Relativistic T×T and T×E Jahn-Teller coupling in tetrahedral systems

It is shown that orbitally triply degenerate spin-doublet states ( ²T₂) in tetrahedral systems exhibit, in addition to the well-known electrostatic Jahn-Teller effects, Jahn-Teller couplings which are of relativistic origin, that is, they arise from the spin-orbit operator. The linear relativistic Jahn-Teller Hamiltonian of a ²T₂ state involving vibrational modes of £ and T₂ symmetry is derived with group-theoretical methods. The ²T₂ × (E + T₂) Jahn-Teller Hamiltonian is transformed to a SO-adapted basis in which the zerothorder spin-orbit-coupling matrix is diagonal. For the 4 × 4 sub-matrices corresponding to the C_3/2 irreducible representation of the spin double group T′_d, the adiabatic potential-energy surfaces and the geometric phases of the adiabatic electronic wave functions are given in analytic form.