Propane, symmetry group

FIGURE 1.16 Isomers of cyclopropane-1,2-dicarboxylic acid, (a) is-l,2-Dicarboxycyclopropane (trans isomers) (b) Z-l,2-Dicarboxycyclopropane isomer, (meso isomer) (c) Molecular models of E- (trans-) 1,2-dimethylcyclo-propane shown in the tube representation. Rotation of the right hand structure about a vertical axis through the center of the cyclopropane will superimpose the two methyl groups. The methylene of the rotated structure will be in the back, rather than the front, and not superimposed, (d) A mirror plane through the methylene and the back carbon-carbon bond is a plane of symmetry. The two carboxyl groups appear not to reflect each other in the model shown but they can rotate freely and will reflect each other on an instantaneous basis. 

The most common types of lipids are esters of glycerol. Glycerol is just propane-1,2,3-triol but it has interesting stereochemistry. It is not chiral as it has a plane of symmetry, but the two primary Oh[ groups are enantiotopic (Chapter 16), If one of them is changed—hy esterification, for example—the molecule becomes chiral. Natural glycerol phosphate is such an ester and it is optically active. 

The gas-phase dipole moment of cis-l,3,5-trimethylcyclohexane, which, in the chair conformation with methyl groups equatorial, possesses symmetry, has been determined. The value of 0.25 0.01 D is close to the value of 0.27 D estimated from group-moment assignments based on propane and isobutane. 

Papuamine (5) contains a central 13-membered ring and has a C2-symmetry axis that passes through the central methylene of the diamino-propane bridge and bisects the ( , )-diene. Barrett and Heathcock completed an asymmetric synthesis of papuamine (Scheme 10) [28,29]. Both groups started their synthesis from C2-symmetric diol (106) and con-... 

Molecules of the lath-like shape can form the thermotropic biaxial nematic phase [23] shown in Fig. 1.9. The point group symmetry of this phase is i 2h the rotation of molecules around their longitudinal axes is considerably hindered. An example of the biaxial nematic is [bis-l-(p-n)-decylbiphenyl)-3-(p-ethoxyphenyl) propane-1,3-dionatocopper] [18]. 

In each instance, the 3-methyl group of 3-methylhexane approaches the hydrogen of propane and both the ethyl and propyl groups are opposite methyl groups of propane. Because of the symmetry of propane, one can always find exactly equivalent interactions for the two enantiomers and propane, no matter what approach you pick. Try it with models. 

Chemically equivalent nuclei are those that have exactly identical environments in the molecule. Another way of saying this is that if we list all the distances between every pair of atomic nuclei in the molecule, two equivalent nuclei will have the same set of distances to nuclei of the same elements. So, for example, all six H atoms in ethane (CH3CH3) are equivalent, but propane (CH3CH2CH3) has two groups the six H atoms at the ends are all equivalent, and the two in the middle are equivalent. Equivalent nuclei experience the same chemical shifts because the symmetry of the molecule requires the electron density at each nucleus to be the same. 

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