关于Jahn—Teller效应

Jahn-Teller效应是一种重要的物理现象,随着分子静态和动态性质研究的不断深入,它在现代化学中的地位变得愈来愈重要了。本文拟对Jahn-Teller效应的物理本质及有关问题做些讨论。一、Jahn-Teller效应与绝热近似对一般的分子体系,其薛定谔方程可表示为 Hψ(γ,Q)=Eψ(γ,Q) (1)其中 H=H_γ+H_Q +V(γ,Q)     

Jahn–Teller Disproportionation Induced Exfoliation of Unit-Cell Scale ϵ-MnO2

Exfoliation of non-layered (structurally) bulk materials at the nanoscale is challenging because of the strong chemical bonds in the lattice, as opposed to the weak van der Waals (vdW) interactions in layered materials. We propose a top-down method to exfoliate ϵ-MnO₂ nanosheets in a family of charge-ordered La_1−xAE_xMnO₃ (AE=Ca, Sr, Ba) perovskites, taking advantage of the Jahn–Teller disproportionation effect of Mn³⁺ and bond-strength differences. ϵ-MnO₂ crystallized into a nickel arsenide (NiAs) structure, with a thickness of 0.91 nm, displays thermal metastability and superior water oxidation activity compared to other manganese oxides. The exfoliation mechanism involves a synergistic proton-induced Mn³⁺ disproportionation and structural reconstruction. The synthetic method could also be potentially extended to the exfoliation of other two-dimensional nanosheet materials with non-layered structures.     

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.     

C^＋60的Jahn—Teller结构畸变

用ＩＮＤＯ系列方法对Ｃ６０的阳离子自由基Ｃ＾＋６０进行几何构型变化，得到Ｄ５ｄ对称性的构型，表明Ｃ＾＋６０确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ结构畸变，形成７种键和４种不等同Ｃ原子，且单键变短，双键变长，键长趋于平均化，体系的正电荷和单电子主要分布在赤道附近，从而导致了赤道附近Ｃ原子的高反应活性。     

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.     

Magnetic criteria of aromaticity in a benzene cation and anion: how does the Jahn–Teller effect influence the aromaticity?

The aromatic/antiaromatic behavior of the Jahn–Teller (JT) active benzene cation and anion has been investigated using Density Functional Theory (DFT) calculations of Nuclear Independent Chemical Shifts (NICS) and magnetic susceptibility. NICS parameters have been scanned along the Intrinsic Distortion Path (IDP) for the benzene cation showing antiaromaticity which decreases with increasing deviation from D_6h to D_2h symmetry. Changes in NICS values along the IDP from D_6h to C_2v in the benzene anion revealed non-aromatic character.     

C_（60）~＋的Jahn－Teller结构畸变

用ＩＮＤＯ系列方法对Ｃ_（６０）的阳离子自由基Ｃ_（６０）~＋进行几何构型优化，得到Ｄ_（５ｄ）对称性的构型，表明Ｃ_（６０）~＋确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ结构畸变，形成７种键和４种不等同Ｃ原子，且单键变短，双键变长，键长趋于平均化，体系的正电荷和单电子主要分布在赤道附近，从而导致了赤道附近Ｃ原子的高反应活性。     

Jahn－Teller变形后C60－的结构和电子光谱

用INDO系列方法对C₆₀^－进行几何构型优化,得到D_3d对称性的构型,表明C₆₀^－确实发生了Jahn-Teller畸变,导致单键变短,双键变长,形成10种键,6种不等同碳原子,并以此构型为基础,计算了C₆₀^－的电子光谱,与实验结果吻合;同时对光谱进行了理论指认;最后对C₆₀^－的3种构型：D_5d,D_3d,D_2h的几何构型、能量、光谱和反应特性进行了分析、比较和总结。     

A Jahn–Teller analysis of K3 and Rb3 in the electronic states 1E′ and 1E″

The potential energy surfaces (PES) of the Jahn–Teller distorted doublet 1²E′ (1B₂/1A₁) ground state and 1²E″ (2B₁/1A₂) excited state of alkali metal trimers (K₃, Rb₃) are studied with three high-level computational chemistry methods whose results are compared: single-reference coupled cluster, equation-of-motion coupled cluster and multi-reference second-order Rayleigh–Schrödinger perturbation theory. The doubly degenerate E electronic state interacts with the twofold degenerate vibrational e mode. We use the E ⊗ e Jahn–Teller effect theory to analyze in detail one- and two-dimensional cuts of the PES as a function of the symmetry-adapted internal coordinates Q_s, Q_x and Q_y and we extract the associated Jahn–Teller parameters. Spin-orbit coupling is accounted for by means of the Effective-Core-Potential-LS technique and spin-orbit splitting constants are extracted. We also provide the geometries, the binding energies and tentative vibronic spectra for the 1²E″ ← 1²E′ transitions.     

