Additivity rule, dipole polarizabilities

The fundamental physico-chemical characteristics which enter into the evaluation of these component forces are the dipole moments, fi, the ionization potentials, /, and the polarizabilities, a, of the base pairs. The polarizabilities may be obtained relatively easily by the use of the usual additivity rules . The problems of the ionization potentials and of the dipole moments are however much more difficult. As concerns the ionization potentials they are completely unknown experimentally for the biological purines and pyrimidines (as they are, in fact, for the great majority of biomolecules). As concerns the dipole moments only those of some simple derivatives of purine, adenine and uracil are known no information exists about the moments of guanine or cytosine. 

The selection rules for the Raman spectrum turn out to depend not on the matrix elements of the electric dipole moment, but on the matrix elements of the molecular polarizability, which we now define. The application of an electric field E to a molecule gives rise to an induced electric dipole moment djnd (which is in addition to the permanent dipole moment d). If E= "> 1 + yl+ >zk, then the induced dipole moment has the components... 

Four thiourea molecules at sites are the building blocks of the unit cell of the crystal of the space group >2. The point group which is relevant for the selection rules is found by deleting the superscript, which yields >2a- Table 2.7-4 lists the details and results of the application of Eqs. I and II from Table 2.7-1. As shown in Fig. 2.7-8, the results are assigned to the components of the polarizability tensor and the dipole moment vector of the crystal, with x and y = a, b, c, which explains the Raman and infrared activity. We see that in addition to the translations of the whole crystal most... 

The complexity of Raman spectra for polymers is reduced as with infrared spectra because vibrations of the same type superimpose. In addition, as with infrared spectroscopy, selection rules aid in determining which molecular vibrations are active. However, the criterion for Raman aetivity is a change in bond polarizability with molecular vibration or rotation in contrast to the infrared criterion of a change in dipole moment (Figure 6.6). This means that, for molecules such as carbon dioxide that show both a change in dipole moment and a change in polarizability,... 

It is the purpose of this appendix to derive and present in convenient form tables of the characters for the molecular symmetry groups described in Chap. 5. (Certain additional information, such as the species (irreducible representations) of the molecular translational and rotational coordinates, and of the dipole moment and the polarizability, will also be indicated. Following the character tables proper, some information on the resolution of direct products will be given. The latter is useful in determining selection rules for overtone and combination transitions (see Chap. 7). Finally, the correlation tables mentioned in Chaps. 6 and 8 will be given. 

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