Point Group. Isomerism

5 Molecular Properties and Spectra 3.4.5.1 Point Group. Isomerism 

Both unsymmetrical species F—F—0 (bent) and F—0=F (bent) were predicted [13] on the basis of the MO calculation for diatomic OF (see p. 67), which may form a weak o bond by overlap of a p orbital of a highly electronegative atom with one lobe of its jt orbital. However, this bonding model was criticized and replaced by a three-center model which does not support the unsymmetrical FFO species [16]. Heats of formation, calculated by the MNDO method [14] for (symmetrical) FOF (18.2 kcal/mol) and for FFO (125.8 kcal/mol), show the former to be the more stable species [15]. 

---

An early attempt to test the disjoint hypothesis compared the magnetic properties of two isomeric tricyclic m-quinonoid non-Kekule molecules 17, formally a biradical with tetraradical resonance structures, and 18, formally a tetraradical (Section 2.3). These molecules belong to the point groups C2 and C2v, respectively, and it will be mnemonically convenient to use those descriptors in what follows. The test derives from the recognition that the connectivities of the two molecules... 

The methane molecule is a very important molecule in organic chemistry, the geometry around the tetravalent carbon atom being basic to the understanding of the structure, isomerism and optical activity of a very large number of compounds. It is a tetrahedral molecule belonging to the tetrahedral point group, Td. 

The question about the isomeric composition of the synthesized samples of the C6QH36 fullerane have not been completely resolved yet. In this work we consider ten C60H36 isomers, which are often formed under the synthetic conditions (Haufler et al. 1990 Ruchardt et al. 1993 Lobach et al. 1997 Billups et al. 1997 Guo and Scuseria 1992 Okotrub et al. 1999 Nossal et al. 2001). Their point groups are T, Th, D3d, Z>3d, S6 (Nos. 91 and 88), C3 (Nos. 3, 4 and 64) and Cv The Schlegel diagrams of the considered isomers are demonstrated in Fig. 4.5, the numbering follows (Clare and Kepert 1994, 1999). 

Draw the formulae of all the possible isomeric butenes and determine their symmetry elements and point groups. Use the flow chart in the appendix to assist you. 

Compounds with trigonal bipyramidal configurations also display isomerism the point groups and infrared active CO-stretching vibrations are given in Table II assuming all ligands have spherical symmetry. 

The experimental results on valence isomerization of benzene can be rationalized by means of correlation diagrams that were first discussed for hexa-fluorobenzene by Haller (l%7). The orbital correlation diagram for the conversion of benzene to dewarbenzene (Figure 7.44a) has been constructed on the basis of a classification of the benzene Jt MOs according to C , symmetry. The full symmetry of benzene is D ,. The symmetry elements common to both point groups Cj, and are E, Cj, and o,(x,z) = o which is the plane through... 

Fig. 2 depicts Raman spectra of rBuSiF2SiF2tBu at two temperatures. In accordance with the ab initio predictions no temperature-dependent rotational isomerism can be observed. Subsequently, the vibrational analysis of /BuSiF2SiF2/Bu was carried out for the point group C2, since the vibrational spectra obey the rule of mutual exclusion Cjh contains inversion as a symmetry operation). 

When a species cannot be superimposed on its mirror image the two forms are known as enantiomers or optical isomers. Most examples with coordination compounds have chelating (e.g. bidentate) ligands (see Topic E3 ). Structures 10 and 11 show respectively the delta and lambda isomers of a tris(chelate) complex, with the bidentate ligands each denoted by a simple bond framework. As discussed in Topic C3. optical isomerism is possible only when a species has no improper symmetry elements (reflections or inversion). Structures 10 and 11 have the point group D3, with only C3 and C2 rotation axes. 

FIGURE 10.23 Dependence of the melting points of isomeric methyl substituted alkanes on the position on the chain of the methyl group. 

J.E. Leonard, Studies in Isomerism Permutations, Point Group Symmetries, and Isomer Counting, Ph.D. Thesis, California Inst. Technol., California 1971. 

The four-atom chain is the simplest system for which rotational isomerism is possible. It is shown in Figure 3-2. Rotational isomers, or conformers, are various forms of the same molecule related by rotation around a bond as axis. The various rotational forms of a molecule are described by the same empirical formula and by the same structural formula. Only the relative positions of the two bonds (or groups of atoms) at the two ends of the rotation axis are changed. The molecular point groups for various rotational isomers may be entirely different. 

The symmetry of a molecule also places restrictions on whether or not it is possible for the molecule to be optically active. Optically active (or chiral) molecules can exist in one of two different isomeric forms known as enantiomers, each of which rotates plane-polarized light in a specific direction. In order for a molecule to be optically active, its optical isomers must consist of nonsuperimposable mirror images. This will occur if the molecule has no other symmetry besides the identity element or a proper rotation. As a result, any molecule having an improper rotational axis (S ) cannot be optically active. This includes the nongenuine improper rotations, S (mirror plane) and 2 (inversion) operations. Thus, only molecules having the point groups CI, C , D , T, O, and I can be optically active. 

Figure 1.19 Various potential components resulting from Eq. (30) for the ground state of Nag. The left-hand panel shows the spherical component (Eq. (31)) given by the continuous line. For comparison the spherical jellium potential (dashed line) is also given. As one can see the two are almost identical and much larger than the two most important nonspherical potential parts vi=2,m=o(f ) (continuous line) and vi=4,m=o r) (dashed line) displayed in the right-hand panel. Note that these two components are strongly fluctuating compared to the smooth spherical part. These potential parts make the optical response different in the three isomeric states. In the end they are responsible for the transition from the molecule with a point-group symmetry to the solid with a space-group symmetry — a problem that has not yet been solved...

OCAMS departs from the WH-LHA procedure by carrying out the analysis in the symmetry point group conunon to the reactant and the product, here C2v The subgroup into which the reacting molecule has to be desymmetrized along the reaction path, or - equivalently - the irreducible representation of the non-totally symmetric symmetry coordinate(s) that has(have) to be incorporated into the reaction coordinate, is determined by a Correspondence Diagram, In its most rudimentary form, we take into account only the occupied orbitals on each side that are considered to be directly involved in the isomerization process. 

---