Relativistic ExT Jahn-Teller effect in tetrahedral systems

It is shown that (2)E states in tetrahedral systems exhibit a linear ExT Jahn-Teller effect which is of purely relativistic origin (that is, it arises from the spin-orbit-coupling operator). The electrostatic interactions give rise to a Jahn-Teller effect which is quadratic in the T displacements. The 4x4 Hamiltonian matrix in a diabatic spin-electron basis is derived by an expansion of the electrostatic electronic Hamiltonian and the Breit-Pauli spin-orbit operator in powers of the Jahn-Teller active normal mode and taking account of symmetry selection rules for the matrix elements. The adiabatic potential-energy functions of the (2)ExT system are doubly degenerate (Kramers degeneracy). For small displacements from the tetrahedral reference geometry, the adiabatic potential-energy surfaces represent a double cone in four-dimensional space, which is a novel topography of Jahn-Teller potential-energy surfaces. The topological phases of the adiabatic electronic wave functions are discussed.