Jahn-Teller Systems Research Articles

Dynamic Jahn-Teller effect in the strong spin-orbit coupling regime

Exotic quantum phases, arising from a complex interplay of charge, spin, lattice and orbital degrees of freedom, are of immense interest to a wide research community. A well-known example of such an entangled behavior is the Jahn-Teller effect, where the lifting of orbital degeneracy proceeds through lattice distortions. Here we demonstrate that a highly-symmetrical 5d1 double perovskite Ba2MgReO6, comprising a 3D array of isolated ReO6 octahedra, represents a rare example of a dynamic Jahn-Teller system in the strong spin-orbit coupling regime. Thermodynamic and resonant inelastic x-ray scattering experiments, supported by quantum chemistry calculations, undoubtedly show that the Jahn-Teller instability leads to a ground-state doublet, resolving a long-standing puzzle in this family of compounds. The dynamic state of ReO6 octahedra persists down to the lowest temperatures, where a multipolar order sets in, allowing for investigations of the interplay between a dynamic JT effect and strongly correlated electron behavior.

A Fundamental Correlative Spectroscopic Study on Li1‐xNiO2 and NaNiO2

AbstractThe intricate relationship between local atomic arrangements and electronic states significantly influences the electrochemical properties of Li‐ion battery cathode materials. Despite decades of investigation, a consensus regarding the local atomic and electronic structure of LiNiO2 remains elusive. This ambiguity stems from the potential distortion of Ni sites, either via Jahn‐Teller (JT) distortion or bond disproportionation (BD), complicating the understanding of the charge compensation mechanism involving Ni and O. This study compares the structures of LiNiO2 and NaNiO2, a JT system, using an innovative approach that integrates bulk spectroscopy techniques on standardized interoperable samples for enhanced reliability. While X‐r and theoretical calculations fail to differentiate between the proposed scenarios, Raman spectroscopy highlights local structural distinctions between monoclinic NaNiO2 and rhombohedral LiNiO2. HAXPES confirms various formal oxidation states for Ni, supported by RIXS data indicating 3d8 states, emphasizing negative charge transfer from Ni and some bond disproportionation in LiNiO2. Regarding charge compensation, XRS and RIXS suggest oxygen hole involvement in redox activity, whereas Raman spectroscopy does not detect molecular oxygen. This comprehensive spectroscopic analysis highlights the importance of correlative characterization workflows in elucidating complex structural‐electrochemical relationships.

Evolution of field induced magnetic phase attributed to higher order magnetic moments in TbVO4

Study of quantum magnetism in rare earth orthovanadates (RVO4, R = rare earth) is a topic which is currently being investigated by the condensed matter physicists. In this work, through both experimental and theoretical tools, we report the presence of field induced magnetic phase, attributed to fifth order susceptibility, in TbVO4, at low temperatures. The structural transition reported around 31 K, results in the formation of pseudospin—{raise0.7exhbox{1} !mathord{left/ {vphantom {1 2}}right.kern-0pt} !lower0.7exhbox{2}} doublet ground state separated by an energy δ. Temperature dependent heat capacity indicates toward an increment in δ, on application of magnetic fields. Above 10 kOe, the Zeeman energy associated with magnetic anisotropy strengthens, resulting in an enhanced splitting of the pseudo-doublet ground state. This increased splitting stabilizes the magnetic phase associated with higher order moments. These observations are further supported by our theoretical model to evaluate δ, as a function of applied field. Our study provides a platform to study the possible presence of higher order moments in other Jahn–Teller systems.

Red Shift in Optical Excitations on Layered Copper Perovskites under Pressure: Role of the Orthorhombic Instability.

The red shift under pressure in optical transitions of layered compounds with CuCl6 4- units is explored through first-principles calculations and the analysis of available experimental data. The results on Cu2+ -doped (C2 H5 NH3 )2 CdCl4 , that is taken as a guide, show the existence of a highly anisotropic response to pressure related to a structural instability, driven by a negative force constant, that leads to an orthorhombic geometry of CuCl6 4- units but with a hole displaying a dominant 3z2 -r2 character (z being the direction perpendicular to the layer plane). As a result of such an instability, a pressure of only 3 GPa reduces by 0.21 Å the longest Cu2+ -Cl- distance, lying in the layer plane, while leaving unmodified the two other metal-ligand distances. Owing to this fact, it is shown that the lowest d-d transition would experience a red shift of 0.34 eV while the first allowed charge transfer transition is also found to be red shifted but only by 0.11 eV that reasonably concurs with the experimental value. The parallel study on Jahn-Teller systems CdCl2 :Cu2+ and NaCl:Cu2+ involving tetragonal elongated CuCl6 4- units shows that the reduction of the long axis by a pressure of 3 GPa is three times smaller than that for the layered (C2 H5 NH3 )2 CdCl4 :Cu2+ compound. Accordingly, the optical transitions of such systems, which involve a positive force constant, are much less sensitive to pressure than in layered compounds. The origin of the red shift under pressure undergone by the lowest d-d and charge transfer transitions of (C2 H5 NH3 )2 CdCl4 :Cu2+ is discussed in detail.