Jahn—Teller变形后—C60^—的结构和电子学谱

用ＩＮＪＤＯ系列方法对Ｃ６０＾－进行几何构型优化，得到Ｄ３ｄ对称性的构型，表明Ｃ６０＾－确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，导致单键变短，双键变长，形成１０种键，６种不等同碳原子，并以此构型为基础，计算了Ｃ６０＾－的电子光谱，与实验结果吻合；同时对光谱进行了理论指认；最后对Ｃ＾６０－的３种构型：Ｄ５ｄ，Ｄ３ｄ，Ｄ２ｈ的几何构型、能量、光谱和反应特性进行了分析、比较和总结。     

C60^2—单态的Jahn—Teller畸变和光谱性质

用ＩＮＤＯ系列方法，对Ｃ６０＾２－单态进行几何构型优化，得到３种不同对称性的构型：Ｄ５ｄ，Ｄ３ｄ，Ｄ２４，表明Ｃ６０＾２－已发生Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，Ｄ５ｄ有４种原子７种键；Ｄ３ｄ有６种原子１０种键；Ｄ２ｈ有９种子１５种键，额外负电荷主要分布在赤道附近，以这３种构型为基础分别计算了Ｃ６０＾２－单态的电子光谱，说明Ｃ６０＾２－的基态应该是三态。     

C60的理论研究—Jahn—Teller变形,电子结构和光谱性质

本文用ＩＮＤＯ系列方法对Ｃ６０进行了几何构型优化，得到Ｄ５ｄ对称性的构型，表明Ｃ６０确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，导致原Ｃ６０Ｉｈ对称性的球体沿五重轴拉长而单键变短双键变长。其额外负电荷主要分布在赤道附近，以此构型为基础，计算了Ｃ６０的电子光谱，与实验值吻合，在对光谱进行理论指认的同时讨论了光谱红移的原因。     

Jahn–Teller coupling and the influence of strain in Tg and Eg ground and excited states – A ligand field and DFT study on halide MIIIX6 model complexes [M = TiIII–CuIII; X = F−, Cl−]

In contrast to well established experimental results of vibronic coupling effects in octahedral dⁿ complexes with E_g ground states (Cu²⁺, Ag²⁺; Cr²⁺, Mn³⁺ etc.), not much useful material is available for the Jahn–Teller (JT) effect in orbital triplet ground states. The present study is concerned with this deficiency, providing data for octahedral halide model complexes with 3dⁿ cations – in particular for Ti^III, V^III and high-spin Co^III, Ni^III with T_2g and T_1g ground states, which involve, to first-order, solely splitting of the π-antibonding t_2g MOs. Besides experimental results – structural and spectroscopic, mainly from d–d spectra – data from computations are needed for a quantitative treatment of the T_g ? (?_g + τ_2g) vibronic interaction as well as in the E_g ? ?_g coupling case (Mn^III, low-spin Ni^III); DFT was the method of choice, if only critically selected outcomes are utilised. The theoretical bases of the treatment are the dⁿ ligand field matrices in O_h, extended by the inclusion of lower-symmetry distortion parameters, and the conventional theory of vibronic coupling. Caution is needed when classifying the effects of interelectronic repulsion; DFT does not reproduce the magnitudes of the Racah parameters B, C, as deduced from the d–d spectra, properly – the presumed reasons are analysed. DFT even allows one to deduce reliable vibronic coupling constants via the analysis of orbitally degenerate excited states (Cr^III, ⁴A_2g ground state). The group-theoretical analysis of the interaction with the JT-active ?_g and τ_2g modes yields D_4h, D_3d and D_2h as the possible distortion symmetries in the case of a T_g ground state. The DFT-calculations give clear evidence, that the D_4h stationary points represent the absolute minima in the T_g ? (?_g + τ_2g) potential surface – in agreement with experiment, where available. For the first time, vibronic coupling constants, characterising JT splitting of ground and excited T_g states, can be presented for trivalent 3dⁿ cations in octahedral halide ligand fields. They turn out to be smaller by a factor of almost 3 in comparison to those, which determine the coupling in σ-antibonding e_g MOs.The tetragonal splitting of T_g states is typically only small, around 0.1 eV, and suggests that strain influences from a specific ligand arrangement and/or the presence of different ligands may modify the potential surface considerably. We have studied such effects via compounds A^IM^IIIF₄, where an elastic strain induced by the host structure, and a binding strain, due to the simultaneous existence of (largely) terminal and of bridging ligands, are active. A novel strain model, in its interplay with JT coupling, is proposed and applied – using energies from the d–d spectra, structural results and data from DFT.Chloride complexes are only known for Ti^III to Fe^III; the rather small electronegativity already of Co^III suggests a reducing ligand-to-metal (3dⁿ) electron transfer for n ≥ 6. Similarly, the low-lying ligand-to-metal charge transfer bands in the d–d spectra of the Cu^IIIF₆^3? complex and the reduced T_g ? ?_g coupling strength suggest a pronounced covalency of the Cu^III–F, and, even more distinctly, of the Cu^III–O bond, which is of interest for superconductivity. The Ni^IIIF₆^3? polyhedron possesses a low-spin configuration in the elpasolite structure. The spectroscopic evidence and the DFT data indicate, that the minimum positions of the alternative _a²A_1g(_a²E_g) and _a⁴A_2g (_a⁴T_1g) potential curves are only ≤0.02 eV apart, giving rise to interesting high-spin/low-spin phenomena. It is the strong E_g ? ?_g as compared to the T_1g ? ?_g coupling, which finally stabilises a spin-doublet ground state in D_4h.We think, that the selected class of solids is unique particularly for the study of Jahn–Teller coupling in T ground states, with model character for other systems. In our overview a procedure is sketched, which uses reliable computational results (here from DFT) for supplementing incomplete experimental data, and presents – on a semiquantitative scale – convincing statements, consistent with chemical intuition. It is also a pleading for ligand field theory, which rationalises d-d spectra in terms of chemical bonding; though the latter spectra provide frequently only rather coarse information, their assistance in the energy analysis is crucial.     

