Classification symmetry plane

In molecules with little or no symmetry, it may still be possible to recognize the main localized-orbital component of certain molecular orbitals. It is then convenient to adopt the label of this localized type as the label of the molecular orbital, even though the molecular symmetry does not coincide with the local symmetry. For instance, in methylenimine again, the 5A orbital is clearly built out of the in-plane 7rc 2 group orbital, with a small NH component. We therefore label the orbital t CU2, although the molecule does not have a vertical symmetry plane. Similarly, the orbitals 7A and 8A of propylene are labeled 7TqH3, tt CU2 (111.49).a Other examples where the local symmetry is sufficiently preserved and only weakly perturbed by the molecular environment are hydrazine (111.34) and methylamine (III.31). In some cases we have omitted the label as no unambiguous classification is possible. 

The point here is that the entire symmetry classification of reaction (69) is based on the presumption that a plane of symmetry is conserved thoughout the hydrogen abstraction process (the plane incorporating the C—H bond and the carbonyl group). If one or more atoms are displaced slightly so as to destroy the symmetry plane the crossing becomes avoided. A comparison of the in-plane and slightly out-of-plane cases is illustrated in Fig. 16a and b (Salem etal., 1975). 

Inherently chiral derivatives can be also obtained from calix[4]arenes if three different units are incorporated in the order ABAC or if only two different phenolic units are present, provided these derivatives are fixed in conformations having no symmetry plane and center. Figure 13 gives a survey of the possibilities. For such a classification, one should keep in mind that hydroxy groups (or methoxy groups but ethoxy groups are on the borderline) can pass the annulus. Their orientation may be necessary in a description of the actual conformation of such compounds. It must not be indicated, however, if different stable stereoisomers are to be... 

We now consider some special points. The point fe(0, 0) is normally called F the points A and Z lie on symmetry planes (see Figure 10.1b) in the interior of the zone the point M lies on a diagonal plane at the corner of the zone. The star of A consists of seven branches. The star of F has no branches since F is invariant under all the point group operators. This latter result is most important in the chemistry of the solid state since it implies that the group of fe = 0 is the whole point group. It follows that the states belonging to fe = 0 can be classified rather easily, for the classification depends only on the point group of the crystal. The point M is equivalent to the point F since they are related by a reciprocal lattice... 

Atoms have complete spherical synnnetry, and the angidar momentum states can be considered as different synnnetry classes of that spherical symmetry. The nuclear framework of a molecule has a much lower synnnetry. Synnnetry operations for the molecule are transfonnations such as rotations about an axis, reflection in a plane, or inversion tlnough a point at the centre of the molecule, which leave the molecule in an equivalent configuration. Every molecule has one such operation, the identity operation, which just leaves the molecule alone. Many molecules have one or more additional operations. The set of operations for a molecule fonn a mathematical group, and the methods of group theory provide a way to classify electronic and vibrational states according to whatever symmetry does exist. That classification leads to selection rules for transitions between those states. A complete discussion of the methods is beyond the scope of this chapter, but we will consider a few illustrative examples. Additional details will also be found in section A 1.4 on molecular symmetry. 

Since the presence of a plane of symmetry in a molecule ensures that it will be achiral, one a q)ro h to classification of stereoisomers as chiral or achiral is to examine the molecule for symmetry elements. There are other elements of symmetry in addition to planes of symmetry that ensure that a molecule will be superimposable on its mirror image. The trans,cis,cis and tmns,trans,cis stereoisomers of l,3-dibromo-rranj-2,4-dimethylcyclobutaijte are illustrative. This molecule does not possess a plane of symmetry, but the mirror images are superimposable, as illustrated below. This molecule possesses a center of symmetry. A center of symmetry is a point from which any line drawn through the molecule encouniters an identical environment in either direction fiom the center of ixnimetry. 

Figure 11.3 illustrates the classification of the MOs of butadiene and cyclobutene. There are two elements of symmetry that are common to both s-cw-butadiene and cyclobutene. These are a plane of symmetry and a twofold axis of rotation. The plane of symmetry is maintained during a disrotatory transformation of butadiene to cyclobutene. In the conrotatory transformation, the axis of rotation is maintained throughout the process. Therefore, to analyze the disrotatory process, the orbitals must be classified with respect to the plane of symmetry, and to analyze the conrotatory process, they must be classified with respect to the axis of rotation. 

An orbital correlation diagram can be constructed by examining the symmetry of the reactant and product orbitals with respect to this plane. The orbitals are classified by symmetry with respect to this plane in Fig. 11.9. For the reactants ethylene and butadiene, the classifications are the same as for the consideration of electrocyclic reactions on p. 610. An additional feature must be taken into account in the case of cyclohexene. The cyclohexene orbitals tr, t72. < i> and are called symmetry-adapted orbitals. We might be inclined to think of the a and a orbitals as localized between specific pairs of carbon... 

Figure 14.9. (a) Orbital correlation diagram for the direct insertion of carbene into an olefin to form cyclopropane. Symmetry classification is with respect to the vertical bisecting mirror plane. (b) State correlation diagram showing the intended correlations and the avoided crossing of states So and S2. 

With the structure assumed above for the Cr—C6H5X system, the common symmetry element is the cr (xz) plane although the n orbitals of the arene moiety are conveniently classified according to their local C2v symmetry as above, the symmetry classification in the complex is with respect to cr and is given in Table IX. 

The classification of molecular symmetry operations that we shall follow here is the conventional one (see, e.g., Tinkham [2]), involving rotations about a specified axis, denoted Cn for a counterclockwise rotation through reflections in a plane, de-... 

A molecule that has a mirror image is also said to be dissymmetric while one that docs not (an achiral molecule) have an enantiomer is noiidissyiinnetric. The classification of a given structure as dissymmetric or nondissymmetric is based upon the presence (or lack) of symmetry elements (axes, planes) in the structure. 

Figure 11.16 Symmetry, basis orbitals, and correlation diagram for the it2s + tt4s cycloaddition. Symmetry classifications are with respect to the mirror plane illustrated.

The basis of the application of group theory to the classification of the normal vibrations of a molecule lies in the fact that the potential and kinetic energies of a molecule are invariant to symmetry operations. A symmetry operation is a physical transformation of the molecule, such as reflection in a mirror plane of symmetry or rotation through 120° about... 

The symmetry classification of wavefunctions is based on the symmetry properties of molecules. Most small molecules possess certain symmetry elements such as a plane (a), or an w-fold axis (OJ, or a centre of symmetry (i), or perhaps a variety of these elements in combination. In order to be as definite as possible we shall develop the argument in terms of a specific example. The ground state of... 

Next, consider the planar AB3 molecule (BF3) shown in Fig. 1-23. This molecule has no special symmetry. It has a C3 axis of rotation without a collinear S6 axis. It has three C2 axes perpendicular to the C3 axis, and therefore falls into the D classification. It has a Ch plane of symmetry perpendicular to the C3 axis and three [Pg.40]

The next example is the hexagonal planar molecule of type A6 or A6B6 (benzene) shown in Fig. 1-24. The molecule is not of a special symmetry. It has a center of symmetry and a C6 axis of symmetry. No S2 axis exists. Since six C2 axes perpendicular to the C6 axis are found, this molecule also falls into the D classification. Since it has a horizontal plane of symmetry perpendicular to the C6 axis, the molecule belongs to the D6h point group. 

---