C3 axis of rotation

Now consider the pyramidal molecule of type AB3 (NH3) shown in Fig. 1-22. This molecule also is not of a special symmetry. It has a C3 axis of rotation but no Sg axis. There are no nC axes perpendicular to the C3 axis, and therefore the molecule belongs to the C classification. Since three vertical... 

From Figure 13, it is seen that a phosphazene trimer (PNCl2)3 has an S3 axis of symmetry. The C3 axis of rotation is perpendicular to the equilateral triangle obtained by joining three phosphorous atoms. The two chlorine atoms bound to each phosphorous atoms are above and below the plane of the triangle. A rotation of 120° followed by reflection in the plane perpendicular to this axis retains the appearance of the molecule with the new positions of the chlorine atoms. A few more operations on the above mentioned molecule can also lead us to derive the following relations. 

The second example is related to the rotational barrier around the C3 axis of benzenechrometricarbonyl, C6H6Cr(CO)3. Our calculations (computing time on an IBM 370/168 10 min) had shown that this barrier would be less than 0.4 kcal. mole-1 (79). The conformational analysis of this molecule was concurrently performed by Schafer (80), using electron diffraction. It appeared that, contrary to chemical intuition but in excellent agreement with our own calculations, the phenyl group could be considered as freely rotating around the C3 axis. 

If the molecule is rotated around the z axis by 120° (360°/3), an equivalent configuration of the molecule is produced. The boron atom does not change its position, and the fluorine atoms exchange places depending upon the direction of the rotation. The rotation described is the symmetry operation associated with the C3 axis of symmetry, and the demonstration of its production of an equivalent configuration of the BF3 molecule is what is required to indicate that the C3 proper axis of symmetry is possessed by that molecule. 

If rotation about an axis by 360°ln followed by reflexion through a plane perpendicular to the axis produces an equivalent configuration of a molecule, then the molecule contains an improper axis of symmetry. Such an axis is denoted by Sn, the associated symmetry operation having been described in the previous sentence. The C3 axis of the PC15 molecule is also an S3 axis. The operation of S3 on PC15 causes the apical (i.e. out-of-plane) chlorine atoms to exchange places. 

A C axis is often called a proper rotational axis and the rotation about it a proper rotation. An improper rotation may be visualized as occurring in two steps rotation by 360E/ followed by reflection across a plane perpendicular to the rotational axis. Neither the axis of rotation nor the mirror plane need be true symmetry elements that can stand alone. For example, we have seen that SiF4 has C3 axes but no C4 axis. Nevertheless, it has three S4 axes, one through each pair of opposite faces of the cube below ... 

The directions of the principal components of the COO chemical shift tensor are shown in Fig. 114. The 022 axis makes an angle of 6° with the direction of the C = O bond and the <733 axis is perpendicular to the COO plane. The local chain axis is approximately perpendicular to the COO plane and nearly parallel to the <733 axis within about 20°. Finally, the C3 axis of the rotating methyl group, designated as zmethyl > is the unique axis of the quadrupolar interaction of the deuterons of the (0)CH3 group. 

Muller and co-workers (02JPC(B)7781) investigated the molecular behavior of perdeuterated 1,3,5-trioxane in a cyclophosphazene inclusion compound by dynamic 2D NMR spectroscopy. The experimental data revealed a relatively complex motional behavior (rotational motion around the C3 axis of the molecule and around the channel long axis) in the phosphazene host channels the ring inversion process was almost uneffected by the host lattice and activation barriers, as reported from solution NMR studies (90JPC8845), were derived. 

If (1) or (2) is not found to be the case, look for a proper axis of rotation of the highest order in the molecule. If none is found, the molecule is of low symmetry, falling into point group C3, Q, or Q. The presence in the molecule of a plane of symmetry or an inversion center will distinguish among these point groups. 

Figure 4.1. The C3 axis of chloromethane. The circle represents the central carbon atom. One hydrogen is starred to follow its position during rotation. It is actually indistinguishable from either of the other hydrogens.

Similar statements can be written to show the combined effects of successive operations. For example, in planar BCI3, the 5 3 improper axis of rotation corresponds to rotation about the C3 axis followed by reflection through the crj, plane. This can be written in the form of equation 3.4. 

Table 3.3 shows the character table for the Cgv point group. The NH3 molecule possesses C3V symmetry, and worked example 3.2 illustrated the principal axis of rotation and planes of symmetry in NH3. In the character table, the presence of three cr planes in NH3 is represented by the notation 3ctv in the top line of the table. The notation 2C3 summarizes the two operations C3 and C3. The operation C3 is equivalent to the identity operator, E, and so is not specihed again. 

In this system some of the dipole-dipole interactions are substantially reduced by the rapid intramolecular rotation of the NH3 ligand around the C3-axis of the metal-nitrogen bond. In fact the static solid-state spectrum of the compound shows just a broad line (half height width of about 2.1 kHz) centered at the same chemical shift as that found for the NH3 protons in the MAS spectrum, but the hydride ligand resonances cannot be detected because the mutual dipolar interaction, not moderated by any intramolecular motion, results in much broader lines. 

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