Minor plane

Fig. 29. Dominant stabilizing pi type orbital interactions in the Cee and Qs conformers of isobutene. The symmetry labels are assigned with respect to a minor plane...

One delntion of cWraSly is that the molecule be nonstfmrinipgsaUe CO its minor image. An equivalent criterion is (hat it not possess an crnpiupcr axis of eolation (page 52). The absence of a minor plane does not insure optical activity because a molecule may have no mirror plane, yet may possess an improper rotational axis. We can, however, be sure that the molecule with a minor plane will be optically inactive. 

Many molecules have more than one C axis. For example, staggered ferrocene has five C, axes, one of which lies in the plane of the paper. Eclipsed ferrocene also has five C, axes, though they are different from the ones in tbe staggered conformcr (Fig. 3.8) In those cases in which more than one rotational axis is present, the one of highest order is termed the principal axis and is usually the s axis. Planes that contain the principal axis are termed vertical planes, crr, and a minor plane perpendicular to the principal axis is called a horizontal plane, aFor example, borazine (Fig. 3.2c) has three vertical planes (one is shown) and one horizontal plane (the plane of the molecule). 

Figure 4-5. Reflection of a vector by a horizontal minor plane.

E = identity operation, C = n-fold proper rotation axis, S = n-fold improper rotation axis, <7h = horizontal mirror plane, <7v = vertical minor plane, <7d = dihedral minor plane, i = inversion center. 

Figure 2. Depiction of possible anion positions in the hexagonal temaiy apatite structure. Stippled planes represent minor planes at z = each containing a triangle of Ca2 atoms...

Fig, 25. Stabilizing pi orbital interactions in cis and trans l,2-difluoro-l,2-dicyanoethylene. Symmetry labels are with respect to a rotational axis (tranr isomer) and minor plane (cis isomer)... 

These molecules have minor planes containing the principal C axis, but no horizontal... 

A carbon atom with two identical substituents (only three different substituents) usually has an internal minor plane of symmetry. The structure is not chiral. 

For each compound, determine whether the molecule has an internal mirror plane of symmetry. If it does, draw the min or plane on a three-dimensional drawing of the molecule. If the molecule does not have an internal minor plane, determine whether or not the structure is chiral. 

Fig. 4.42 Breaks of the minor symmetry by the molecular tilt. Due to the collective tilt of molecules the zy plane is no longer a minor plane. Three vectors, namely, molecular dipole moment Pj, the normal to the layers h and the director n form the right-handed triple of vectors. For the tilt angle equal to (—17) the triple changes the sense of chirality, i.e. becomes left-handed. As a result, right-handed and left-handed domains are observed...

Improper Rotation, S 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 3dOV" followed by reflection across a plane perpendicular to the rotational axis. Neither the axis of rotatian nor the minor 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 ... 

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