Abstract
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 D2d 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.
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