Homotopic groups

Homotopic Groups Not distinguishable under any conditions, chiral or achiral. To have homotopic groups, a molecule must have a finite axis of rotation. Thus the only molecules which cannot have homotopic groups are those whose point groups are Ci, CS) Q, and CCXJV. 

Nuclear magnetic resonance chemical shift differences can serve as an indicator of molecular symmetry. If two groups have the same chemical shift, they are isochronous. Isochrony is a property of homotopic groups and of enantiotopic groups under achiral conditions. Diastereotopic or constitutionally heterotopic groups will have different chemical shifts (be anisochronous), except by accidental equivalence and/or lack of sufficient resolution. 

For homotopic groups, chemical shifts are indistinguishable in chiral or achiral solvents, that is, the groups are isochronous. 

Homotopic groups cannot be distinguished by any means whatsoever they are chemically entirely identical. 

With [2H4]ethylene glycol as a substrate one observes a moderate isotope effect kn/k1H = 2) on the Kmax of the dioldehydratase reaction. This is much less than the value of ca. 10 observed with 1,2-propanediol. The application of partially de-uterated substrates allows one to measure an isotope effect arising through intramolecular competition between otherwise homotopic groups. Such intramolecular isotope effects can be substantiated by appropriate product analysis for deuterium. 

Hofmann rearrangement, 118 Homotopic groups, 9 Homotropenylium, 152 Huckel array, 85 Huckel MO theory, 35, 86 Huckel 4n + 2 rule, 150, 151 Hund s rule, 114 Hunsdiecker reaction, 305-307 Hybridization, 15, 16... 

Unlike the above, the two hydrogen atoms labeled Ha and Hb in propane 184 are homotopic because a C2 operation converts one into the other, so that they are considered to be equivalent in all possible ways. Even if one of these hydrogen atoms is replaced by a substituent other than methyl and hydrogen, resultant molecule is not chiral. Homotopic groups remain indistinguishable under chiral influence, i.e., in the presence of chiral ligands. 

FIGURE 5.1 Four organic molecules containing homotopIc groups or atoms, (a) f-butylcyclohexane (b) mesitylene ... 

The classification of defects in nematics represents a straightforward example of the applications of homotopic group theory [14, 15], The reader is referred to reviews of the subject [19-21, 23, 52]. This topological approach confirms the absence of walls, the existence of Mobius lines, the mutual annihilation of thin threads and the existence of singular points. More importantly, it shows that defects combine and merge according to the rules of multiplication of the two-element Abelian group Z2. 

If one hydrogen in dichloromethane is substituted with one deuterium, an achiral compound results. This molecule is identical to its mirror image, and the two hydrogens in dichloromethane are equivalent and homotopic. Homotopic groups have identical chemical shifts in all environments. 

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