Symmetry of the molecule

Consider trans-C2H2Cl2. The vibrational normal modes of this molecule are shown below. What is the symmetry of the molecule Eabel each of the modes with the appropriate irreducible representation. 

As for diatomic molecules (Section 7.2.5.2) fhe vibrational (vibronic) transitions accompanying an electronic transition fall into the general categories of progressions and sequences, as illustrated in Figure 7.18. The main differences in a polyatomic molecule are that there are 3A — 6 (or 3A — 5 for a linear molecule) vibrations - not just one - and that some of these lower the symmetry of the molecule as they are non-totally symmetric. 

This concerted model assumes furthermore that the symmetry of the molecule is conserved so that the activity of all its subunits is either equally low or equally high, that is, all structural changes are concerted. Subsequently Daniel Koshland, University of California, Berkeley, postulated a sequential model in which each subunit is allowed independently to change its tertiary structure on substrate binding. In this model tertiary structural changes in the subunit with bound ligand alter the interactions of this... 

It is particularly interesting to consider the influence of the substituents R and Rj in diphenylol alkanes of the type shown in Figure 20.12. Such variations will influence properties because they affect the flexibility of the molecule about the central C-atom, the spatial symmetry of the molecule and also the interchain attraction, the three principal factors determining the physical nature of a high polymer. 

The examples that have been presented in this section illustrate the approach that is used to describe structure and reactivity effects within the framework of MO description of structure. In the chapters that follow, both valence bond theory and MO theory will be used in the discussion of structure and reactivity. Qualitative valence bond terminology is normally most straightforward for saturated systems. MO theory provides useful insights into conjugated systems and into effects that depend upon the symmetry of the molecules under discussion. 

The dihedrals for the remaining two hydrogens are best visualized with a Newman projection. They are located above and below the plane of the C-C-C bond. H5 is the hydrogen below the plane, and its dihedral is 60°. The dihedral for H6 could be expressed as either 300° or -60° we ll use the latter to express the symmetry of the molecule. Here are the Z-matrix lines for these atoms ... 

C atoms are labelled a-e (see text), (b), (c) Line drawings of the two enantiomers of C76 viewed along the short C2 rotation axis and illustrating the chiral D2 symmetry of the molecule. 

If a proton is removed from one COOH group, as shown in Fig. 466, and transferred to a distant water molecule to form (HjO)+, the symmetry of the molecule is lost. On the other hand, if the proton is now removed from the other COOH group and transferred to a water mole-... 

STRATEGY In each case, we must decide on the shape of the molecule by using the VSFPR model and then decide whether the symmetry of the molecule results in the cancellation of the dipole moments associated with the bonds. If necessary, refer to Fig. 3.7. 

Most informative in this context is vibrational spectroscopy since the number of signals observed depends on the molecular size as well as on the symmetry of the molecule and, if it is part of a condensed phase, of its environment. In particular, Raman spectroscopy has contributed much to the elucidation of the various allotropes of elemental sulfur and to the analysis of complex mixtures such as hquid and gaseous sulfur. 

The final expression is the classical limit, valid above a certain critical temperature, which, however, in practical cases is low (i.e. 85 K for H2, 3 K for CO). For a homonuclear or a symmetric linear molecule, the factor a equals 2, while for a het-eronuclear molecule cr=l (Tab. 3.1). This symmetry factor stems from the indistinguishable permutations the molecule may undergo due to the rotation and actually also involves the nuclear partition function. The symmetry factor can be estimated directly from the symmetry of the molecule. 

A subscripted lowercase letter represents the symmetry of the molecule the earlier in the alphabet, the more symmetrical the molecule being described, e.g., propellant 134a. 

The characters Xj for the examples in the previous section were calculated following the method described in Section 8.9, that is, on the basis of Cartesian displacement coordinates. Alternatively, it is often desirable to employ a set of internal coordinates as the basis. However, they must be well chosen so that they are sufficient to describe the vibrational degrees of freedom of the molecule and that they are linearly independent The latter condition is necessary to avoid the problem of redundancy. Even when properly chosen, the internal coordinates still do not usually transform following the symmetry of the molecule. Once again, the water molecule provides a very simple example of this problem. 

If a molecule contains one or more unpaired electrons it is usually possible to detect an electron spin resonance signal and at a very low concentration of unpaired electrons, commonly 1018 spins with modem instruments. Several pieces of information can be obtained in this way. The number of unpaired spins can be found, the symmetry of the molecule in the region of the unpaired electron can be determined, and, if the unpaired electron is delocalized over nuclei with nuclear spins, then the extent of delocalization can be determined. Perhaps more importantly for our purpose, the rotational time of molecules can be determined from line shape studies. 

The deviation from a true tetrahedral geometry that we find for the molecules Be(OX)42, B(OX)4, and C(OX)4 is common to all A(OX)4, A(NX2)4, and A(CX2Y)4 molecules, all of which have two bond angles smaller than, and four greater than, 109.5° or two angles larger than 109.5° and four smaller than 109.5°. In each case the overall symmetry of the molecule, which depends on the relative orientation of the ligands, is D2d or S4. Some examples... 

Now consider Structure 6.15. In this case, there is no such symmetry and so all the signals of the spectrum of this compound would be expected to be broadened or duplicated Always consider the symmetry of the molecule in anticipation of the extent of rotameric complexity. 

Notice that if the molecule has axial symmetry, Dxx = Dyy so that E=0. If the molecule has octahedral symmetry, Dxx = Dyy = Dzz so that D = E=0. Thus the appearance of a zero-field splitting into two or three levels tells the spectroscopist something about the symmetry of the molecule. It is possible, of course, to do spectroscopy on these energy levels at zero magnetic field. Our concern here is the effect of zero-field splitting on the ESR spectrum where a magnetic field is applied. 

The solid-state structure of 168, Figure 79, confirms the very high symmetry of the molecule. The zinc-ruthenium bonds are 2.66 A long on average, and thus considerably longer than the sum of the covalent radii of these metals. 

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