A combined Jahn-Teller and pseudo-Jahn-Teller effect: an exactly solvable model

The problem of an (ns) 2 ion in an isolated regular octahedron of ligands with an A lg ground state and a T lu excited state is solved exactly for the case of the linear vibronic coupling approximation and a harmonic potential energy. The excited state is susceptible to a T(X)( tau 2g + epsilon g ) Jahn-Teller effect (JTE). Three regimes can be found: (i) The difference in energy between the ground and excited states exceeds a certain threshold, so that the interaction does not result in instability. The A lg level is the ground state. (ii) The excited state has a very strong JTE, so that its energy is lowered far below the A lg state. (iii) There is strong interaction between the two levels, a pseudo-Jahn-Teller effect (PJTE) mixes the excited state into the ground state and a dipole moment arises. Through the mixing-in of the excited state, the tau 2g or epsilon g deformations are also present in the ground state. Only trigonally or tetragonally deformed octahedra with an additional dipolar distortion in the case of a PJTE are expected. A condition for strong PJTE is derived, which is shown to be reached more easily for two electrons than for one electron in the ground state.