Relativistic Jahn-Teller and pseudo-Jahn-Teller couplings in D _2d systems

The Hamiltonian for linear and quadratic Jahn-Teller (JT) and pseudo-JT (PJT) coupling as well as zeroth-order and linear spin-orbit (SO) coupling in the ²E+ ^2B2 electronic multiplet in D _2d systems is derived. The SO coupling is described by the microscopic Breit-Pauli operator. It is shown that the ²E state exhibits a ²E×e JT effect which is of relativistic origin, that is, it arises from the SO operator. The relativistic PJT coupling of the ²E and ^2B2 states involves the normal modes of ^b1, ^b2 and e symmetry. The ²E×( ^b1+ ^b2+e) JT Hamiltonian is analytically transformed to a SO-adapted electronic basis in which the zeroth-order SO operator is diagonal. In the special case of ²E- ²B degeneracy, the ( ²E+ ^2B2)×( ^b1+ ^b2+e) JT + PJT Hamiltonian also is transformed to a SO-adapted basis.