Relativistic theory of the Jahn-Teller effect: p-orbitals in tetrahedral and trigonal systems

A relativistic generalization of Jahn-Teller theory is presented which includes spin-orbit coupling effects beyond low-order Taylor expansions in vibrational coordinates. For the example of a p-electron in tetrahedral and trigonal environments, the matrix elements of the Breit-Pauli spin-orbit- coupling operator are expressed in terms of the matrix elements of the electrostatic electronic potential. Employing expansions of the latter in invariant polynomials in symmetry-adapted nuclear coordinates, the spin-orbit induced Jahn-Teller coupling terms are derived for the T-2 x (t(2) + e) and (E + A) x (e + a) Jahn-Teller problems up to arbitrarily high orders. The linear G(3/2) x (t(2) + e) Jahn-Teller Hamiltonian of Moffitt and Thorson [Phys. Rev. 108, 1251 (1957)] for tetrahedral systems is generalized to higher orders in vibrational displacements. The Jahn-Teller Hamiltonians derived in the present work are useful for the interpolation and extrapolation of Jahn-Teller distorted potentialenergy surfaces of molecules and complexes with heavy elements as well as for the calculation of vibronic spectra of such systems. (C) 2016 AIP Publishing LLC.