Jahn-Teller Problem Research Articles

Low-lying resonances in the linear relativistic Jahn-Teller problem [formula omitted] in octahedral molecules with a heavy central atom

The symmetry properties of vibronic Hamiltonian of the linear G3/2,g×(t2g+eg) relativistic John-Teller system are investigated and the separation of angular and radial variables is achieved. Transformation to radial adiabatic representation allows us to obtain four biradial adiabatic potential energy surfaces. Two upper surfaces include potential wells and contain quasi discrete resonances. In this work we found the positions of low-lying resonances.

Classical approach based on full-size adiabatic potential energy surfaces to the thermal expansion of the Jahn-Teller molecules. Example of niobium tetrahalides NbX4 (X = Br, I)

The methods of CASSCF, the perturbation theory and taking into account relativistic effects were applied to study the structure of NbX4 (X = Br, I) molecules in the ground and excited electronic states. Due to Jahn-Teller distortion of the Td structure, the compressed D2d structure corresponds to minimum on the lower sheet of PES. For 2E ⊗ e Jahn-Teller problem the vibronic Schrödinger equation has been solved in the diabatic basis. The original method was used for the simulation of available gas-phase electron diffraction data. A good agreement between experimental and theoretical results supports the reliability of the theoretical data.

Vibrational and vibronic structure of isolated point defects: The nitrogen-vacancy center in diamond

We present a theoretical study of vibrational and vibronic properties of a point defect in the dilute limit by means of first-principles density functional theory calculations. As an exemplar we choose the negatively charged nitrogen-vacancy center, a solid-state system that has served as a testbed for many protocols of quantum technology. We achieve low effective concentrations of defects by constructing dynamical matrices of large supercells containing tens of thousands of atoms. The main goal of the paper is to calculate luminescence and absorption lineshapes due to coupling to vibrational degrees of freedom. The coupling to symmetric $a_1$ modes is computed via the Huang-Rhys theory. Importantly, to include a nontrivial contribution of $e$ modes we develop an effective methodology to solve the multi-mode $E \otimes e$ Jahn-Teller problem. Our results show that for NV centers in diamond a proper treatment of $e$ modes is particularly important for absorption. We obtain good agreement with experiment for both luminescence and absorption. Finally, the remaining shortcomings of the theoretical approach are critically reviewed. The presented theoretical approach will benefit identification and future studies of point defects in solids.

Regularized Born-Oppenheimer molecular dynamics

While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.

Jahn-Teller Effect and Spin-Orbit Coupling: Friends or Foes?

The Jahn-Teller effect is one of the most fundamental phenomena important not only for physics, but also for chemistry and material science. Solving the Jahn-Teller problem and taking into account strong electron correlations we show that quantum entanglement of the spin and orbital degrees of freedom via spin--orbit coupling strongly affects this effect. Depending on the number of $d$ electrons it may quench (electronic configurations $t_{2g}^2$, $t_{2g}^4$, and $t_{2g}^5$), partially suppress ($t_{2g}^1$) or in contrast induce ($t_{2g}^3$) Jahn-Teller distortions. Moreover, in certain situations, interplay between the Jahn-Teller effect and spin--orbit coupling promotes formation of the "Mexican hat" energy surface facilitating various quantum phenomena.

Jahn-Teller effect enhanced by spin-orbit coupling. From theory to Experiment:Example of niobium tetrachloride NbCl4

The ground and lower-lying excited electronic states of NbCl4 molecule were systematically studied by the complete active space self-consistent field (CASSCF) and multiconfigurational quasi-degenerate second-order perturbation (MCQDPT2) methods. Scalar-relativistic effects and spin-orbit coupling (SOC) have been taken into account employing the third-order Douglas-Kroll-Hess (DKH) Hamiltonian and full Breit-Pauli operator, respectively. The high-symmetrical Td structure with spin-orbit ground 2G3/2 state undergoes Jahn-Teller distortion along all non-totally symmetric vibrational coordinates. As a result the compressed (2E1/2 state) and elongated (2E3/2 state) D2d structures correspond to minimum and first order saddle point on the lower sheet of adiabatic potential energy surface (APES). The height of the warping barrier in the trough of APES and the Jahn-Teller stabilization energy are 179 and 438 cm−1, respectively. For two-mode 2E⊗e Jahn-Teller problem the vibronic Schrödinger equation has been solved in the diabatic basis. It was shown, the topology of the lower sheet determined mainly the energies and wave functions ground and few low-lying vibronic levels. The original methodology of the simulation of gas-phase electron diffraction (GED) data was developed. This methodology is based on the analytic description of some APES numerically obtained. The computed radial distribution function and thermal average parameters were compared with the experimental GED data. A good agreement between experimental and theoretical results supports the reliability of the theoretical data.

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn-Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn-Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D6h ) hexasilabenzene (Si6 H6 ) to the buckled (D3d ) structure involves identifying the second-order donor-acceptor, hyperconjugative interactions (E2 i → j ) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S0 /Sn states and those for the donor (filled)-acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E2 i → j interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.

