Bond polarisabilities and group dipole moments

In section 9.2.2 above it is shown that the refractive index of a medium is related to the high-frequency deformational polarisability of its mole- 

The high-frequency polarisation of a molecule consists almost entirely of the slight rearrangement of the electron clouds forming the bonds between the atoms. It is the polarisabilities of individual bonds that are assumed to be additive, to a good approximation. If the molecules are randomly oriented, then so are all the bonds of a particular type. The sum of the polarisabilities of all the bonds of this type must therefore be isotropic, so the polarisability for an individual bond can be replaced by a scalar average value called the mean value or spherical part of the tensor. These scalar values can be added together arithmetically for the various bonds within the molecule to obtain the spherical part of the polarisability for the molecule. This is what has so far been called a.  

It is possible to find values of the mean polarisabilities a, for a set of different types of bond i by determining the refractive indices for a large number of compounds containing only these types of bond. The value of 

A similar argument to the above can be used to deduce the molecular dipole for a molecule if the dipoles of its constituent parts are known. It has been found that the additivity scheme works best for dipoles if group dipoles are used, i.e. each type of molecular group in a molecule, such as a 

COOH group, tends to have approximately the same dipole moment independently of the molecule of which it is a constituent part. Equation (9.16), which applies to dilute solutions of polar molecules in a non-polar solvent, can be used to find fi for a range of different molecules. This is done by plotting against /T the values calculated for the left-hand side of the equation from values of e measured at various temperatures T. The gradient of the straight line plot is Njs,iJ /(9sgk), from which /x is easily 

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