Multipolar Electric Polarizabilities

Linear Multipolar Electric Polarizabilities. Just as equation (40) served for defining the 2 -pole permanent electric moment, one can generalize the definition of the induced dipole (68) by introducing that of an induced 2 -pole moment. Assuming the inducing factor to be a uniform extamal electric field E, one has ... 

In many a case, when calculating for multipolar molecules, one is justified in neglecting the anisotropy of linear electric polarizability, leading in general (Kielich" ) to the formula ... 

As mentioned above, for the H2-He pair two principal induction mechanisms exist multipole and overlap induction. Multipolar induction occurs mainly in the electric quadrupole field of H2 which polarizes the colli-sional partner (He). Qualitatively, the nature of the partner X is of little significance as long as it is polarizable. Quantitatively, one expects highly polarizable species (like Xe) to give rise to much stronger rotational lines than more weakly polarizable atoms (like He). Mainly for that reason, the rotational lines of H2-He are much weaker than those of H2-H2. (Another reason is that for H2-H2, molecule 1 induces a dipole in 2 and 2 induces one in 1, thereby doubling the intensities.)... 

One other aspect of nonprimitive electric double layer theories which is particularly relevant to the inner Stern region are the models for the water molecule and the ions. The simplest models for a water molecule and an ion are a hard-sphere point dipole and point charge, respectively. A more realistic model of the hard-sphere water molecule would include quadrupoles and octupoles and also polarizability. However the hard-sphere property is best avoided and replaced, for example, by a Lennard-Jones potential. An alternative to a multipolar water model are three point charge sites associated with the atoms within the water molecule. 

This technique has been applied in the analysis of the electronic structure of stoichiometric and non-stoichiometric (111) surfaces of BaFj and CaF2 crystals [85-88] or in the case of AI2O3 crystals by Guo, Ellis and Lam [89-91]. Vg t could also represent an applied static electric field as used for evaluation of static polarizabilities as discussed below. In the latter case, we could evaluate the multipolar moments separately, thus obtaining the static polarizability, induced by a field of the form [92]... 

In this chapter we shall always consider molecules having zero charge and a finite dipole moment. Moreover, we suppose that the distances between the molecules are not too small with respect to their sizes, and that the higher electric moments are very small. In this case, the main term in the multipolar expansion is the one which represents the dipole-dipole interaction. We shall neglect the other terms. This means that in this approxknation the dipole moment ft and the polarizability a entirely determine the electrostatic bdiavior of the molecule. 

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