A valence bond analysis of electronic degeneracies in Jahn-Teller systems: low-lying states of the cyclopentadienyl radical and cation

The lowest doublet electronic state of the cyclopentadienyl radical (CPDR) and the lowest singlet state of the cyclopentadienyl cation (CPDC) are distorted from the highly symmetric D(5h) structure due to the Jahn-Teller effect. A valence bond analysis based on the phase-change rule of Longuet-Higgins reveals that in both cases the distortion is due to the first-order Jahn-Teller effect. It is shown that, while for the radical an isolated Jahn-Teller degeneracy is expected, in the case of the cation the main Jahn-Teller degeneracy is accompanied by five satellite degeneracies. The method offers a chemically oriented way for identifying the distortive coordinates.     

Structure and bonding of the vanadium(III) hexa-aqua cation. 2. Manifestation of dynamical Jahn-Teller coupling in axially distorted vanadium(III) complexes

Ground-state spin-Hamiltonian parameters, magnetic data, and electronic Raman spectra of hexacoordinate vanadium(III) complexes are calculated with consideration to the ((3)A (3)E) e vibronic interaction and compared to experimental data. It is shown that the zero-field-splitting of the (3)A(g) (S(6)) ground term may be reduced significantly by the dynamical Jahn-Teller effect, particularly when the pi-anisotropy of the metal-ligand bonding interaction is significant, and the energy of the Jahn-Teller active vibration is comparable to the diagonal axial field. The dynamical Jahn-Teller effect may also give rise to a significant enhancement in the Raman intensity of overtones and higher harmonics of Jahn-Teller active vibrations, when the energies of these transitions fall in the proximity of intra-(3)T(1g) (O(h)) electronic Raman transitions. A simple method of conducting vibronic coupling calculations is described, employing ligand field matrices generated by angular overlap model calculations, which may in principle be applied to any transition metal complex.     

Jahn-Teller effect for short-lived states: study of the complex potential energy surfaces

The Jahn-Teller effect for bound electronic states has been investigated for many decades. In contrast, nothing is known regarding its occurrence for short-lived electronic states. Here we investigate the linear and the quadratic E multiply x e Jahn-Teller effect for degenerate resonance states with special regard to the complex potential energy surfaces. We find many new phenomena for both the real and imaginary parts of the potential energy surfaces including additional minima and intersections. Possible simplifications of the equations describing the adiabatic potential energy surfaces are discussed. We also briefly investigate other Jahn-Teller effects in linear approximation. The theoretical concepts are exemplified by calculating ab initio data for the degenerate Pi(*)-type resonance states of the tris(boramethyl)amin anion along two different doubly degenerate vibrational modes.     

The Jahn-Teller effect in solid state chemistry of transition metal compounds

The general features of the local and cooperative Jahn-Teller effect of dⁿ cations with E_g ground states in octahedral coordination and simple model structures are discussed. Examples of different cooperative Jahn-Teller ordering patterns and of phase transitions from static to partially dynamic and finally fully dynamic Jahn-Teller determined structures are given. While in general a tetragonally elongated coordination of the Jahn-Teller ions is favored, the compressed configuration may be stabilized under certain conditions also. It is demonstrated by some examples that the extent of the Jahn-Teller distortion depends on the symmetry and connection pattern of the polyhedra in the host lattice structure. Finally it is shown that the crossover between high- and low-spin configurations of d⁷ cations is strongly influenced by the additional Jahn-Teller stabilization of the low-spin ²E_g state.     

Density functional theory study of the Jahn-Teller effect and spin-orbit coupling for copper and gold trimers

The Born-Oppenheimer potential energy hypersurfaces of copper and gold trimers were calculated using density functional theory with an analytic potential. The calculated Jahn-Teller distortion energies, pseudorotation barriers, dissociation, and isomerization energies for the two trimers are discussed. Global minima from the surfaces were optimized using the density functional theory method as well as the coupled cluster-singles-doubles-with-triples energies technique. The agreement of the optimized structures with the analytic potential was very good. The Mulliken population analysis compared favorably with the experimental electron spin resonance results. Spin-orbit coupling was subsequently included and the effect was significant for gold, but negligible for copper. The spin-orbit effect suppressed the Jahn-Teller distortion of the gold trimer, and the potential surface with the spin-orbit effect included was also obtained. The spin-orbit splitting for the D(3h) geometry of the gold trimer was in excellent agreement with the most recent infrared spectroscopic results.     