Two Jahn–Teller systems involved in different kinds of crystal-to-crystal transformations

Two Jahn–Teller systems involved in different kinds of crystal-to-crystal transformations

Enhanced Parameter Estimation with Periodically Driven Quantum Probe.

I propose a quantum metrology protocol for measuring frequencies and weak forces based on a periodic modulating quantum Jahn–Teller system composed of a single spin and two bosonic modes. I show that, in the first order of the frequency drive, the time-independent effective Hamiltonian describes spin-dependent interaction between the two bosonic modes. In the limit of high-frequency drive and low bosonic frequency, the quantum Jahn–Teller system exhibits critical behavior which can be used for high-precision quantum estimation. A major advantage of the scheme is the robustness of the system against spin decoherence, which allows it to perform parameter estimation with measurement time not limited by spin dephasing.

Structure and dynamics of electronically excited molecular systems

AbstractStructure and dynamics of electronic excited states of molecular systems is of contemporary interest to understand a rich variety of processes ranging from molecular spectroscopy to reaction dynamics. Developments over the past decades have established that coupling of electronic and nuclear motion is a generic feature in polyatomic molecular systems which causes a breakdown of the Born–Oppenheimer approximation. Such a coupling leads to conical intersections in non‐linear and glancing degeneracy in linear polyatomic systems. While the former case is quite general and has wide variances depending on the nature of the coupling on the symmetry ground, the latter one is specific to the linear systems having axial symmetry. The Jahn–Teller (JT) systems form a subclass in the former category and the latter category constitutes the Renner–Teller (RT) systems. These systems are characterized by high point group symmetry and orbital degeneracy. The latter splits upon distortion along suitable symmetry reducing nuclear displacement. The JT or the RT split component states may undergo symmetry allowed coupling among another JT or RT split component states or with some non‐degenerate states. These are termed as the pseudo‐JT and pseudo‐RT coupling, respectively. We have studied a variety of photo‐induced molecular processes with the aid of ab initio quantum chemistry and first principles quantum dynamics methods. We will document here some of the important developments in the field focusing on the work done on the JT and RT systems primarily in our own laboratory.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Software > Quantum Chemistry Structure and Mechanism > Molecular Structures

Vibronic mean-field and perturbation theory for Jahn-Teller and pseudo-Jahn-Teller molecules

A generalisation of vibrational mean-field theory is developed for non-adiabatic Jahn-Teller and pseudo-Jahn-Teller molecules with coupled vibrational and electronic degrees of freedom treated within a quasi-diabatic framework. Solutions to the vibronic self-consistent field equations of motion generate qualitatively correct zeroth-order vibronic wavefunctions even in the strong coupling limit. These serve as an efficient basis for further perturbative or variational corrections. Particular attention is paid to complications arising in multi-mode Jahn-Teller systems, where the degenerate ground state exhibits artificial symmetry-breaking in the mean-field approximation. This effect is shown to behave like a second-order phase transition, with the symmetry of finite-temperature mean-field solutions restored above a critical temperature.

Ground State and Optical Excitations in Compounds with Tetragonal CuF64- Units: Insight into KAlCuF6 and CuFAsF6.

It has been argued that AAlCuF6 (A = K, Cs) and CuFAsF6 are the only known crystals that exhibit compressed CuF64- units due to the Jahn-Teller effect. However, no grounds for this singular behavior have yet been reported. By means of first-principles calculations on such compounds and the isomorphous compounds involving Zn2+ ions instead of Cu2+, we prove that neither the ground state nor the equilibrium geometry of CuF64- complexes in KAlCuF6 and CuFAsF6 is the result of a Jahn-Teller effect. In contrast, it is shown that the internal electric field, ER(r), created by the rest of the lattice ions upon the localized electrons in the complex, plays an important role in understanding this matter as well as the d-d transitions of these two compounds. The energy of an optical transition is shown to involve two contributions: the intrinsic contribution derived for the isolated CuF64- unit at equilibrium and the extrinsic contribution coming from the ER(r) field. Aside from reproduction of the experimental d-d transitions observed for KAlCuF6, it is found that in CuFAsF6 the b1g(x2 - y2) → a1g(3z2 - r2) transition is not the lowest one due to the stronger effects from the internal field. Interestingly, the intrinsic contribution corresponding to that transition can simply be written as β(Req - Rax) where Req and Rax are the equatorial and axial Cu2+-F- distances and β = 2.7 eV/Å is the same for all systems involving tetragonal CuF64- units and an average metal-ligand distance close to 2.03 Å. This shows the existence of a common point shared by the Jahn-Teller system KZnF3:Cu2+ and other non-Jahn-Teller systems such as KAlCuF6, CuFAsF6, K2ZnF4:Cu2+, and Ba2ZnF6:Cu2+. Although most Jahn-Teller systems display an elongated geometry, there are however many Cu2+ compounds with a compressed geometry but hidden by an additional orthorhombic instability. The lack of that instability in KAlCuF6 and CuFAsF6 is also discussed.

