Ethane, One Internal Rotational Degree of Freedom

If we plot some property of the ethane molecule, say, its potential energy, as a function of the torsion angle, we obtain a curve with threefold periodicity. In crystallographic parlance we have a repeating one-dimensional pattern with the line group pm and periodicity t = 120°. The special positions (fixed points) at a = 0° and 60° (modulo 120°) correspond to structures with special symmetry at 0° the eclipsed conformations with D31, symmetry, at 60° the staggered conformations with 3d symmetry. A general position corresponds to a chiral conformation with Z 3 symmetry only. Note that the order of D3 is half that of or 3d but the number of isometric Dj conformations is double the number of isometric 1)31, or conformations. 

2 Simplified Symmetry Analysis of Conformationally Flexible Molecules 

Given the constitution (connectedness) of a molecule, the internal coordinates are separated into those which are regarded as being fixed (at least for the purpose of the analysis) and those which, for one reason or another, may vary over a large range 

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