DFT Study on Structural Distortion and Vibronic Coupling of Vanadyl Porphyrin Anion and Cation

The geometries of one-electron reduced/oxidized species （[TOP]-/[VOP] ＋） of vanadyl por- phyrin （VOP） have been calculated with PBE1PBE method. The results show that for both [VOP]- and [VOP]＋ the ground states are triplet, in which one of the two unpaired electron occupies the dxy orbital of the V atom while the other occupies the n-orbital of porphyrin ring. Thus both [VOP]- and [VOP]＋ can be considered as n-radicals. The ground state of neutral VOP molecule is doublet with the unpaired electron occupying dxy orbital of V atom. In contract to the C4v symmetry of neutral VOP molecule, [VOP]- anion has a ＂rectangular＂ distorted C2v structure due to Jahn-Teller effect. The linear vibronic coupling constants for the Jahn-Teller active modes of [TOP]- were evaluated and the node patterns of frontier KS orbitals are used to explain the reason why the distortion occurs along specific modes. The ground state [VOP]＋ has a porphyrin ring with pronounced bond length alternation due to pseudo-Jahn-Teller effect, causing its symmetry declined from C4v to Ca. The bond length alternation is well explained with the node patterns of re-constructed frontier KS orbitals.     

铜镁铝三元水滑石的姜-泰勒效应

采用密度泛函理论(DFT),用CASTEP程序模块,对类水滑石(CuxMg3-xAl-LDHs,x=0-3)周期性模型进行几何全优化,通过分析各体系的结构参数、电子排布、氢键、Mulliken电荷布居、结合能,总结出体系中的姜-泰勒效应和结构稳定性规律.结果表明,姜-泰勒效应不仅存在于d轨道未排满的Cu2+中,在p轨道未排满的Mg2+中也可能存在,且未饱和的d、p轨道共同影响着金属离子姜-泰勒畸变的大小.在CuxMg3-xAl-LDHs(x=0-3)中,铝八面体和镁八面体分别以稳定的拉长的八面体形式存在.而随着Cu2+的增加,铜八面体逐渐从压扁的八面体向稳定的拉长的八面体形式转变,体系获得了逐渐增多的姜-泰勒稳定化能.总体上,随着Cu2+的增加,体系中姜-泰勒效应导致的畸变使主客体间的氢键和静电作用力均有减弱趋势,且体系的结合能绝对值逐渐减小,故体系稳定性下降.这有助于从理论上进一步认识含铜水滑石的姜-泰勒效应.     

Nuclear dynamics for a three-state Jahn-Teller model system

We report wavepacket dynamics on a model system with a three-state conical intersection. Quantum wavepacket dynamics using the multiconfigurational time-dependent Hartree method have been carried out for the T ? (e + t(2)) Jahn-Teller problem, using a Jahn-Teller vibronic model Hamiltonian. The effects of the magnitude of the coupling parameters and of the initial position of the wavepacket on the dynamics around the three-state conical intersection have been considered. It was found that the effect of the coupling strength is not dramatic for the population transfer in most cases, but the details of the dynamics and the involvement of the different modes are affected by it.     

B(OCH3)3电子结构的Hel紫外光电子能谱研究

人们知道，Hel紫外光电子能借（PES）提供研究分子轨道能量、能级次序、成键类型以及由光电子峰强度所反映的电离轨道特性等信息是其他手段没有的，因而PES技术已广泛地用于众多化合物分子电子结构的研究中．有机础化合物由于它们高的反应活性作为合成试剂而信受人们重视［‘－     

ZnSe: Fe2+中的动态Jahn-Teller效应和远红外光谱的研究

推导了3d4/3d6离子基态 5D在立方晶体场、自旋-轨道耦合和动态Jahn-Teller效应作用下的哈密顿矩阵,并用对角化该哈密顿矩阵的方法研究了Fe2+在ZnSe中的远红外光谱,理论计算与实验符合得好.研究表明,在ZnSe∶ Fe2+中,比晶体场理论分析多出的分裂谱线是Fe2+与ZnSe晶格间的动态Jahn-Teller效应引起的.还预测了其它Jahn-Teller效应分裂谱.所推导的哈密顿矩阵对研究3d4/3d6离子在立方晶体中的精细光谱、电子顺磁共振谱和动态Jahn-Teller分裂都是有用的.     

