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     

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     

C60系列结构,制备分离方法与性质的研究进展

本文综述地评述了Ｃ６０的结构，制备分离方法，及其衍生物表现出的异常的物理、化学性质，其碱金属盐呈现导电性或超导性、铁磁性、光学非线性、耐磨擦性能等。为进一步研究Ｃ６０及其衍生物提供了信息。     

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.     

BaxC60 fullerides: π Electronic peculiarities of the C60 molecule and their consequences for the solid state

The electronic structure of Ba_xC₆₀ fullerides was studied theoretically under special consideration of π electronic effects in the C₆₀ molecule. Band structure data were derived by an intermediate neglect of differential overlap (INDO) crystal orbital (CO) approach. Different electronic configuration were evaluated in the Ba-doped C₆₀ fullerides. Ba_xC₆₀ solids with x=0, 3, 4, 6 are insulators. For a Ba₅C₆₀ model extrapolated from the crystal structure of Ba₆C₆₀, a finite band gap is also predicted. For a Ca₅C₆₀-like structure of Ba₅C₆₀, a quasi-degeneracy between a metallic configuration and an insulating Mott-like state was found. With an increasing Ba-to-C₆₀ charge transfer (CT), sizable changes in the π system of C₆₀ occur. In the neural molecule and for not too high an electron count, the π electrons form more or less electronically isolated hexagon–hexagon (6–6) “double” bonds with only minor hexagon–pentagon (6–5) “double-bond” admixtures. In the vicinity of C₆₀¹²⁻, the 6–6 bonds have lost most of their double-bond character while it is enhanced for the 6–5 bonds. In highly charged anions, the π electron system of the soccer ball approaches a configuration with 12 decoupled 6π electron pentagons. For electron numbers between C₆₀ and C₆₀¹²⁻, the net π bonding is not weakened. The INDO CO results of the Ba_xC₆₀ solids are supplemented by INDO MO and ab initio (3-21 G* split-valence basis) calculations of molecular C₆₀ and some highly charged anions. Ab initio geometry optimizations show that the bond alternation of C₆₀ with short 6–6 and long 6–5 bonds is inverted in C¹²⁻₆₀. The high acceptor capability of C₆₀ is explained microscopically on the basis of quantum statistical arguments. In the π electron configurations of C₆₀ and C₆₀¹²⁻, the influence of the Pauli antisymmetry principle (PAP) is minimized. The quantum statistics of (π) electron ensembles with a deactivated PAP is of the so-called hard-core bosonic (hcb) type. In these ensembles, the on-site interaction is fermionic while the intersite interaction is bosonic. Energetic consequences of the quantum statistical peculiarities of π systems are explained with the aid of simple model systems; we selected annulenes and polyenes. Computational tools in this step are Green's function quantum Monte Carlo (GF QMC) and full configuration interaction (CI) calculations for the π electrons of the model systems. These many-body techniques were combined with a Pariser–Parr–Pople (PPP) Hamiltonian. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 333–373, 1997     

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.

     

Theoretical study on the structures and electron spectra of C60M12 (M=Li,Na, Be)

Intermediate neglect of differential overlap (INDO) method was used to study the structures and the electronic spectra of C₆₀M₁₂ (M=Li, Na, Be). The calculations indicate that in the minimal energy configuration of C₆₀M₁₂ (M=Li, Na) the C₆₀ cage still retains I_h symmetry and the 12 Li or Na atoms are symmetrically located above the pentagons of the C₆₀ cage, whereas the difference between the double and single bonds has been significantly reduced. In contrast, because six electrons are filled in the fivefold‐degenerated h_g orbital of C₆₀, the C_s structure of C₆₀Be₁₂ has illustrated the occurrence of Jahn‐Teller distortion. Based on the optimized geometries, the electronic absorption spectra were calculated and the nature of red shift was discussed. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 505–509, 1999     

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.     

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     

Degree of electron–nuclear entanglement in molecular states

The degree of electron–nuclear entanglement in molecular states is analyzed. This entanglement has, generally, two sources: delocalization of the electronic and nuclear wave functions and vibronic coupling. For a diatomic molecular ground‐state with a single potential energy minimum, it is demonstrated that the entanglement is a function of the product of the vibrational energy and the Born–Huang potential energy correction evaluated at the minimum. In the case of a double‐well potential energy surface, the deviation from maximal entanglement is determined by the overlap of the electronic and nuclear wave functions evaluated at and around the two minima. The adiabatic states of the E⊗ϵ Jahn–Teller model are shown to be maximally entangled and a relation between the degree of entanglement and Ham's reduction factor for this model is derived. Numerical calculations in the E⊗ϵ model demonstrate a nontrivial relation between entanglement and vibronic coupling. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 526–533, 2000     

Revealing the A‐Site Effect of Lead‐Free A3Sb2Br9 Perovskite in Photocatalytic C(sp3)−H Bond Activation

The lead‐free halide perovskite A₃Sb₂Br₉ is utilized as a photocatalyst for the first time for C(sp³)?H bond activation. A₃Sb₂Br₉ nanoparticles (A₃Sb₂Br₉ NPs) with different ratios of Cs and CH₃NH₃ (MA) show different photocatalytic activities for toluene oxidation and the photocatalytic performance is enhanced when increasing the amount of Cs. The octahedron distortion caused by A‐site cations can change the electronic properties of X‐site ions and further affect the electron transfer from toluene molecules to Br sites. After the regulation of A‐site cations, the photocatalytic activity is higher with A₃Sb₂Br₉ NPs than that with classic photocatalysts (TiO₂, WO₃, and CdS). The main active species involved in photocatalytic oxidation of toluene are photogenerated holes (h⁺) and superoxide anions (^.O₂^?). The octahedron distortion by A‐site cations affecting photocatalytic activity remains unique and is also a step forward for understanding more about halide‐perovskite‐based photocatalysis. The relationship between octahedron distortion and photocatalysis can also guide the design of new photocatalytic systems involving other halide perovskites.     

