Anisotropy and Stereochemistry

As previously indicated (p. 43), the moment induced in a particle by a unit incident electric vector is—except with spherically symmetrical (isotropically polarizable) bodies—a function of the orientation of the particle relatively to the polarizing field E. In the general case, therefore, molecular polarizability must be regarded as a tensor of the second order. Adopting rectangular space-fixed co-ordinates, each component of the induced moment m is a linear vector function of the three components of E  

The nine coefficients characterize the transformation of the components of one vector (field) into those of the other (induced moment)—e.g. bxy transforming Ey into one of the three parts of mx. In matrix symbolism the preceding three equations are incorporated in the tensor equation 

As the co-ordinates are rectangular, ( / ) is, for an optically inactive molecule, a symmetrical tensor, i.e. byx = bxy, bzx = bxz, and bzy = byz, so that six independent elements only are required in its matrix. A geometrical interpretation of ( f ), by which it may be visualized, is as a tensor ellipsoid (cf. Gans, 1932, or Bottcher, 1952, for explanations) in the present relevance this is a polarizability ellipsoid. The symmetric 

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