Phase transitions in CuZrF6 and CrZrF6: A Mössbauer and EPR study of local and cooperative Jahn-Teller distortions

CuZrF₆ and CrZrF₆ undergo phase transitions between 100 and 450K, which are induced by crystal packing effects and changes from dynamical to static Jahn-Teller distortions of the Cu(Cr)F₆ octahedra. We analyzed in particular the transitions of the Jahn-Teller type using ⁵⁷Fe²⁺, doped into the Cu²⁺(Cr²⁺) sites, as a Mössbauer probe. The quadrupole splitting is large in the region of static distortions and essentially reflects the distortion symmetry of the host Cu(Cr)F₆ polyhedra, while it vanishes in the case of a dynamical Jahn-Teller effect. Ligand field, EPR, and magnetic data are given in addition and are discussed with respect to the structures of the host compounds and the cooperative Jahn-Teller order of the tetragonally elongated Cu(Cr)F₆ polyhedra in the low-temperature phases.     

The Jahn-Teller and Barnett effects

In the usual formulation of the Jahn-Teller effect a simplification is made in going from the adiabatic to the crude adiabatic approximation in which the electronic parts of the vibronic wavefunction are assumed independent of the nuclear coordinates. This then neglects momentum coupling in the vibronic coupling matrix. The momentum coupling has been termed the molecular Barnett effect when the active vibration transforms as the irreducible representation of a rotation in the molecular point group. Experimental evidence for the molecular Barnett effect has recently been found. In this paper the various point groups in which momentum and Barnett coupling can occur are investigated. A vibration capable of momentum coupling is contained in the asymmetric direct product of the degenerate electronic state and, as with the Jahn-Teller effect, is possible in the orbitally degenerate electronic states of molecules of all non-linear point groups. A static distortion along such a coordinate will lift the electronic degeneracy. Unlike the Jahn-Teller effect, however, in some point groups a minimum complexity of the molecule is required before such coupling can occur. In particular it will be absent in the degenerate electronic states of such simple molecules of the form X₃(D_3h); XY₃(C_3v, D_3h); XY₄(T_d); and XY₆(O_h).     

铜锌镁铝四元水滑石的微观结构及其姜-泰勒畸变

采用密度泛函理论(DFT),选取CASTEP程序模块,对铜锌镁铝四元水滑石[(M)-IV-LDHs(M=Cu,Zn,Mg,Al)]周期性模型进行几何全优化,从各体系的结构参数、电子排布、Mulliken电荷布居、结合能、氢键等方面,研究了体系中的姜-泰勒效应、氯离子位置对层板畸变及体系稳定性的影响.优化结果表明,姜-泰勒效应不仅存在于d轨道未排满的Cu2+中,也存在于理论上d轨道排满的Zn2+与p轨道未排满的Mg2+中.氯离子排在金属上方的体系,其金属畸变程度大于氯离子排在非金属上方的体系.同时,对于本文选取的8个CuAl-IV-LDHs体系,结合能绝对值按照1-8号逐渐降低,体系的稳定性下降,最终转变为不稳定的压扁的八面体构型.这有助于从理论上对含铜四元水滑石的姜-泰勒效应进一步认识.     

Pu4+分子离子的几何构型与Jahn-Teller

It demorstrates six stable geometrical configurations of electronic states for Pu4+ using the density functional method B3LYP with relativistic effective core potentials. The most stable electronic state of Pu4+ is of the planar C2v configuration. The Jahn-Teller distortions from the configurations Pu4+(Td) and Pu4+(D4h) exist. The analysis of the relationships among these various geometrical configurations, based on the Jahn-Teller effect, vibronic interaction and the resolution of group representations, is in agreement with the calculated results.     

The Jahn-Teller effect in CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) studied by zero kinetic energy photoelectron spectroscopy

The Jahn-Teller effect in CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) has been found experimentally by zero kinetic energy (ZEKE) photoelectron spectroscopy using coherent extreme ultraviolet (XUV) radiation. The vibronic bands of CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) at about 4500 cm(-1) above the ground states have been recorded. The spectra consist mainly of the Jahn-Teller active C-C[triple bond]N bending (v(8)), the CN stretching (v(2)), the CH(3) (CD(3)) deforming (v(6)), and the C-C stretching (v(4)) vibronic excitations. The Jahn-Teller active vibronic bands (v(8)) have been assigned with a harmonic model including linear and quadratic Jahn-Teller coupling terms, taking into account only the single mode vibronic excitation. The ionization potentials of CH(3)CN and CD(3)CN have also been determined, and their values are 12.2040(+/-0.001) and 12.2286(+/-0.001) eV, respectively.     