Diabatic neural network potentials for accurate vibronic quantum dynamics-The test case of planar NO3.

A recently developed scheme to produce high-dimensional coupled diabatic potential energy surfaces (PESs) based on artificial neural networks (ANNs) [D. M. G. Williams and W. Eisfeld, J. Chem. Phys. 149, 204106 (2019)] is tested for its viability for quantum dynamics applications. The method, capable of reproducing high-quality ab initio data with excellent accuracy, utilizes simple coupling matrices to produce a basic low-order diabatic potential matrix as an underlying backbone for the model. This crude model is then refined by making its expansion coefficients geometry-dependent by the output neurons of the ANN. This structure, strongly guided by a straightforward physical picture behind nonadiabatic coupling, combines structural simplicity with high accuracy, reproducing ab initio data without introducing unphysical artifacts to the surface, even for systems with complicated electronic structure. The properties of diabatic potentials obtained by this method are tested thoroughly in the present study. Vibrational/vibronic eigenstates are computed on the X̃ and à states of NO3, a notoriously difficult Jahn-Teller system featuring strong nonadiabatic couplings and complex spectra. The method is investigated in terms of how consistently it produces dynamics results for PESs of similar (fitting) quality and how the results depend on the ANN size and ANN topography. A central aspect of this work is to understand the convergence properties of the new method in order to evaluate its predictive power. A previously developed, high-quality model utilizing a purely (high-order) polynomial ansatz is used as a reference to showcase improvements of the overall quality which can be obtained by the new method.

Quantum dynamics and geometric phase in E⊗e Jahn-Teller systems with general Cnv symmetry.

E ⊗ e Jahn-Teller (JT) systems are considered the prototype of symmetry-induced conical intersections and of the corresponding geometric phase effect (GPE). For decades, this has been analyzed for the most common case originating from C3v symmetry and these results usually were generalized. In the present work, a thorough analysis of the JT effect, vibronic coupling Hamiltonians, GPE, and the effect on spectroscopic properties is carried out for general Cnv symmetric systems (and explicitly for n = 3-8). It turns out that the C3v case is much less general than often assumed. The GPE due to the vibronic Hamiltonian depends on the leading coupling term of a diabatic representation of the problem, which is a result of the explicit n, α, and β values of a CnvEα ⊗ eβ system. Furthermore, the general existence of n/m (m∈N depending on n, α, and β) equivalent minima on the lower adiabatic sheet of the potential energy surface (PES) leads to tunneling multiplets of n/m states (state components). These sets can be understood as local vibrations of the atoms around their equilibrium positions within each of the local PES wells symmetrized over all equivalent wells. The local vibrations can be classified as tangential or radial vibrations, and the quanta in the tangential mode together with the GPE determine the level ordering within each of the vibronic multiplets. Our theoretical predictions derived analytically are tested and supported by numerical model simulations for all possible Eα ⊗ eβ cases for Cnv symmetric systems with n = 3-8. The present interpretation allows for a full understanding of the complex JT spectra of real systems, at least for low excitation energies. This also opens a spectroscopic way to show the existence or absence of GPEs.

Understanding the Structure and Ground State of the Prototype CuF2 Compound Not Due to the Jahn-Teller Effect.

