Relativistic Jahn-Teller and pseudo-Jahn-Teller couplings in D2d 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 E-2 + B-2(2) electronic multiplet in D-2d systems is derived. The SO coupling is described by the microscopic Breit-Pauli operator. It is shown that the E-2 state exhibits a E-2 x e JT effect which is of relativistic origin, that is, it arises from the SO operator. The relativistic PJT coupling of the E-2 and B-2(2) states involves the normal modes of b(1), b(2) and e symmetry. The E-2 x (b(1) + b(2) + 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 E-2 - B-2 degeneracy, the (E-2 + B-2(2)) x (b(1) + b(2) + e) JT + PJT Hamiltonian also is transformed to a SO-adapted basis. (C) 2012 Elsevier B. V. All rights reserved.