Читать книгу Solid State Chemistry and its Applications - Anthony R. West - Страница 81

The relationships between point symmetry and structure are best illustrated by examples of small molecules. The methylene dichloride molecule, CH₂Cl₂, Fig. 1.58, possesses (i) a single 2‐fold axis which bisects the H–С–H and Cl–С–Cl bond angles and (ii) two mirror planes (a). The 2‐fold axis is parallel to the line of intersection of the mirror planes. These symmetry elements may be represented as in (b), in which the 2‐fold axis is perpendicular to the plane of the paper and the mirror planes appear in projection as horizontal and vertical lines. From inspection of Fig. 1.55, it is seen that CH₂C1₂ belongs to point group mm2. However, the number of equivalent positions in mm2 is four (c), which does not appear to tally with the realities of the CH₂CI₂ molecule. Thus, if we place a H atom at one equivalent position, there should be only two possible equivalent positions in the molecule, as there are only two H atoms present. This apparent anomaly is resolved by letting the equivalent positions in Fig. 1.55(c) lie on the vertical mirror plane instead of to either side of the mirror. This yields the arrangement shown in Fig. 1.58(c), which now has only two equivalent positions. Thus, positions 1 and 2 in Fig. 1.55(c) become the single position A in Fig. 1.58(c). We can now distinguish between the general equivalent positions of a point group and the special equivalent positions; the latter arise when the general positions lie on a symmetry element such as a mirror plane or rotation axis. Thus, A and В in Fig. 1.58(c) are both special positions.

Figure 1.58 The symmetry of the methylene dichloride molecule, CH2Cl2, point group mm2.

Figure 1.59 The symmetry of the methyl chloride molecule, CH3Cl, point group 3m.

As a second example, the point symmetry of the methyl chloride molecule, CH₃CI is shown in Fig. 1.59. The molecule possesses one 3‐fold axis along the direction of the С–Cl bond (a). It has no 2‐fold axes but has three mirror planes oriented at 60° to each other; one is shown in (b). The 3‐fold axis coincides with the line of intersection of the mirror planes. The symmetry elements are shown as a stereogram in (c) and by comparison with Appendix E, we see that the point group is 3m. The six general equivalent positions in 3m are given in (d). We again have the problem that there are more equivalent positions than possible atoms and this is overcome by allowing the general positions to lie on the mirror planes (e); the number of positions is thereby reduced to three.