Interplay Between Relaxation and Resonance in Ultrasound Attenuation by the Cubic Crystal ZnSe:Cr

Resonance ultrasound attenuation, albeit broadened, is observed in doped cubic crystal ZnSe with a part of the Zn2+ ions substituted by magnetic anisotropic Cr2+ ions. In the tetrahedral selenium environment the latter form a T term Jahn–Teller (JT) center with a T⊗e JT problem and three equivalent distortions along the three tetragonal axes. In sufficiently strong magnetic fields (B > 4 T) applied along the [001] direction the degeneracy of the ground state is removed, and the ultrasound wave propagating along [110] and polarized along (at T = 1.3 K) does not interact with the center, its impurity attenuation being reduced to zero. By comparison, this allows to estimate the contribution of the Cr centers to the attenuation of ultrasound in the ZnSe:Cr crystal in zero magnetic field. The experimental data revealed a strong dependence of the attenuation on the ultrasound frequency, evidencing for the resonance nature of the attenuation: there is no frequency dependence in relaxational attenuation with the relaxation time much larger than the period of the ultrasonic wave. The resonance attenuation is attributed to transitions between the ground state energy levels, split by spin‐orbital interaction. The high sensitivity of the resonance absorption on the ultrasound power is also discussed.

Berry phase of adiabatic electronic configurations in fullerene anions

The selection rule on vibronic angular momentum of $t_{1u}^n \otimes h_g$ Jahn-Teller problem ($n = $ 1-5) is reinvestigated. It is shown that among three adiabatic orbitals only two have nonzero Berry phase. Thus, the Berry phase of adiabatic electronic configurations depends on the spin multiplicity as well as the number of electrons. On this basis, the general relation between the Berry phase and the angular momentum is described. It allows, in particular, to clarify the nature of vibronic states arising from high spin configurations. In comparison with the previous solution for the low-lying vibronic states for bimodal systems, the present solutions correctly fulfill all the symmetry requirement.

Vibronic Ground-State Degeneracies and the Berry Phase: A Continuous Symmetry Perspective.

We develop a geometric construction to prove the inevitability of the electronic ground-state (adiabatic) Berry phase for a class of Jahn-Teller (JT) models with maximal continuous symmetries and N > 2 intersecting electronic states. Given that vibronic ground-state degeneracy in JT models may be seen as a consequence of the electronic Berry phase and that any JT problem may be obtained from the subset that we investigate in this Letter by symmetry-breaking, our arguments reveal the fundamental origin of the vibronic ground-state degeneracy of JT models.

Jahn-Teller effect and large-amplitude motion in [formula omitted] studied by high-resolution photoelectron spectroscopy of CH4

This article presents the current status of the knowledge of the rovibronic energy-level structure of CH4+ obtained by high-resolution photoelectron spectroscopy. The results of previous investigations are summarized and extended by new results obtained by double-resonance experiments involving vacuum-ultraviolet and mid-infrared laser radiation. These experiments have led to assignments of the nuclear-spin symmetry of 303 rovibrational levels of CH4+ with up to 3575cm−1 of internal excitation. A two-dimensional model of the pseudorotational motion of CH4+ is also presented, with which the positions and vibronic symmetry of the low-lying vibronic levels of CH4+ can be predicted. The model maps the F⊗(f⊕e) Jahn-Teller problem for the e and f2 modes corresponding to the CH bending motion onto a sphere, including the effects of both linear and quadratic Jahn-Teller coupling terms. The pseudorotation eigenstates are obtained by solving the two-dimensional Schrödinger equation using a basis of spherical harmonics.

Manifestation of the Jahn-Teller effect in elastic moduli of strontium fluorite crystals doped with chromium ions

Attenuation and phase velocity of ultrasound have been measured in strontium fluoride single crystal doped with chromium in the temperature range of 4 – 185 K at 56 -162 MHz. Anomalies have been found for all the normal modes corresponding to the non-vanishing elastic moduli of a cubic crystal. Interpretation of the observed anomalies has been done in the framework of relaxation in the system of Jahn-Teller (JT) complexes CrF8 subject to full T2g ⊗(eg + t2g) JT problem. Relaxation time has been calculated from the experimental data on ultrasonic attenuation and adiabatic and isothermal contributions of the impurity subsystem to the total elastic moduli have been obtained.

Andrew Liehr and the structure of Jahn-Teller surfaces

The present article is an attempt to draw attention to a seminal work by Andrew Liehr “Topological aspects of conformational stability problem” [1, 2] issued more than half century ago. The importance of this work stems from two aspects of static Jahn-Teller and pseudo-Jahn-Teller problems fully developed by the author. First, the work of Liehr offers an almost complete overview of adiabatic potential energy surfaces for most known Jahn-Teller problems including linear, quadratic and higher-order vibronic couplings. Second, and most importantly, it identifies the factors defining the structure of Jahn-Teller surfaces. Among them, one should specially mention the minimax principle stating that the distorted Jahn-Teller systems tend to preserve the highest symmetry consistent with the loss of their orbital degeneracy. We believe that the present short reminiscence not only will introduce a key Jahn-Teller scientist to the young members of the community but also will serve as a vivid example of how a complete understanding of a complex problem, which the Jahn-Teller effect certainly was in the beginning of 1960s, can be achieved.

