Leonid V. Poluyanov

Relativistic E×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. The adiabatic potential-energy functions of the (2)E x T 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.

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. 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.

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. It is shown that the (2)T(2g) manifold exhibits, in addition to the well-known electrostatic JT effects, linear JT couplings which are of relativistic origin, that is, they arise from the SO operator. While only the e(g) mode is JT-active in the (2)E(g) state in the nonrelativistic approximation, the t(2g) mode becomes JT-active through the SO operator. Both electrostatic as well as relativistic forces contribute to the (2)T(2g) - (2)E(g) pseudo-JT coupling via the t(2g) mode. The relevance of these analytic results for the static and dynamic JT effects in octahedral complexes containing heavy elements is discussed.

Spin-orbit vibronic coupling in Π3 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. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.

Calculation of the vibronic structure of the X̃Π2 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. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While spin-orbit effects are small in FCN(+), the large spin-orbit splitting of the X (2)Pi state of the BrCN(+) leads to a complete quenching of the Renner-Teller effect. The X (2)Pi state of the ClCN(+) is shown to be of particular interest: here the resonance condition for linear-relativistic Renner-Teller coupling is approximately fulfilled. This coupling mechanism leads to a significant intensity transfer to vibronic levels with odd quanta of the bending mode. The calculated spectrum indicates that this novel relativistic vibronic-coupling effect should be observable in high-resolution (electron energy resolution of the order of a few meV) photoelectron spectra of ClCN.

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. The vibronic line spectra and the band shapes of the photoelectron spectra were simulated with time-dependent quantum wave-packet methods. The results provide insight into the interplay of electrostatic and relativistic JT couplings and SO splittings in the complex photoelectron spectra of these systems.

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+. The theory of spin-orbit coupling in trigonal JT/PJT systems is extended beyond the standard model of JT theory by an expansion of the microscopic Breit-Pauli operator up to second order in symmetry-adapted vibrational coordinates. It is shown that a linear E × e JT effect of relativistic origin exists in C(3v) systems which vanishes at the planar (D(3h)) geometry. The linear relativistic 2E – 2A PJT coupling, on the other hand, persists at the planar geometry

A semiclassical approach to the non-adiabatic dynamics problem involving three electronic states in linear triatomic systems

The local non-adiabatic dynamics near an accidental degeneracy of Σ+ = Π type in a linear triatomic system has been investigated in the context of the semiclassical approximation. An exact analytical solution of the time-dependent semiclassical equations has been found for rectilinear trajectories of the bending (π) vibrational modes. The S-matrix and transition probabilities associated with this three-state problem, which have a non-Landau-Zener character, have been defined in analytical terms. The expressions obtained for the transition probabilities may be useful in the context of the trajectory surface hopping method.

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 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.

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled π 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. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.