Three Internal Rotational Degrees of Freedom

A molecule with equal torsion angles 0,0,0 (point symmetry C3) corresponds to a point with hexagonal coordinates 0,0,0 situated on the threefold axis passing through the origin of the unit cell. 

We proceed as before. A Ph4X molecule is regarded as a set of four rigid rotors on a frame of symmetry. An arbitrary conformation is then specified by four torsion angles, 01,02.03.04 along coordinates coa, Wb. where the labels 

D each refer to a given phenyl group. Each observed conformation then corresponds to a point (0i.02.03.04) in four-dimensional space, and the distribution of such points, with allowance for the symmetry aspects of the problem, can be interpreted, as before, in energy terms. There are two questions that have to be settled before we start How do we choose the zero positions of the torsion angles And how do we choose the sequence of labels  

In order to label a given arbitrary conformation in a standard way we first use the above relationships to compute all possible values of the four torsion angles. Ring A is chosen as the one with torsion angle closest to -(-90°, this defines ring C  

For the Ph4X molecules an additional set of 16 pure translation operations has to be included to allow for the additional equivalent conformations obtained by applying 180° rotations of the phenyl groups. These translations are  

---