Index-picking rules

The number of multipole parameters is reduced by the requirements of symmetry. As discussed in chapter 3, the only allowed multipolar functions are those having the symmetry of the site, which are invariant under the local symmetry operations. For example, only / = even multipoles can have nonzero populations on a centrosymmetric site, while for sites with axial symmetry the dipoles must be oriented along the symmetry axis. For a highly symmetric site having 6 mm symmetry, the lowest allowed / 0 is d66+ all lower multipoles being forbidden by the symmetry. The index-picking rules listed in appendix D give the information required for selection of the allowed parameters. 

The matrix M 1 is given in appendix I. In all but triclinic point groups, site-symmetry restrictions limit the allowed functions beyond the / even requirement. The symmetry-allowed multipolar density functions are given by the index-picking rules of appendix D, section D.3, and are listed in Table 10.1. 

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