Pseudo Jahn–Teller origin tracking for symmetry breaking in halogenabenzene: How can a bird fly?

The cyclic iodabenzene molecule (CH)₅I was first introduced and characterized as planar configuration and zwitterionic valence structure by Glukhovtsev in 1991. Recently, it caused researchers' great interest due to the theoretical discovery of a stable bird‐like structure by Hoffmann et al. in 2017 which has similar electronic structure and charge distribution as well‐known Meisenheimer complex C₆H. Inspired by this, we continue to tell the halogenabenzene story by revealing the origin of the bird‐like structure and understanding how the electronic behavior affects the geometrical symmetry for a molecule. By combining the Pseudo Jahn–Teller effect (PJTE) theory with the ab initio calculations for halogenabenzenes (CH)₅X (X = F, Cl, Br, I) and C₆H, it is illustrated that the vibronic coupling of ¹A₁ ground state and ¹B₁ excited states with C_2v planar structure along the out‐of‐plane b₁ distortion triggers the symmetry breaking of planar configuration to form a preferred bird‐like structure. This interpretation can be also applied to explain their different stabilization energies by analyzing numerically the energy gaps of coupled electronic states and PJTE vibronic coupling parameters. Taking use of the PJTE formulation above, we also tracked the origin of restoring to be planar for (CH)₅X²⁺ cation, as well as their isoelectronic species (CH)₅O⁺ and (CH)₅N, and suggests an effective strategy to stabilize the planar configuration for halogenabenzenes.     

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     

Steric Control of the Electronic Ground State in Six-Coordinate Copper(II) Complexes

Replacing the 3- and 3′′-protons of the ligand 2,6-di(pyrazol-1-yl)pyridine L by mesityl groups changes the electronic ground state of [Cu(L)₂]²⁺ complexes from {d}¹ to {d}¹. This is the best example so far for a “homoleptic” Jahn–Teller-compressed six-coordinate Cu^II complex.     

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 ).     

Nitrogen‐doped C60 as a robust catalyst for CO oxidation

The O₂ activation and CO oxidation on nitrogen‐doped C₅₉N fullerene are investigated using first‐principles calculations. The calculations indicate that the C₅₉N fullerene is able to activate O₂ molecules resulting in the formation of superoxide species ( ) both kinetically and thermodynamically. The active superoxide can further react with CO to form CO₂ via the Eley–Rideal mechanism by passing a stepwise reaction barrier of only 0.20 eV. Ab initio molecular dynamics (AIMD) simulation is carried out to evidence the feasibility of the Eley–Rideal mechanism. In addition, the second CO oxidation takes place with the remaining atomic O without any activation energy barrier. The full catalytic reaction cycles can occur energetically favorable and suggest a two‐step Eley–Rideal mechanism for CO oxidation with O₂ catalyzed by the C₅₉N fullerene. The catalytic properties of high percentage nitrogen‐doped fullerene (C₄₈N₁₂) is also examined. This work contributes to designing higher effective carbon‐based materials catalysts by a dependable theoretical insight into the catalytic properties of the nitrogen‐doped fullerene. © 2017 Wiley Periodicals, Inc.     

水溶性五加成二甘肽C60衍生物的合成

通过伯氨氢原子在一定条件下发生α－消除得到活性中间体氮烯的方法，合成了水溶性五加成C60二甘肽衍生物，产率12．3％。     

P2‐Na0.67AlxMn1−xO2: Cost‐Effective,Stable and High‐Rate Sodium Electrodes by Suppressing Phase Transitions and Enhancing Sodium Cation Mobility

Sodium layered P2‐stacking Na_0.67MnO₂ materials have shown great promise for sodium‐ion batteries. However, the undesired Jahn–Teller effect of the Mn⁴⁺/Mn³⁺ redox couple and multiple biphasic structural transitions during charge/discharge of the materials lead to anisotropic structure expansion and rapid capacity decay. Herein, by introducing abundant Al into the transition‐metal layers to decrease the number of Mn³⁺, we obtain the low cost pure P2‐type Na_0.67Al_xMn_1?xO₂ (x=0.05, 0.1 and 0.2) materials with high structural stability and promising performance. The Al‐doping effect on the long/short range structural evolutions and electrochemical performances is further investigated by combining in situ synchrotron XRD and solid‐state NMR techniques. Our results reveal that Al‐doping alleviates the phase transformations thus giving rise to better cycling life, and leads to a larger spacing of Na⁺ layer thus producing a remarkable rate capability of 96 mAh g^‐1 at 1200 mA g^‐1.