Geminal approach to vibronic models of superconductivity in crystals. I. The Jahn–Teller effect

Electronic geminals constructed as linear combinations of binary products of site functions are used to formulate a vibronic model of superconductivity in crystals that is based upon the approximation of independent correlated electron pairs obtained variationally from an electron‐pair Hamiltonian and the Jahn–Teller effect. The cyclic symmetry of the system is taken into account and the geminals are sorted into doubly degenerate pairs. The Herzberg–Teller expansion of the pair Hamiltonian in terms of vibrational modes leads directly to the Jahn–Teller effect. A contact transformation of the vibronic Hamiltonian containing only linear terms lowers the energy of the system by a second‐order term associated with the Jahn–Teller stabilization energy. A possible model for superconductivity in solids is proposed on the basis of the Jahn–Teller effect. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Structure and electronic structure of polyacene

It is shown that infinite long polyacene chains may have three energetically close but structurally distinct isomers (a symmetrical, sym, form and two lower symmetry forms: one with double bonds in a trans and another isomer with double bonds in a cis pattern). The energetics is based on solid state MNDO theory. We discuss that the symmetrical form has a substantial energy gap E_g in the Hartree–Fock approach owing to exact exchange terms, which are nonlocal. Broken symmetry Hartree–Fock (HF ) solutions for polyacene are also described. An angularly distorted structure suggested earlier on Jahn–Teller grounds is found to be energetically not favorable.     

A Genuine Jahn–Teller System with Compressed Geometry and Quantum Effects Originating from Zero‐Point Motion

First‐principle calculations together with analysis of the experimental data found for 3d⁹ and 3d⁷ ions in cubic oxides proved that the center found in irradiated CaO:Ni²⁺ corresponds to Ni⁺ under a static Jahn–Teller effect displaying a compressed equilibrium geometry. It was also shown that the anomalous positive g_∥ shift (g_∥?g₀=0.065) measured at T=20 K obeys the superposition of the |3 z²?r²? and |x²?y²? states driven by quantum effects associated with the zero‐point motion, a mechanism first put forward by O'Brien for static Jahn–Teller systems and later extended by Ham to the dynamic Jahn–Teller case. To our knowledge, this is the first genuine Jahn–Teller system (i.e. in which exact degeneracy exists at the high‐symmetry configuration) exhibiting a compressed equilibrium geometry for which large quantum effects allow experimental observation of the effect predicted by O'Brien. Analysis of the calculated energy barriers for different Jahn–Teller systems allowed us to explain the origin of the compressed geometry observed for CaO:Ni⁺.     

S5 graphs as model systems for icosahedral Jahn–Teller problems

The degeneracy of the eigenvalues of the adjacency matrix of graphs may be broken by non-uniform changes of the edge weights. This symmetry breaking is the graph-theoretical equivalent of the molecular Jahn–Teller effect (Ceulemans et al. in Proc Roy Soc 468:971–989, 2012). It is investigated for three representative graphs, which all have the symmetric group on 5 elements, S ₅ , as automorphism group: the complete graph K₅, with 5 nodes, the Petersen graph, with 10 nodes, and an extended K₅ graph with 20 nodes. The spectra of these graphs contain fourfold, fivefold, and sixfold degenerate manifolds, respectively, and provide model systems for the study of the Jahn–Teller effect in icosahedral molecules. The S ₅ symmetries of the distortion modes of the quintuplet in the Petersen graph yield a resolution of the product multiplicity in the corresponding $ H \otimes \left( {g + 2h} \right) $ icosahedral Jahn–Teller problem. In the extended Petersen graph with 20 nodes, a selection rule prevents the Jahn–Teller splitting of the sextuplet into two conjugate icosahedral triplets.     

Novel spectroscopic effects in molecular transitions involving degenerate electronic states

We discuss the intricate Jahn—Teller-like and non-Jahn—Teller spectroscopic patterns which result via the recently revealed cross-quadratic terms involves modes of different symmetry which arise in the nuclear potential of degenerate electronic states of non-linear molecules.     

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 (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) 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/S_n 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.     

Jahn–Teller Effects in Molecular Cations Studied by Photoelectron Spectroscopy and Group Theory

The traditional “ball‐and‐stick” concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn–Teller (JT) effect which is very common in open‐shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo‐Jahn–Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of “antiaromaticity” are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential‐energy surface are separated by substantial barriers.     

