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     

Pseudo Jahn–Teller effects of triphenylene dianion

Pseudo Jahn–Teller effects of triphenylene dianion were discussed by molecular orbital method. While the triplet ground state preferred a D_3h geometry, singlet states were subject to symmetry lowering to have C_2v geometries. The resultant geometries were rationalized to amplitude patterns of the degenerate frontier orbitals.     

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     

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.     

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.     

Dynamic nonlinear Jahn–Teller effect of the type E ⊗ ϵ

By applying the projection operator method it is shown that the complicated Hamiltonian of a E ? ? JT system with nonlinear coupling coefficients can be written in terms of two Hamiltonians which are simple to handle and transform according to irreducible representations E, A₁, and A₂ of C_3v point group. A variational approach is then used to calculate the ground state energy, using the Hamiltonian that transforms according to E, as an explicit function of the linear and nonlinear coupling parameters. The energies calculated in the strong coupling limit are finally compared with the corresponding previously calculated energies.     

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⁺.     

Jahn–Teller Effect in Circulenes: X‐ray Diffraction Study of Coronene and Corannulene Radical Anions

Single‐crystal X‐ray diffraction studies of two polyaromatic radical anions crystallized as sodium salts, namely [Na(DME)₃]⁺[C₂₀H₁₀^?] ( 1 ) and [Na(DME)₃]⁺[C₂₄H₁₂^?] ( 2 ) are reported. This allowed the first structural evaluation of Jahn–Teller (JT) effects for monoreduced circulenes and a comparison between bowl‐shaped corannulene and planar coronene. The C_s and D_2h symmetrical distortions are found to fit the experimental data for C₂₀H₁₀^.? and C₂₄H₁₂^.?, respectively. The continuous symmetry measure (CSM) analysis was carried out to provide a quantitative measure of the JT distortions in 1 and 2 . In addition, the X‐ray crystallographic results were fully supported by DFT calculations.     

An Unusual Stable Mononuclear MnIII Bis‐terpyridine Complex Exhibiting Jahn–Teller Compression: Electrochemical Synthesis,Physical Characterisation and Theoretical Study

The mononuclear manganese bis‐terpyridine complex [Mn(tolyl‐terpy)₂](X)₃ ( 1 (X)₃; X=BF₄, ClO₄, PF₆; tolyl‐terpy=4′‐(4‐methylphenyl)‐2,2′:6′,2“‐terpyridine), containing Mn in the unusual +III oxidation state, has been isolated and characterised. The 1 ³⁺ ion is a rare example of a mononuclear Mn^III complex stabilised solely by neutral N ligands. Complex 1 ³⁺ is obtained by electrochemical oxidation of the corresponding Mn^II compound 1 ²⁺ in anhydrous acetonitrile. Under these conditions the cyclic voltammogram of 1 ²⁺ exhibits not only the well‐known Mn^II/Mn^III oxidation at E_1/2=+0.91 V versus Ag/Ag⁺ (+1.21 V vs. SCE) but also a second metal‐based oxidation process corresponding to Mn^III/Mn^IV at E_1/2=+1.63 V (+1.93 V vs. SCE). Single crystals of 1 (PF₆)₃?2 CH₃CN were obtained by an electrocrystallisation procedure. X‐ray analysis unambiguously revealed its tetragonally compressed octahedral geometry and high‐spin character. The electronic properties of 1 ³⁺ were investigated in detail by magnetic measurements and theoretical calculations, from which a D value of +4.82 cm^?1 was precisely determined. Density functional and complete active space self consistent field ab initio calculations both correctly predict a positive sign of D, in agreement with the compressed tetragonal distortion observed in the X‐ray structure of 1 (PF₆)₃?2 CH₃CN. The different contributions to D were calculated, and the results show that 1) the spin–orbit coupling part (+2.593 cm^?1) is predominant compared to the spin–spin interaction (+1.075 cm^?1) and 2) the excited triplet states make the dominant contribution to the total D value.     

Analysis of the Symmetry of Crystal Packing Forces by Methyl Proton Tunneling: A Strategy for the Unambiguous Assignment of the Magnetic Jahn – Teller Effect in Molecules

Intrinsic and extrinsic forces behind the distortion in metal atom clusters can be readily distinguished provided that the clusters are embedded in a suitable ligand environment and that the tunneling of the protons in the peripheral ligands is then analyzed by inelastic neutron scattering. For the [Cr₃O(OOCCH₃)₆(H₂O)₃]Cl⋅6 H₂O model system studied, the tunneling process is very sensitive to the local environment. Thus a tool is available to allow a better assessment of the cause of structural distortions.     

Distortions of π‐Coordinated Arenes with Anionic Character

A qualitative analysis of the distortions that operate on the π system of bridging arenes with anionic character is presented and substantiated by computational studies at the density functional B3LYP and CASSCF levels. The observed effects of bonding to two metal atoms and of the negative charge are an expansion of the arene ring due to the partial occupation of π* orbitals, an elongation or compression distortion accompanied by a loss of the equivalence of carbon‐carbon bonds due to a Jahn–Teller distortion of the arene dianions, and a ring puckering due to a second‐order Jahn–Teller distortion that may appear independently of the existence of the first‐order effect. The workings of the orbital mixing produced by these distortions have been revealed in a straightforward way by a pseudosymmetry analysis of the HOMOs of the distorted conformations. The systems studied include Li^I and Y^III adducts of benzene, as well as trimethylsilyl‐substituted derivatives in the former case. An analysis of the structural data of a variety of purported di‐ and tetraanionic arene ligands coordinated to transition metals in several bridging modes has reproduced the main geometrical trends found in the computational study for the benzene and trimethylsilyl‐substituted benzene dianions, allowing a classification of the variety of structural motifs found in the literature.     

