Spin–Orbit Vibronic Coupling in Jahn–Teller and Renner Systems

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

Four modifications of the Jahn-Teller effects. The problem of observables: spin-orbit interaction, tunneling splitting, and orientational polarization of solids

In a semi-review paper, we first show that Landau's fundamental idea of the origin of spontaneous symmetry breaking (SSB) in atomic matter due to electronic degeneracy, termed the Jahn-Teller effect (JTE) and further developed into the pseudo-JTE (PJTE), was appended recently with two more modifications, the hidden JTE (h-JTE) and hidden PJTE (h-PJTE). All four versions of JTEs are defined in the adiabatic approximation by their adiabatic potential energy surfaces (APES), which possess a common feature - the lack of a minimum in the high-symmetry configuration, thus confirming (and extending) the Landau idea of SSB. However, although serving as a qualitative indication of the SSB and consequent possible (virtual) properties of the system, the APES by themselves are not experimentally observable directly, and this important feature of JTEs is often ignored. Taking spin-orbit interaction as an example, we show that just perturbation of the APES does not reveal its observable reduction by the JTE, which emerges only after solving the Schrödinger equation with this APES. Following the multi-minimum nature of the latter, this leads to tunneling splitting of the vibrational states in the minima wells or over-the-barrier (hindered) rotations, resulting in novel properties, one of them being the reduction of the spin-orbit coupling. We demonstrate the methodology of solving such problems by using the example of electric field polarization of the BaTiO₃ crystal, which leads to a novel effect: orientational polarization of solids.

Vibronic Coupling in Spherically Encapsulated, Diatomic Molecules: Prediction of a Renner-Teller-like Effect for Endofullerenes

In the year 1933, Herzberg and Teller realized that the potential energy surface of a triatomic, linear molecule splits into two as soon as the molecule is bent. The phenomenon, later dubbed the Renner–Teller effect due to the detailed follow-up work of Renner on the subject, describes the coupling of a symmetry-reducing molecular vibration with degenerate electronic states. In this article, we show that a very similar type of nonadiabatic coupling can occur for certain translational degrees of freedom of diatomic, electronically degenerate molecules when trapped in a nearly spherical or cylindrical quantum confinement, e.g., realized through electromagnetic fields or molecular encapsulation. We illustrate this on the example of fullerene-encapsulated nitric oxide, and provide a prediction of its interesting, perturbed vibronic spectrum.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices

One-particle transition density matrices and natural transition orbitals enable quantitative description of electronic transitions and interstate properties involving correlated many-body wave functions within the molecular orbital framework. Here we extend the formalism to the analysis of tensor properties, such as spin-orbit couplings (SOCs), which involve states of different spin projection. By using spinless density matrices and Wigner-Eckart's theorem, the approach allows one to treat the transitions between states with arbitrary spin projections in a uniform way. In addition to a pictorial representation of the transition, the analysis also yields quantitative contributions of hole-particle pairs into the overall many-body matrix elements. In particular, it helps to rationalize the magnitude of computed SOCs in terms of El-Sayed's rules. The capabilities of the new tool are illustrated by the analysis of the equation-of-motion coupled-cluster calculations of two transition metal complexes.