Cubic point group family

The CH4 molecule has symmetry. The relationship between a tetrahedron and cube that we illustrated in Figure 4.6 is seen formally by the fact that the point group belongs to the cubic point group family. This family includes the and Oj, point groups. Table 4.3 shows part... 

The CH4 molecule has Tj symmetry. The relationship between a tetrahedron and cube that we illustrated in Figure 5.6 is seen formally by the fact that the point group belongs to the cubic point group family. This family includes the Tj and O], point groups. Table 5.3 shows part of the character table. The C3 axes in CH4 coincide with the C—H bonds, and the C2 and 54 axes coincide with the x, y and z axes defined in Figure 5.6. Under symmetry, the orbitals of the C atom in CH4 (Figure 5.20a) are classified as follows ... 

The crossover modulus is the value of G (and G") at the frequency where the two moduli are equal, i.e, where the curves of G co) and G (o) cross (see Fig. 5.5). An objective identification of the crossover point can be made by fitting the points on both curves in the vicinity of this point with cubic splines. Bafna [35] has pointed out that this empirical correlation is based on data for a single family of polypropylenes, i.e. a group of polymers having similar molecular weight distributions, and that it cannot be expected to be valid for other groups of polymers. 

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