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     

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.     

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.     

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.     

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 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.     

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     

E ⊗ ϵ Jahn–Teller anharmonic coupling for an octahedral system

The coupling between doubly degenerate electronic states and doubly degenerate vibrations is analyzed for an octahedral system on the basis of the introduction of an anharmonic Morse potential for the vibronic part. The vibrations are described by anharmonic coherent states and their linear coupling with the electronic states is considered. The matrix elements of the vibronic interaction are built and the energy levels corresponding to the interaction Hamiltonian derived. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Evidence of Amine–CO2 Interactions in Two Pillared‐Layer MOFs Probed by X‐ray Crystallography

Two pillared‐layer metal–organic frameworks (MOFs; PMOF‐55 and NH₂‐PMOF‐55) based on 1,2,4‐triazole and terephthalic acid (bdc)/NH₂‐bdc ligands were assembled and display framework stabilities, to a certain degree, in both acid/alkaline solutions and toward water. They exhibit high CO₂ uptakes and selective CO₂/N₂ adsorption capacities, with CO₂/N₂ selectivity in the range of 24–27, as calculated by the ideal adsorbed solution theory method. More remarkably, the site and interactions between the host network and the CO₂ molecules were investigated by single‐crystal X‐ray diffraction, which showed that the main interaction between the CO₂ molecules and PMOF‐55 is due to multipoint supramolecular interactions of C?H???O, C???O, and O???O. Amino functional groups were shown to enhance the CO₂ adsorption and identified as strong adsorption sites for CO₂ by X‐ray crystallography.     

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.     

Structural investigations of carrageenan–surfactant systems by synchrotron X‐ray scattering

Small‐angle X‐ray scattering by means of synchrotron radiation was used to study the interaction of κ‐ and ι‐carrageenan of different molar mass in the presence of the gel‐inducing ions, K⁺, with the ionic surfactants cetylpyridinium chloride (CPC) and dodecylpyridinium chloride (DPC). This interaction resulted in a more or less complete shrinking of the gel and in the formation of ordered periodic structures of the surfactant in conjunction with the carrageenan molecules. The influence of the polymer concentration for a given surfactant concentration, the content of surfactant for the same concentration of the polysaccharide, the molar mass, and the linear charge density of the polymer were all investigated. Decreasing the length of the alkyl chain of the surfactant, increasing the charge density of the polymer chain, and increasing the polymer concentration for the samples explored improved the ordering in the carrageenan–surfactant complexes. The structures of the κ‐carrageenan–CPC complexes were investigated as a function of temperature during reversible heating–cooling cycles, and it was shown that the addition of the surfactant lead to a more pronounced temperature stability of polymer network. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2851–2859, 2000     

Thermotropic Liquid Crystals Based on Extended 2,5‐Disubstituted‐1,3,4‐Oxadiazoles: Structure–Property Relationships,Variable‐Temperature Powder X‐ray Diffraction,and Small‐Angle X‐ray Scattering Studies

A class of extended 2,5‐disubstituted‐1,3,4‐oxadiazoles R¹‐C₆H₄‐{OC₂N₂}‐C₆H₄‐R² (R¹=R²=C₁₀H₂₁O 1 a , p‐C₁₀H₂₁O‐C₆H₄‐C?C 3 a , p‐CH₃O‐C₆H₄‐C?C 3 b ; R¹=C₁₀H₂₁O, R²=CH₃O 1 b , (CH₃)₂N 1 c ; F 1 d ; R¹=C₁₀H₂₁O‐C₆H₄‐C?C, R²=C₁₀H₂₁O 2 a , CH₃O 2 b , (CH₃)₂N 2 c , F 2 d ) were prepared, and their liquid‐crystalline properties were examined. In CH₂Cl₂ solution, these compounds displayed a room‐temperature emission with λ_max at 340–471 nm and quantum yields of 0.73–0.97. Compounds 1 d , 2 a – 2 d , and 3 a exhibited various thermotropic mesophases (monotropic, enantiotropic nematic/smectic), which were examined by polarized‐light optical microscopy and differential scanning calorimetry. Structure determination by a direct‐space approach using simulated annealing or parallel tempering of the powder X‐ray diffraction data revealed distinctive crystal‐packing arrangements for mesogenic molecules 2 b and 3 a , leading to different nematic mesophase behavior, with 2 b being monotropic and 3 a enantiotropic in the narrow temperature range of 200–210 °C. The structural transitions associated with these crystalline solids and their mesophases were studied by variable‐temperature X‐ray diffractometry. Nondestructive phase transitions (crystal‐to‐crystal, crystal‐to‐mesophase, mesophase‐to‐liquid) were observed in the diffractograms of 1 b, 1 d , 2 b, 2 d , and 3 a measured at 25–200 °C. Powder X‐ray diffraction and small‐angle X‐ray scattering data revealed that the structure of the annealed solid residue 2 b reverted to its original crystal/molecular packing when the isotropic liquid was cooled to room temperature. Structure–property relationships within these mesomorphic solids are discussed in the context of their molecular structures and intermolecular interactions.     

