Spin-orbit vibronic coupling in Π4 states of linear triatomic molecules.

The Renner vibronic-coupling problem in Π electronic states of linear molecules is analyzed with rigorous and systematic inclusion of spin-orbit (SO) coupling. The 8 × 8 Hamiltonian matrix of a Π state in the diabatic electronic representation has been constructed by a Taylor expansion in the bending normal mode up to second order. As previously found for Π states and Π states, SO-induced vibronic-coupling terms that are linear in the bending amplitude exist in addition to the quadratic electrostatic Renner coupling.

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 T2 × (t2 + e) and (E + A) × (e + a) Jahn-Teller problems up to arbitrarily high orders.

The (E + A) × (e + a) Jahn-Teller and pseudo-Jahn-Teller Hamiltonian including spin-orbit coupling for trigonal systems.

The Hamiltonian describing E × e Jahn-Teller (JT) coupling and (E + A) × (e + a) pseudo-JT (PJT) coupling is developed beyond the standard JT theory for the example of XY3 systems, taking the bending modes of a and e symmetry into account. For the electrostatic (spin-free) Hamiltonian, the conventional Taylor expansion up to second order in symmetry-adapted displacements is replaced by an expansion in invariant polynomials up to arbitrarily high orders. The relevance of a systematic high-order expansion in the three large-amplitude bending modes is illustrated by the construction of an eighth-order three-sheeted three-dimensional ab initio potential-energy surface for PH3+.

Jahn-Teller, pseudo-Jahn-Teller, and spin-orbit coupling Hamiltonian of a d electron in an octahedral environment.

Starting from the model of a single d-electron in an octahedral crystal environment, the Hamiltonian for linear and quadratic Jahn-Teller (JT) coupling and zeroth order as well as linear spin-orbit (SO) coupling in the (2)T(2g) + (2)E(g) electronic multiplet is derived. The SO coupling is described by the microscopic Breit-Pauli operator. The 10 × 10 Hamiltonian matrices are explicitly given for all linear and quadratic electrostatic couplings and all linear SO-induced couplings.

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3.

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.

Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4.

The group-V tetrahedral cluster cations P(4)(+), As(4)(+), Sb(4)(+), and Bi(4)(+) are known to exhibit exceptionally strong Jahn-Teller (JT) effects of electrostatic origin in their (2)E ground states and (2)T(2) excited states. It has been predicted that there exist, in addition, JT couplings of relativistic origin (arising from the spin-orbit (SO) operator) in (2)E and (2)T(2) states of tetrahedral systems, which should become relevant for the heavier elements. In the present work, the JT and SO couplings in the group-V tetramer cations have been analyzed with ab initio relativistic electronic structure calculations.

Relativistic E x T 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 4 x 4 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.

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell.

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed.

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules.

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed.

Calculation of the vibronic structure of the photodetachment spectra of CCCl- and CCBr-.

The vibronic structure of the closely spaced and strongly coupled X 2Sigma+ and A 2Pi states in the photodetachment spectra of CCCl- and CCBr- has been calculated by considering Sigma-Pi vibronic coupling together with spin-orbit coupling. The stretching modes are treated within the so-called linear-vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations.

Calculation of the vibronic structure of the X2Pi photoelectron spectra of XCN, X=F, Cl, and Br.

The vibronic structure of the photoelectron spectra of the X (2)Pi state of XCN(+) (X=F, Cl, and Br) has been calculated, assuming that the X (2)Pi state can be considered as an isolated electronic state. The Renner-Teller coupling of the two components of the (2)Pi state via the degenerate bending mode as well as spin-orbit coupling effects are taken into account. The two stretching modes are treated within the so-called linear vibronic-coupling model.

Spectroscopic effects of first-order relativistic vibronic coupling in linear triatomic molecules.

It has recently been shown that there exists, in addition to the well-known nonrelativistic Renner-Teller coupling, a linear (that is, of the first order in the bending distortion) vibronic-coupling mechanism of relativistic (that is, spin-orbit) origin in 2II electronic states of linear molecules [L. V. Poluyanov and W.