Analogies between Jahn–Teller and Rashba spin physics

In 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.     

Density functional theory of born couplings: Consequences for electron flow in Jahn–Teller molecules and superconductors

The dynamics of Jahn–Teller systems has recently been discussed in terms of generalized electronic charge and current densities in nuclear-coordinate space. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, was a crucial component of this formulation. Here, a densitybased treatment of Born couplings is derived from first-principles quantum mechanics beyond the Born–Oppenheimer approximation. Because of the degenerate electronic configuration of a Jahn–Teller molecule, there are an infinite number of ways in which the charge distribution can be oriented for the same energy, leading to a vanishing bond hardness for the molecule in the symmetric nuclear configuration. Further, the moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, leading to unhindered rotation of the charge cloud. This leads to the dynamical Jahn–Teller problem, namely, the coupling of electronic and nuclear motions through the Born coupling terms. Applications to superconductivity theory are discussed. © 1995 John Wiley & Sons, Inc.     

An investigation of the electron density of a Jahn–Teller‐distorted CrII cation: the crystal structure and charge density of hexakis(acetonitrile‐κN)chromium(II) bis(tetraphenylborate) acetonitrile disolvate

In the crystal structure of the title homoleptic Cr^II complex, [Cr(CH₃CN)₆](C₂₄H₂₀B)₂·CH₃CN, the [Cr(CH₃CN)₆]²⁺ cation is a high‐spin d⁴ complex with strong static, rather than dynamic, Jahn–Teller distortion. The electron density of the cation was determined by single‐crystal X‐ray refinements using aspherical structure factors from wavefunction calculations. The detailed picture of the electronic density allowed us to assess the extent and directionality of the Jahn–Teller distortion of the Cr^II cation away from idealized octahedral symmetry. The topological analysis of the aspherical d‐electron density about the Cr^II cation showed that there are significant valence charge concentrations along the axial Cr—N axes. Likewise, there were significant valence charge depletions about the Cr^II cation along the equatorial Cr—N bonds. These charge concentrations are in accordance with a Jahn–Teller‐distorted six‐coordinate complex.     

Relativity and the Jahn–Teller,Berry pseudorotations of TBP clusters: group theory,spin–orbit and combinatorial nuclear spin statistics of TBP Desargues–Levi isomerization graph

Jahn–Teller and Berry pseudorotations in transition metal and main group clusters such as Hf₅, Ta₅, W₅ and Bi₅ are interesting because of the competition between relativistic effects and pseudorotations. Topological representations of various isomerization pathways arising from the Berry pseudorotation of pentamers constitute the edges of the Desargues–Levi graph. We have computed the combinatorics for multinomial colorings of the vertices, edges and 10-faces of the Desargues–Levi isomerization graph for all irreducible representations and the nuclear spin statistics of spin-7/2 ¹⁸¹Ta₅ as well as the TBP composite cluster particles. Topological insights into Jahn–Teller and Berry pseudorotations and relativistic effects are provided.     

Orbit–orbit interaction in the NO–Fe(II)Hemoproteins studied by the low-temperature magnetic circular dichroism: Dynamic Jahn–Teller effect detected by MCD

This paper analyzes the low-temperature magnetic circular dichroism of NO–Fe(II)hemoproteins in detail. We include the Jahn–Teller effect in our consideration of the low-temperature MCD results.     

Density functional theory for Jahn–Teller systems

The first discussion of the dynamics of Jahn–Teller systems in terms of the electronic density as the fundamental variable was given by W.J. Clinton in 1960, where the degenerate electronic configuration of a Jahn–Teller molecule was interpreted in terms of the infinite number of ways in which the charge distribution can be oriented for the same energy. The moving nuclear framework serves as the perturbation necessary to define the orientation of the charge density, with no activation energy required to put the charge cloud into motion. Recently, this notion of the electronic charge cloud in a Jahn–Teller molecule sweeping out the potential surface over which the nuclei move has found mathematical expression in our work in terms of a generalized electronic current density in nuclear-coordinate space [N. Sukumar and B.M. Deb, Int. J. Quantum Chem. 40 , 501 (1991)]. The introduction of the electronic phase as a function of both electronic and nuclear coordinates, in addition to the electronic density, is a crucial component of this formulation. In the present work, the density-based treatment is extended to the nonadiabatic situation, with the Born couplings interpreted as nonadiabatic currents in parameter space. Abelian and non-Abelian gauge transformations of these currents are discussed. © John Wiley & Sons, Inc.     