Bismuth Tri‐ and Tetraarylcarboxylates: Crystal Structures,In Situ X‐ray Diffraction,Intermediates and Luminescence

A systematic investigation of the systems Bi³⁺/carboxylic acid/HNO₃ for the tri‐ and tetracarboxylic acids pyromellitic acid (H₄Pyr), trimellitic acid (H₃Tri) and trimesic acid (H₃BTC) acid led to the discovery of five new bismuth carboxylates. Structural characterisation allowed the influence of the linker geometry and the Bi³⁺:linker molar ratio in the starting solution on the crystal structure to be determined. The crystallisation of three selected compounds was investigated by in situ energy‐dispersive X‐ray diffraction. Three new crystalline intermediates were observed within minutes, and two of them could be isolated by quenching of the reaction mixture. Their crystal structures were determined from laboratory and synchrotron X‐ray powder diffraction data and allowed a possible reaction pathway to be established. In depth characterisation of the luminescence properties of the three bismuth pyromellate compounds was carried out. Fluorescence and phosphorescence could be assigned to (mainly) ligand‐ and metal‐based transitions. The polymorphs of Bi(HPyr) exhibit different luminescence properties, although their structures are very similar. Surprisingly, doping of the three host structures with Eu³⁺ and Tb³⁺ ions was only successful for one of the polymorphs.     

Quantum‐Chemical and Electrochemical Investigation of the Electrochemical Windows of Halogenated Carborate Anions

The range of electrochemical stability of a series of weakly coordinating halogenated (Hal=F, Cl, Br, I) 1‐carba‐closo‐dodecaborate anions, [1‐R‐CB₁₁X₅Y₆]^? (R=H, Me; X=H, Hal, Me; Y=Hal), has been established by using quantum chemical calculations and electrochemical methods. The structures of the neutral and dianionic radicals, as well as the anions, have been optimized by using DFT calculations at the PBE0/def2‐TZVPP level. The calculated structures are in good agreement with existing experimental data and with previous calculations. Their gas‐phase ionization energies and electron affinities were calculated based on their optimized structures and were compared with experimental (cyclic and square‐wave) voltammetry data. Electrochemical oxidation was performed in MeCN at room temperature and in liquid sulfur dioxide at lower temperatures. All of the anions show a very high resistance to the onset of oxidation (2.15–2.85 V versus Fc^0/+), with only a minor dependence of the oxidation potential on the different halogen substituents. In contrast, the reduction potentials in MeCN are strongly substituent dependent (?1.93 to ?3.32 V versus Fc^0/+). The calculated ionization energies and electron affinities correlate well with the experimental redox potentials, which provide important verification of the thermodynamic validity of the mostly irreversible redox processes that are observed for this series. The large electrochemical windows that are afforded by these anions indicate their suitability for electrochemical applications, for example, as supporting electrolytes.     

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 ).     

Revealing the Dynamic Structure of Complex Solid Catalysts Using Modulated Excitation X‐ray Diffraction

X‐ray diffraction (XRD) is typically silent towards information on low loadings of precious metals on solid catalysts because of their finely dispersed nature. When combined with a concentration modulation approach, time‐resolved high‐energy XRD is able to provide the detailed redox dynamics of palladium nanoparticles with a diameter of 2 nm in 2 wt % Pd/CZ (CZ=ceria–zirconia), which is a difficult sample for extended X‐ray absorption fine structure (EXAFS) measurements because of the cerium component. The temporal evolution of the Pd(111) and Ce(111) reflections together with surface information from synchronous diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) measurements reveals that Ce maintains Pd oxidized in the CO pulse, whereas reduction is detected at the beginning of the O₂ pulse. Oxygen is likely transferred from Pd to Ce³⁺ before the onset of Pd re‐oxidation. In this context, adsorbed carbonates appear to be the rate‐limiting species for re‐oxidation.