Insulating CuF2 is considered a prototype compound displaying a Jahn-Teller effect (JTE) which gives rise to elongated CuF64- units. By means of first-principles calculations together with an analysis of experimental data of both CuF2 and Cu2+-doped ZnF2, we demonstrate that such an idea is not correct. For ZnF2:Cu2+, we find that CuF64- units are compressed always along the Z local axis with a hole essentially in a 3 z2- r2 antibonding orbital, in agreement with experimental EPR data that already underline the absence of a JTE. The structure of the monoclinic CuF2 crystal also comes from compressed CuF64- complexes, although hidden by an additional orthorhombic instability due to a negative force constant of b2g and b3g local modes. The associated distortion, similar to that involved in K2CuF4 and other layered Cu2+ compounds, is also shown to be developed for ZnF2:Cu2+ upon increasing the copper concentration. The origin of this cooperative effect is discussed together with the differences between non-Jahn-Teller systems like ZnF2:Cu2+ and CuF2 and true Jahn-Teller systems like KZnF3:Cu2+. From present results and those on layered compounds, the usual assumption of a JTE for explaining the properties of d9 ions in low-symmetry lattices can hardly be right.

Explaining the optical spectrum of CrF2and CuF2model materials: role of the tetragonal to monoclinic instability

The properties of MF2 (M = Cr, Cu) model compounds are usually interpreted assuming a Jahn-Teller effect leading to elongated MF64- units. By means of the analysis of experimental data and first-principles calculations on both the monoclinic P21/c structure and the parent rutile structure (tetragonal P42/mnm space group), we prove that such an assumption is not correct. It is shown that in MF2 compounds, the MF64- complexes are actually compressed in the parent phase but along a different direction, a situation that is however hidden by an additional orthorhombic instability due to a negative force constant of b2g and b3g modes of the cell. This distortion plays a key role in understanding the high experimental value of the lowest d-d transition energy, E1 = 1.23 and 0.93 eV for CrF2 and CuF2, respectively, when compared to the value E1 = 0.40 eV derived for the Jahn-Teller system of KZnF3:Cu2+. Aside from reproducing reasonably the experimental values of spin allowed d-d transitions of both compounds, our first-principles calculations show the existence of an accidental degeneracy involving the yz and xy levels in the final P21/c structure. Moreover, the internal electric field of CrF2 and CuF2 is found to be much less anisotropic than in layered compounds like K2CuF4 and thus it has little influence on the d-d transition energy. The influence of the (3z2 - r2) - (x2 - y2) hybridization, caused by the orthorhombic distortion, on the electronic density and the magnetic coupling between layers is also briefly discussed. The present results stress that the interpretation of experimental data using simple parameterized models can lead to wrong conclusions.

Vibronic states in conical intersections: manifestations of centrifugal energy and non-adiabaticity in optical spectra of Jahn-Teller systems

Quantum states in conical intersections of adiabatic potentials in Jahn-Teller systems, known as Slonczewski resonances, are considered. It is shown that centrifugal forces associated with the rotation of the Jahn-Teller deformation (pseudorotation) play an important role in these resonances causing appearance of gaps in the energy spectrum of these states. In addition, the decay of these states, caused by non-adiabaticity, decreases with increasing angular momentum of the pseudorotation. As a result, states with a large momentum acquire a long lifetime. The optical spectra of the A1→E electronic transition with different values of the pseudorotational angular momentum are presented. In these spectra, centrifugal energy gaps and the stabilization of levels with a large pseudorotation momentum are clearly identified.

Neural network diabatization: A new ansatz for accurate high-dimensional coupled potential energy surfaces.

A new diabatization method based on artificial neural networks (ANNs) is presented, which is capable of reproducing high-quality ab initio data with excellent accuracy for use in quantum dynamics studies. The diabatic potential matrix is expanded in terms of a set of basic coupling matrices and the expansion coefficients are made geometry-dependent by the output neurons of the ANN. The ANN is trained with respect to ab initio data using a modified Marquardt-Levenberg back-propagation algorithm. Due to its setup, this approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This novel ANN diabatization approach has been applied to the low-lying electronic states of NO3 as a prototypical and notoriously difficult Jahn-Teller system in which the accurate description of the very strong non-adiabatic coupling is of paramount importance. Thorough tests show that an ANN with a single hidden layer is sufficient to achieve excellent results and the use of a "deeper" layering shows no clear benefit. The newly developed diabatic ANN potential energy surface (PES) model accurately reproduces a set of more than 90 000 Multi-configuration Reference Singles and Doubles Configuration Interaction (MR-SDCI) energies for the five lowest PES sheets.

Manifestation of vibronic dynamics in infrared spectra of Mott insulating fullerides

The fine structure and temperature evolution of infrared spectra have been intensively used to probe the nature of Jahn-Teller dynamics in correlated materials. At the same time, a theoretical framework to adequately extract the information on the complicated vibronic dynamics from infrared spectra is still lacking. In this work, the first-principles theory of the infrared spectra of dynamical Jahn-Teller system is developed and applied to the Mott-insulating ${\mathrm{Cs}}_{3}{\mathrm{C}}_{60}$. With the calculated coupling parameters for Jahn-Teller and infrared active vibrational modes, the manifestation of the dynamical Jahn-Teller effect in infrared spectra is elucidated. In particular, the temperature evolution of the infrared line shape is explained. The transformation of the latter into Fano resonance type in metallic fulleride is discussed on the basis of obtained results.

