Pair polarizability tensor, interaction-induced polarizabilities

In general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

Besides the isotropic overlap-induced dipole component familiar from the rare gas pairs, we will now in general have other significant induced dipole components if molecules are present, namely multipole-induced and distorted frame-induced dipole components, see Chapter 4 for details. Moreover, these anisotropic dipole components couple with the polarizability tensor and thus give rise to simultaneous transitions in two (or perhaps more) molecules. Furthermore, molecules in general interact with more or less anisotropic forces which to some extent does also affect the spectra of molecular systems. 

Equation (1) specifically refers to EFP-EFP interactions. EFP-QM interactions are discussed later. Ecoui refers fo the Coulomb portion of fhe electrostatic interaction. This term is obtained using the distributed multipolar expansion introduced by Stone, with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion poinfs (fhree at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. Ejn is the induction or polarization part of fhe electrostatic interaction. This term is represented by the interaction of fhe induced dipole on one fragment with the permanent dipole on another fragment, expressed in terms of the dipole polarizability. Although this is just the first term of fhe polarizability expansion, it is robust, because the molecular polarizability is expressed as a tensor sum of localized molecular orbital (LMO) polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in fhe molecule. This dipole-induced dipole term is iterated to self-consistency, so some many body effects are included. 

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