Additive atomic multipole moments

Thus any molecular multipole moment may be decomposed into additive atomic multipole moments (AAMMs)... 

London-van der Waals forces, which are multipole interactions produced by correlation between fluctuating induced multipole moments in two nearly uncharged polar molecules. These forces also include dispersion forces that arise from the correlation between the movement of electrons in one molecule and those of neighboring molecules. The van der Waals dispersion interaction between two molecules is generally very weak, but when many groups of atoms in a polymeric structure act simultaneously, the van der Waals components are additive. 

To evaluate this expression for distributions expressed in terms of their multipolar density functions, the potential <1> and its derivatives must be expressed in terms of the multipole moments. The expression for charge distribution has been given in chapter 8 [Eq. (8.54)]. Since the potential and its derivatives are additive, a sum over the contributions of the atom-centered multipoles is again used. The resulting equation contains all pairwise interactions between the moments of the distributions A and B, and is listed in appendix J. 

We see that when the origins are located on atoms, we have an intermediary situation and it might be sufficient to have a few multipoles per atom. This is what the concept of what is called the cumulative multipole moments is all about (CAMM ). Besides the isotropic atomic charges qa = calculated in an arbitrary population analysis, we have, in addition, higher multipoles (atomic... 

FIM can also be used to study properties, such as the surface induced dipole moment and the effective polarizability of some surface atoms, kink site atoms and adsorbed atoms etc. The charge distribution of a surface atom is obviously completely different from that of a free atom because of its interaction with the surface and in addition surface atoms are partially shielded by itinerant charges of the surface. The charge distribution of a surface atom can be described by the magnitudes of the electric multipoles of the atom. 

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