Quadrupole point charge arrangement

Consider a perfectly tetrahedral distribution of four point charges —q, —q, +q, and +q, drawn schematically in the following figure. Does this arrangement result in a pure quadrupole field If not, what other multipoles contribute to the electric field ... 

The electric quadrupole transition arises from a displacement of charge that has a quadrupolar nature. An electric quadrupole consists of four point charges with overall zero charge and zero dipole moment. It may be pictured as two dipoles arranged so that their dipole moments cancel. An electric quadrupole has even parity. Electric quadrupole transitions are much weaker than magnetic dipole and induced electric dipole transitions. At this moment no experimental evidence exists for the occurrence of quadrupole transitions in lanthanide spectra, although some authors have claimed the existence of such transitions (e.g. Chrysochoos and Evers 1973). However, the so-called hypersensitive transitions (see sect. 8) are eonsidered as pseudo-quadrupole transitions, because these transitions obey the selection rules of quadrupole transitions. 

Therefore, it has at most five independent components, and fewer if the molecule has some symmetry. Symmetric top molecules have only one independent component of , and, in such cases, the axial component is often referred to as the quadrupole moment. A quadrupolar distribution can be created from four charges of the same magnitude, two positive and two negative, by arranging them in the form of two dipole moments parallel to each other but pointing in opposite directions. Centro-symmetric molecules, like CO2, have a zero dipole moment but a non-zero quadrupole moment. 

A FIGURE 10.6 Arrangements of point electric charges that result in pure electric multipole fields. These correspond to the spherical harmonics ij, (monopole), Yi (dipole), (quadrupole), and (octopole). 

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