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

It is shown that orbitally triply degenerate spin-doublet states (T-2(2)) 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 T-2(2) state involving vibrational modes of E and T-2 symmetry is derived with group-theoretical methods. The T-2(2) x (E + T-2) Jahn-Teller Hamiltonian is transformed to a SO-adapted basis in which the zeroth-order spin-orbit-coupling matrix is diagonal. For the 4 x 4 sub-matrices corresponding to the G(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. (C) 2010 Published by Elsevier B.V.