Anomalous polarization in the resonance Raman effect of octahedral hexachloroiridate (IV) ion

A rigorous resonance Raman effect was observed for the octahedral IrCl₆^2? ion. Anomalous polarization was found for all the observed Raman bands including the totally symmetric ν₁ band. The relation between the enomaly in the depolarization degree and the Jahn-Teller effect in the excited electronic state is suggested.     

Jahn-Teller Effects in a Vanadate-Stabilized Manganese-Oxo Cubane Water Oxidation Catalyst

Heuristic rules that allow identifying the preferred mixed-valence isomers and Jahn-Teller axis arrangements in the water oxidation catalyst [(Mn₄O₄)(V₄O₁₃)(OAc)₃]ⁿ⁻ and its activated form [(Mn₄O₄)(V₄O₁₃)(OAc)₂(H₂O)(OH)]ⁿ⁻ are derived. These rules are based on computing all combinatorially possible mixed-valence isomers and Jahn-Teller axis arrangements of the Mn^III atoms, and associate energetic costs with some structural features, like crossings of multiple Jahn-Teller axes, the location of these axes, or the involved ligands. It is found that the different oxidation states localize on different Mn centers, giving rise to clear Jahn-Teller distortions, unlike in previous crystallographic findings where an apparent valence delocalization was found. The low barriers that connect different Jahn-Teller axis arrangements suggest that the system quickly interconverts between them, leading to the observation of averaged bond lengths in the crystal structure. We conclude that the combination of cubane-vanadate bonds that are chemically inert, cubane-acetate/water bonds that can be activated through a Jahn-Teller axis, and low activation barriers for intramolecular rearrangement of the Jahn-Teller axes plays an essential role in the reactivity of this and probably related compounds.     

Jahn-Teller and Pseudo Jahn-Teller Effects: Influences on the Electronic Structures of Small Transition,Main Group and Mixed Metal Clusters

Structural Chemistry - The present review article focuses on the impact of the Jahn-Teller effect (JTE) including hidden JTE and pseudo JTE on the ground and low-lying electronic structures of...     

One-photon mass-analyzed threshold ionization spectroscopy of 1,3,5-trifluorobenzene: the Jahn-Teller effect and vibrational analysis for the molecular cation in the ground electronic state

One-photon mass-analyzed threshold ionization spectrum of 1,3,5-trifluorobenzene was obtained by using vacuum ultraviolet radiation generated by four-wave difference frequency mixing in Kr. The Jahn-Teller parameters for the e' modes (nu(8)-nu(14)) of 1,3,5-C(6)H(3)F(3)(+) in the ground electronic state needed for spectral analysis were taken from the density functional theory results initially and were upgraded through fits to the experimental results. Excellent agreement was achieved between the experimental and calculated Jahn-Teller energy levels. Assignments of the Jahn-Teller inactive modes were accomplished by referring to the calculated frequencies and the selection rule. The ionization energy of 1,3,5-trifluorobenzene determined from the position of the 0-0 band was 9.6359+/-0.0006 eV.     

Why are some ML2 molecules (M = Ca, Sr, Ba; L = H, F, Cl, Br) bent while others are linear? Implications of the pseudo Jahn-Teller effect

The unexpected bent geometries of some alkaline earth dihalides and dihydrides, ML(2) (M = Ca, Sr, Ba; L = H, F, Cl, Br) have been explained in the literature using various models that attribute the effect to different phenomena like covalency, metal core polarization, sd-hybridization, and electron pair repulsion. We employ (based on first principles) the pseudo Jahn-Teller effect, as the only source of instability of high-symmetry configurations in nondegenerate states, to analyze the origin of the geometry of these systems and show that this approach explains all of their main structural features, including the topology of the Laplacian of the electron density and the vibrational frequencies. The main contribution to the distortion of the linear configuration is due to the pseudo Jahn-Teller mixing by bending of the sigma(u) HOMO formed by the ligand orbitals with the unoccupied pig orbitals of the metal (with main d(xz) and d(yz) character), resulting in new covalency which stabilizes the bent configuration. We show that the model approaches to the problem, mentioned above, are either restricted particular cases of the pseudo Jahn-Teller interaction, or they yield very small contributions to the instability that do not explain the origin of the bending. All of our conclusions are supported by high-quality ab initio calculations.