Multipolar polarizabilities pair polarizability tensor

In a dense medium, collisional effects as well as time and space fluctuations of multipolar molecular fields will in general lead to changes in the molecular polarizability tensor. Then, according to Eq. (1), the pair polarizability tensor of two molecules A and B, Aap, acquires an incremental collision-induced... 

Some time ago we contributed to the development of the irreducible spherical tensor multipolar theory of light scattering [13,28], According to Ref. 13, the M component of the A th-rank dipole-arbitrary order multipole linear polarizability of a pair of interacting molecules A and B reads as... 

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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