Einfluss von H‐Brückenbindungen auf die Jahn–Teller‐Verzerrung in den Kettenstrukturen von 2,2′‐bipyMn(H2PO4)F2·H2O und 2,2′‐bipyMn(H2PO4)2F

In the system 2,2′‐bipyridine/Mn^III/HF/H₃PO₄/H₂O two compounds with chain structures could be prepared and characterised by X‐ray structure analyses. 2,2′‐bipyMn(H₂PO₄)F₂·H₂O ( 1 ): monoclinic, twinned, space group P2₁/c, Z = 4, a = 6.7883(4), b = 10.9147(5), c = 17.8102(8) Å, β = 100.142(4)°, R = 0.0328. 2,2′‐bipyMn(H₂PO₄)₂F ( 2 ): triclinic, space group P , Z = 2, a = 6.675(1), b = 10.715(1), c = 11.013(1) Å, α = 107.595(9)°, β = 90.994(9)°, γ = 95.784(8)°, R = 0.0252. Both compounds show chain structures with trans‐bridging dihydrogenphosphate ligands and bipy and two fluorine ligands for ( 1 ), or bipy, fluorine and an additional dihydrogenphosphate, respectively, for ( 2 ) in equatorial positions. Due to the pseudo‐Jahn–Teller effect, Mn^III shows elongated octahedral coordination with ferrodistortive ordering along the chain direction. The distortion is remarkably higher in ( 1 ) than in ( 2 ). This is discussed in context with additional hydrogen bonds along the chain in ( 2 ).     

Improved Pöschl–Teller potential energy model for diatomic molecules

By employing the dissociation energy and the equilibrium internuclear distance for a diatomic molecule as explicit parameters, we construct an improved Pöschl–Teller potential energy model. We analyze the average absolute deviations of the improved Pöschl–Teller and Morse potentials from the experimental Rydberg–Klein–Rees (RKR) potentials for six diatomic molecules. It is found that the improved Pöschl–Teller potential is more accurate than the Morse potential in fitting experimental RKR potential curves over a large range of internuclear distances for six molecules examined.     

Synthesis,X‐ray Single‐Crystal Structure Determination,and Magnetic Properties of [Rb(benzo[18]crown‐6)]+ Salts Containing Well‐Ordered Fulleride Trianions C603−

Finally, a structure with well‐resolved C ₆₀ ^3? ions and S=1/2 spin system : The two novel title compounds have clearly S=1/2 and not S=3/2 electronic states, as expected for the occupation of the triply degenerate LUMO of C_60. These structures with well‐ordered fullerene trianions show that the expected Jahn–Teller distortion is not observable in X‐ray diffraction experiments.

     

A comparative study of the pseudo Jahn–Teller instability of linear molecules Ag3 and I3 and their positive and negative ions

In confirmation of the general idea of pseudo Jahn–Teller origin of instability of high-symmetry configurations of polyatomic systems that determines their geometry, a series of six molecules, Ag₃ⁿ and I₃ⁿ, n=−1,0,+1, were investigated. The electronic structure of the ground state of all the six molecules in the linear configuration was calculated by the extended-Hückel method with atomic charge and electron configuration self-consistency, while the excited state energy levels and wavefunctions were estimated in the single transition approximation. Then, the orbital vibronic constants, bare force constants and the vibronic contribution of the appropriate excited states to the instability of the linear configuration were evaluated.

The obtained results show that in both series, silver and iodine, the curvature of the adiabatic potential of the linear configuration, in the direction of the bending distortions, decreases from the negative ions to the neutral atoms to the positive ions and becomes negative in the latter two cases, thus explaining the origin of the experimentally observed geometries. The numerical data give a detailed insight into: (1) the origin of the linear→bent distortions as being due to the additional covalency created by the σ–π overlap in the bent configuration; (2) the specific excited states that contribute to this process of geometry formation; and (3) the difference between the silver and iodine series.     

The adiabatic‐to‐diabatic transformation angle and the berry phase for coupled jahn–teller/renner–teller systems: The F + H2 as a case study

The approach to calculate improved, two‐state, adiabatic‐to‐diabatic transformation angles (also known as mixing angles), presented before (see Das et al., J Chem Phys 2010, 133, 084107), was used here while studying the F + H₂ system. However, this study is characterized by two new features: (a) it is the first of its kind in which is studied the interplay between Renner–Teller (RT) and Jahn–Teller (JT) nonadiabatic coupling terms (NACT); (b) it is the first of its kind in which is reported the effect of an upper singular RT‐NACT on a lower two‐state (JT) mixing angle. The fact that the upper NACT is singular (it is shown to be a quasi‐Dirac δ‐function) enables a semi‐analytical solution for this perturbed mixing angle. The present treatment, performed for the F + H₂ system, revealed the existence of a novel parameter, η, the Jahn–Renner coupling parameter (JRCP), which yields, in an unambiguous way, the right intensity of the RT coupling (as resembled, in this case, by the quasi‐Dirac δ‐function) responsible for the fact that the final end‐of‐the contour angle (identified with the Berry phase) is properly quantized. This study implies that the numerical value of this parameter is a pure number (independent of the molecular system): η = $ 2\sqrt 2 /\pi $ (= 0.9003) and that there is a good possibility that this value is a novel characteristic molecular constant for a certain class of tri‐atomic systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011