Atomic multipole moments, higher-order

For a set of atomic parameters q, m, Vq, Vwi that satisfy the set of constraints described above, namely equations (8) and (11), and the exact reproduction of the molecular quadrupole moment by the atomic charges and dipoles, equations (12) and (13) are accurate to the same order as equations (6) and (7). It is just that for force field calculations and molecular modeling the former equations are more useful. (In fact, the use of atomic moments often yields more accurate energies than the truncated series in equation (6) because the atomic charges and dipoles automatically generate all higher-order molecular multipoles, and sometimes with good accuracy. In such cases the molecular potential may be more accurate with the use of atomic parameters than with the use of just two molecular multipoles.)... 

Higher-order atomic multipoles can similarly be defined in terms of particular elements of the molecular octupolar and hexadecapolar tensors. A detailed discussion of the properties of these quantities is given in Refs. 7 and 8. Here we merely note that (a) the atomic dipole moments thus defined are... 

In sections 2.7, 2.10, and 2.11 we have expanded the radiation fields of an arbitrary charge distribution by the use of simple and direct methods. This technique is adequate for a discussion of excited atoms since only the electric dipole, and occasionally the magnetic dipole and electric quadrupole terms are significant. However, in nuclear physics higher-order terms are frequently required and it is clear that a more general and powerful technique should be used. In this method the charge distribution is expanded in terms of its multipole moments and the radiation fields are constructed from spherical waves which have well-... 

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