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The relation between the properties of a specific crystallographic site andthe properties of the full crystal is discussed by using spherical tensors. Theconcept of spherical tensors is introduced and the way it transforms under thesymmetry operations of the site and from site to site is described in detail.The law of spherical tensor coupling is given and illustrated with the exampleof the electric dipole and quadrupole transitions in x-ray absorptionspectroscopy. The main application of the formalism is the reduction ofcomputation time in the calculation of the properties of crystals by bandstructure methods. The general approach is illustrated by the examples ofsubstitutional chromium in spinel and substitutional vanadium in garnet.

Site symmetry and crystal symmetry: a spherical tensor analysis