Achirotopic plane

The stereocenters in all three stereoregular polymers are achirotopic. The polymers are achiral and do not possess optical activity. The diisotactic polymers contain mirror planes perpendicular to the polymer chain axis. The disyndiotactic polymer has a mirror glide plane of symmetry. The latter refers to superposition of the disyndiotactic structure with its mirror image after one performs a glide operation. A glide operation involves movement of one structure relative to the other by sliding one polymer chain axis parallel to the other chain axis. 

A good illustration of the usefulness of the concepts local symmetry and chirotopicity is provided by the case of glycerol. The question as to whether the protons of the C,H20 groups are equivalent is problematic for most professional chemists. The answer is that they are not They are chirotopic (property ) and diastereotopic (relationship ). The issue that leads most chemists astray is the symmetry plane, which is the clue to that the molecule is achiral. However, only atoms within the symmetry plane are achirotopic. those outside are chirotopic. 

The number of classes, equal to 5, is derived considering all the possible conditions for chirotopicity of the catalytic sites corresponding to L. If they are not chirotopic, i.e. if they are achirotopic (e.g. they are bisected by a horizontal mirror plane), there are two possibilities only the two sites are equal (class I catalysts) or different from each other (class II catalysts). If, on the contrary, they are chirotopic, three possibilities exist the two catalytic sites are homotopic (equal) - related by a twofold symmetry axis (class III catalysts), enan-tiotopic - related by a vertical mirror plane (class IV catalysts) or diastereotopic (different from each other) - no symmetry element is present (class V catalysts). As a consequence, only five classes of metallocene catalysts may exist if interconversion among stereoisomers is not taken into account [122]. 

The terms enantiotopic and diastereotopic describe the relationship between a pair of atoms or groups in a molecule. Sometimes it is also useful to describe the local environment of a single atom, group, or location in a molecule (even if it does not coincide with an atomic center) as chiral or not. A chirotopic atom or point in a molecule is one that resides in a chiral environment, whereas an achirotopic atom or point does not. All atoms and all points associated with a chiral molecule are chirotopic. In achiral molecules, achirotopic points are those that remain unchanged (are invariant) upon execution of an S that is a. symmetry operation of the molecule. For most situations, this means that the point either lies on a mirror plane or is coincident with the center of inversion of the molecule. Importantly, there will generally be chirotopic points even in achiral molecules. 

These terms can be clarified by looking at some specific examples. In the following ro-tamers of ) cso-l,2-dichloro-l,2-dibromoethane, the only achirotopic site in rotamer A is the point of inversion in the middle of the structure. Every atom is in a locally chiral environment, and so is chirotopic. For rotamer B, all points in the mirror plane (a plane perpendicular to the page of fhe paper) are achirotopic. All other points in these conformers are chirotopic, existing at sites of no symmefry. In other words, all other points in these conformers feel a chiral environment, even though the molecule is achiral. 

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