Section 2.2.13.2. Interpretation for bonding

Chemical bonding is often described by considering orbitals (e.g. a or a atomic orbital) which are defined in polar coordinates, where the z axis is special, in contrast to Cartesian coordinates, where x, y and z are equivalent. Consider for example an atom coordinated by ligands (e.g. forming an octahedron). Then the application of group theory, ligand-field theory etc. requires a certain coordinate system provided one wishes to keep the standard notation of the corresponding spherical harmonics. If this octahedron is rotated or tilted with respect to the global (unit-cell) coordinate system, a local coordinate system is needed to allow an easy orbital interpretation of the inter­actions between the central atom and its ligands. This applies also to spectroscopy or electric field gradients.

The two types of reasons mentioned above may or may not lead to the same choice of a local coordinate system, as is illustrated for the example of rutile in Section 2.2.16.2.