Local normal modes and lattice dynamics

The calculation of phonon dispersion for crystalline solids with r atoms in a unit cell requires solving a 3r-dimensional eigenvalue problem. We propose a simplified approach to lattice dynamics which yields approximate analytical expressions and accurate numerical solutions to phonon dispersion without explicitly solving this eigenvalue problem. This is accomplished by a coordinate transformation to the normal modes of the isolated primitive unit cell, which is extended over the entire crystal by Fourier transformation, so each phonon branch is labelled by the irreducible representations of the symmetry group of the unit cell from which the atomic displacements can be readily identified from standard group theoretic methods. The resulting dynamical matrix is analyzed perturbatively, with the diagonal elements as the zeroth-order matrix and the off-diagonal elements as the perturbation. The zeroth-order matrix provides approximate analytical expressions for the phonon dispersions, the first-order terms vanish, with the higher-order terms converging to the exact solutions. We describe the application of this method to a one-dimensional diatomic chain, graphene, and hexagonal close-packed zirconium. In all cases, the zeroth-order solution provides reasonable approximations, while the second-order solutions already show the rapid convergence to the exact dispersion curves. This methodology provides insight into the lattice dynamics of crystals, molecular solids, and Jahn–Teller systems, while significantly reducing the computational cost. Similarities between our method and other techniques that use local basis sets for calculating electronic and vibrational properties of materials are discussed. We conclude by exploring extensions that widen the scope of our approach.

The Jahn-Teller Distortion at High Pressure: The Case of Copper Difluoride

The opposing effects of high pressure (in the GPa range) and the Jahn-Teller distortion led to many intriguing phenomena which are still not well understood. Here we report a combined experimental-theoretical study on the high-pressure behavior of an archetypical Jahn-Teller system, copper difluoride (CuF2). At ambient conditions this compound adopts a distorted rutile structure of P21/c symmetry. Raman scattering measurements performed up to 29 GPa indicate that CuF2 undergoes a phase transition at 9 GPa. We assign the novel high-pressure phase to a distorted fluorite structure of Pbca symmetry, iso-structural with the ambient-pressure structure of AgF2. Density functional theory calculations indicate that the Pbca structure should transform to a non-centrosymmetric Pca21 polymorph above 30 GPa, which, in turn, should be replaced by a cotunnite phase (Pnma symmetry) at 72 GPa. The elongated octahedral coordination of the Cu2+ cation persists up to the Pca21–Pnma transition upon which it is replaced by a capped trigonal prism geometry, still bearing signs of a Jahn-Teller distortion. The high-pressure phase transitions of CuF2 resembles those found for difluorides of transition metals of similar radius (MgF2, ZnF2, CoF2), although with a much wider stability range of the fluorite-type structures, and lower dimensionality of the high-pressure polymorphs. Our calculations indicate no region of stability of a nanotubular polymorph observed for the related AgF2 system.

Quantifying the effects of higher order coupling terms on fits using a second order Jahn-Teller Hamiltonian

The limitations associated with the common practice of fitting a quadratic Hamiltonian to vibronic levels of a Jahn-Teller system have been explored quantitatively. Satisfactory results for the prototypical X∼2E′ state of Li3 are obtained from fits to both experimental spectral data and to an “artificial” spectrum calculated by a quartic Hamiltonian which accurately reproduces the adiabatic potential obtained from state-of-the-art quantum chemistry calculations. However the values of the Jahn-Teller parameters, stabilization energy, and pseudo-rotation barrier obtained from the quadratic fit differ markedly from those associated with the ab initio potential. Nonetheless the RMS deviations of the fits are not strikingly different. Guidelines are suggested for comparing parameters obtained from fits to experiment to those obtained by direct calculation, but a principal conclusion of this work is that such comparisons must be done with a high degree of caution.

Ground state in E ⊗ e Jahn-Teller and Renner-Teller systems: Account of nonadiabaticity.

The ground and lower excited states of an E⊗e Jahn-Teller system with linear and quadratic vibronic coupling are considered, taking nonadiabaticity into account. Our calculations confirm a common opinion that in the case of a weak quadratic coupling, the ground state is doubly degenerate and the first excited state is nondegenerate for any linear coupling. However, with increasing quadratic coupling for weak linear coupling, the nondegenerate state becomes the ground state. The values of vibronic parameters are found at which the ground state changes.