Jahn—Teller effects in substituted benzene cations. IV. Intermode interactions and intensity anomalies in sym-trifluorobenzene ions

A theoretical treatment of coupling between Jahn—Teller modes is given which includes both linear and quadratic Jahn—Teller coupling. Effects of two and three mode interactions on the B?²A″₂ → X?²E″ transition of the sym-trifluorobenzene ions are studied, within the linear coupling approximation, for modes 6, 7, 8 and 9. Quadratic coupling effects are considered in a companion paper (part V). The results show that discrepancies previously noted between observed relative band intensities and those calculated on the basis of single Jahn—Teller modes cannot be accounted for by multimode interactions or by Fermi resonance effects operating in conjunction with Jahn—Teller effects. Jahn—Teller combination bands are shown to have several components, the most intense of which are assigned. Particular attention is paid to various possible assignments of the 8^0,0_{1,$\text{1}\text{2}$} and 6^0,0_{3,$\text{1}\text{2}$} vibronic transitions in the light of the multimode interaction analyses.     

Über das System Ba2Zn1−xCuxUO6 — ein schwingungsspektroskopischer Nachweis des Jahn-Teller-Effekts

On the System Ba₂Zn_1?xCu_xUO₆. A Vibrational Spectroscopic Proof of the Jahn Teller Effect The ordered perovskites Ba₂ZnUO₆ (cubic, space group Fm3m) and Ba₂CuUO₆ (tetragonal, space group I₄/mmm) form solid solutions. For small Cu content the lattice symmetry is cubic, with x ≥ 0.25 an increasing tetragonal distortion (c/a √2 > 1) is observed. From the vibrational spectra and in accordance with the factor group analysis the symmetry of the UO₆ octahedra is for small Cu content O_h and on the Cu-rich side D_4h. In the region of the lattice vibrations (T₂ field) the lifting of the degeneracy — due to the Jahn Teller effect of Cu²⁺ — leads to a band separation, which decreases with sinking copper content. Therefore the Jahn Teller effect is easily noticeable with vibrational spectroscopic methods. In the corresponding series with W^VI the vibrational spectroscopic investigations lead qualitatively to the same results as in the U^VI system. As further examples the stacking polytypes Ba₂ZnTeO₆ and Ba₂CuTeO₆ are considered. The vibrational spectra show, that the Jahn Teller effect in this lattice, which is strengthened by partial face-sharing of octahedra, is less pronounced than in the perovskites in which only corner-sharing is present.     

Suppression of Jahn–Teller term-split band edge states in the x-ray absorption spectra of non-crystalline Zr silicates and Si oxynitride alloys,and alloys of ZrO2 with Y2O3

Jahn–Teller (J–T) term-split states in nanocrystalline transition metal and trivalent rare earth elemental and complex oxides reduce the band gap, and tunnelling barrier height at interfaces with crystalline Si substrates. These states are identified by x-ray absorption spectroscopy and spectroscopic ellipsometry. Alloys for suppression of J–T d-state degeneracy removal are identified as: (i) non-crystalline Zr/Hf silicates and Si oxynitrides and (ii) ZrO₂–Y₂O₃ alloys with high concentrations of randomly distributed O-vacancies that promote cubic crystalline symmetry.     

Aspects of spin-orbit effects in compounds containing heavy elements

This perspective article discusses some widely-known and some less-known consequences of spin-orbit effects in inorganic chemistry, and provides a brief outline of the theoretical methods currently in use, along with a discussion of recent developments and selected applications. This is of critical importance in the interpretation of the electronic delocalization, optical and magnetic properties and Jahn–Teller effects of compounds containing heavy elements.     

Effects of AgNPs-coating on the electrochemical performance of LiMn2O4 cathode material for lithium-ion batteries

Journal of Solid State Electrochemistry - The Jahn–Teller effect and severe side reactions with liquid electrolyte have been considered as the main obstacles to the further application of...     

Simplest proof of the Jahn–Teller theorem for molecular systems

A new simple proof of the Jahn–Teller theorem for molecular systems is presented. The proof is based on some general properties of symmetric square representation characters that simplify their explicit treatment and minimize the use of tables. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007