Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.