Strong Jahn-Teller coupling of ionic Eg orbitals to a cluster in the harmonic approximation

A study is made of two useful perturbation schemes describing theE _g orbitals of a paramagnetic ion coupled very strongly to a cluster surrounding a cubically symmetric lattice site in the harmonic approximation. The two methods correspond to the cases when the vibrational states have low and large angular momentum. The limitations of both approaches are discussed and the zero order eigenvalues and eigenfunctions are given in each case.