title: Relativistic theory of the Jahn-Teller effect: p-orbitals in tetrahedral and trigonal systems.
abstract: 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 T2 × (t2 + e) and (E + A) × (e + a) Jahn-Teller problems up to arbitrarily high orders. The linear G3/2 × (t2 + 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 potential-energy surfaces of molecules and complexes with heavy elements as well as for the calculation of vibronic spectra of such systems.
authors.affiliation: Department of Chemistry, Technische Universität München, D-85747 Garching, Germany.
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Domcke
authors.affiliation: Max-Planck-Institut für Festkörperforschung, Stuttgart, Germany.
authors.forename: Daniel
authors.initials: D
authors.lastname: Opalka
authors.affiliation: Institute of Chemical Physics, Academy of Sciences, Chernogolovka, Moscow 142432, Russia.
authors.forename: Leonid V
authors.initials: LV
authors.lastname: Poluyanov