Jahn-Teller effect in molecular electronics: quantum cellular automata

The article summarizes the main results of application of the theory of the Jahn-Teller (JT) and pseudo JT effects to the description of molecular quantum dot cellular automata (QCA), a new paradigm of quantum computing. The following issues are discussed: 1) QCA as a new paradigm of quantum computing, principles and advantages; 2) molecular implementation of QCA; 3) role of the JT effect in charge trapping, encoding of binary information in the quantum cell and non-linear cell-cell response; 4) spin-switching in molecular QCA based on mixed-valence cell; 5) intervalence optical absorption in tetrameric molecular mixed-valence cell through the symmetry assisted approach to the multimode/multilevel JT and pseudo JT problems.

Analogies between Jahn–Teller and Rashba spin physics

AbstractIn developing physical theories, analogical reasoning has been found to be very powerful, as attested by a number of important historical examples. An analogy between two apparently different phenomena, once established, allows one to transfer information and bring new concepts from one phenomenon to the other. Here, we discuss an important analogy between two widely different physical problems, namely, the Jahn–Teller distortion in molecular physics and the Rashba spin splitting in condensed matter physics. By exploring their conceptual and mathematical features and by searching for the counterparts between them, we examine the orbital texture in Jahn–Teller systems, as the counterpart of the spin texture of the Rashba physics, and put forward a possible way of experimentally detecting the orbital texture. Finally, we discuss the analogy by comparing the coexistence of linear Rashba + Dresselhaus effects and Jahn–Teller problems for specific symmetries, which allow for nontrivial spin and orbital textures, respectively.

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.

Density functional theory study of the multimode Jahn–Teller problem in the open-shell corannulenes and coronenes

Analysis of the multimode Jahn–Teller (JT) distortion in anions and cations of corannulene and coronene is presented, combining multideterminantal-DFT (MD-DFT) and Intrinsic Distortion Path (IDP) methods. The JT distortion is derived from the sum of contributions of all possible JT active normal modes. The CC stretching modes play the most important role in the stabilization of the systems, in all investigated species, pushing the nuclei toward the minima on the potential energy surface. The further inspection of the IDP revealed that the relaxation of the geometry arrives in the final part of the path and is encountered by the softest vibrational modes. The same trend was observed in cyclopentadienyl radical, benzene anion, benzene cation and fullerene ions. This gives microscopic origin into the mechanism of the distortion and provides general behavior of the JT effect in these similar molecules. Moreover, MD-DFT and IDP, as fast and fully non-empirical approaches, can be considered as a reliable tool for better understanding of the JT effect.

Time-dependent Jahn-Teller problem: phonon-induced relaxation through conical intersection.

A theoretical study of time-dependent dynamical Jahn-Teller effect in an impurity center in a solid is presented. We are considering the relaxation of excited states in the E⊗e-problem through the conical intersection of the potential energy. A strict quantum-mechanical treatment of vibronic interactions with both the main Jahn-Teller active vibration and the nontotally symmetric phonons causing the energy loss is given. The applied method enables us to calculate the time-dependence of the distribution function of the basic configurational coordinate. We have performed a series of numerical calculations allowing us, among other relaxation features, to visualise the details of the relaxation through the conical intersection. In particular, we elucidate how the Slonczewski quantization of the states in the conical intersection affects the relaxation.

Symmetry assisted consideration of the dynamic pseudo Jahn-Teller problem in mixed-valence species with square topology: Intervalence optical bands

Here we report the evaluation of the electronic and vibronic levels of mixed-valence tetra-ruthenium (2Ru(II) + 2Ru(III)) systems (assembled as two coupled Creutz-Taube complexes) for which possible molecular implementations of quantum-dot cellular automata was proposed. These complexes are representatives of Robin and Day classes I, II, and III and therefore the vibronic coupling is crucially important for the adequate description of the magnetic characteristics and profiles of the intervalence optical bands. We apply recently suggested symmetry-adapted approach to the accurate solution of the dynamic pseudo Jahn-Teller problems (1B1g, 21A1g, 1B2g, 1Eu) ⊗ (b1g + eu) and (3A2g, 3B1g, 23Eu) ⊗ (b1g + eu) in bi-electronic mixed-valence species with square topology. The algorithm for the solution of the eigen-problem takes full advantage of the point symmetry arguments and therefore the full matrix of the Jahn-Teller JT Hamiltonian is blocked according to the irreps of the point group. The vibronic basis is used for the evaluation of the shape-functions of the intervalence optical absorption in mixed-valence tetra-ruthenium (2Ru(II) + 2Ru(III)) complexes.

Symmetry Assisted Consideration of the Dynamic Pseudo Jahn-Teller Problem in Mixed-Valence Species with Square Topology: Intervalence Optical Bands

Symmetry Assisted Consideration of the Dynamic Pseudo Jahn-Teller Problem in Mixed-Valence Species with Square Topology: Intervalence Optical Bands