meso), and hence is achiral (despite having chirality centers).

If compound is rotated and the resulting Fisher projection has exactly the same configuration after its rotation, what does that mean in terms of chirality? (I'm not talking about enantiomers here,) It will have a different enantiomer (and hence not be meso), and will be polarizable, but the compound itself has exactly the same perspective if you rotate it. Does this hold any signifance chemically or stereochemically, or is it meaningless?

Take for example D-idaric acid (2S,3R,4R,5S)-2,3,4,5-tetrahydroxyhexanedioic acid).

In the below example of Idaric acid, the enantiomer appears to be a different compound. When the compound is rotated 180 degrees, it looks exactly the same.

Idaric acid

In the below example of galactaric acid, when the compound is rotated 180 degrees, it is a different image. This is despite it being meso.

Galactaric acid

Obviously, being meso has a lot of chemical significance (no polarization of light). But does a compound possessing the property of being rotated 180 degrees, and having the same image (in Fischer form) present any chemical significance compared to a compound that doesn't do this?

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    $\begingroup$ Be careful when manipulating Fischer projections. You are allowed to rotate around an axis perpendicular to the page (described as 'rotate 180 deg), but you can't rotate around an axis in the plane of the page (described as 'vertical flip'). I believe what you're doing is really drawing the mirror image, which is not the same thing. Remember that the Fischer projection implies that all of the horizontal bonds are coming out of the plane and the vertical bonds are going into the plane. The vertical flip would place the horizontal bonds into the plane. $\endgroup$ – jerepierre Apr 3 '15 at 13:08
  • $\begingroup$ I didn't think of that jerepierre, good point, thanks. $\endgroup$ – user4779 Apr 3 '15 at 14:04
  • $\begingroup$ Related: What is the perfect definition for chirality? $\endgroup$ – Martin - マーチン Dec 11 '17 at 5:15
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The property that you are describing for D-idaric acid is called C2 symmetry. This means that when you rotate a molecule (or any object) by 180 degrees, it appears identically to the original orientation. In D-idaric acid, the C2 symmetry axis is halfway along the bond between C3 and C4.

Having a C2 symmetry axis doesn't tell us if the compound is chiral or not. Achiral compounds have an (internal) plane of symmetry or a point of symmetry. D-Idaric acid does not meet either of these requirements and is a chiral molecule.

Galactaric acid does not have a C2 symmetry axis but does have a plane of symmetry. Galactaric acid is achiral. Since galactaric acid has stereocenters but is not chiral, we describe it as meso.

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  • $\begingroup$ I'll add a couple of examples of the chemical utility of C2 compounds when I get a chance later. $\endgroup$ – jerepierre Apr 3 '15 at 13:04
  • $\begingroup$ Just the answer I'm looking for thank you. When you mention both D-Idaric acid and Galactaric acid having C2 symmetry, I notice Galactaric acid isn't the same when rotated 180 degrees? $\endgroup$ – user4779 Apr 3 '15 at 14:17
  • $\begingroup$ @user4779 Sorry, that wasn't correct. Galactaric acid is not C2 symmetric. $\endgroup$ – jerepierre Apr 3 '15 at 14:34
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You can have "symmetric" chiral molecules like you describe.

This is a subtle point and your particular choice isn't chiral.

In typical organic chemistry, instructors mention about mirror images, but leave some of the subtle details to later courses.

There are many types of chiral molecules and some of them look quite symmetric. Consider a pinwheel or propeller. You can rotate along the axis of the propeller and it will be symmetric, but there's a tilt/twist to the blades:

enter image description here

So these two images are mirror, but there's a chiral axis and the direction of rotation is reversed. They are enantiomers. This case has three-way symmetry, but it's possible to have a "two leaf" pinwheel that's still chiral. Proper rotations don't make mirror images.

Your case, D-idaric acid, is C2 symmetric.

enter image description here

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