C_（60）~（2－）单态的Jahn－Teller畸变和光谱性质

用ＩＮＤＯ系列方法，对Ｃ单态进行几何构型优化，得到３种不同对称性的构型：Ｄ５ｄ、Ｄ３ｄ、Ｄ２ｈ。表明Ｃ已发生Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，Ｄ５ｄ有４种原子７种键；Ｄ３ｄ有６种原子１０种键；Ｄ２ｈ有９种原子１５种键。额外负电荷主要分布在赤道附近。以这３种构型为基础分别计算了Ｃ单态的电子光谱，说明Ｃ的基态应该是三态。     

Excited state structural dynamics and Herzberg–Teller coupling of tetraphenylporphine explored via resonance Raman spectroscopy and density functional theory calculation

Resonance Raman spectra of free-base tetraphenylporphine (TPP) were obtained with 397.9, 416, and 435.7 nm excitation wavelengths and density functional calculations were done to elucidate the electronic transitions and the resonance Raman spectra (RRs) of TPP. The RRs indicate that the Franck–Condon region photodynamics for S₀ → S₄ electronic state is predominantly along the C_m–ph stretch while that for S₀ → S₃ electronic state is predominantly along the porphin ring C_βC_β stretch. Non-totally symmetric vibrational modes were regularly presented in resonance Raman spectra: the shorter the excitation wavelengths were, the stronger intensity the modes had, which can be interpreted in terms of electric dipole transition moments caused by Franck–Condon and Herzberg–Teller coupling.Four non-total symmetry vibrational mode υ_52, υ₆₄, υ₉₇ and υ₁₃₀ in A₂ irreducible representative of TPP were observed in 397.9, 416 and 435.7 nm resonance Raman spectrum. With the shorter wavelength laser excitations at 416 or 397.9 nm, the A₂ vibrational modes show more enhanced Raman intensity by comparison with those in the TPP spectrum excited at 435.7 nm.     

Jahn－Teller畸变后D_（2h） C_（60）~－的电子结构和光谱

用ＩＮＤＯ系列方法对Ｃ_（６０）自由基负离子进行了几何构型优化，得到Ｄ_（２ｈ）对称性的构型，表明Ｃ_（６０）~－确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，导致单键变短，双键变长，形成１５种键，９种不等同碳原子，其额外负电荷主要分布在赤道附近。以此构型为基础，计算了Ｃ_（６０）~－的电子光谱，与实验值吻合，在对光谱进行理论指认的同时讨论了光谱红移的原因。     

Average energy and quantum similarity of a time dependent quantum system subject to Pöschl–Teller potential

Journal of Mathematical Chemistry - Exact solutions of time-dependent Schrödinger equation in presence of generalized Pöschl–Teller like potential plus oscillator potential are...