Topological representations of Jahn-Teller distortions

Topological representations (top-reps), which originally were developed to model molecular polyhedral isomerization processes, can be extended to depict the relationships between the polygons and polyhedra involved in Jahn-Teller (JT) distortions. Using this approach, the top-rep of the E ? (b _1g + b _2g) distortion of square planar molecules to rectangle and rhombus isomers becomes a rhombus in which the vertices alternately represent distortions to the rectangle and rhombus isomers. Similarly the top-rep of the E ? e distortion of regular O_h octahedra to elongated D_4h tetragonal bipyramids becomes a triangle in which the vertices represent the three distinct tetragonal bipyramids from a given octahedron and the edge midpoints represent lower symmetry rhombic D_2h intermediates. A regular octahedron can be used as a top-rep for the T ? (e + t ₂) distortions of regular octahedra if the 6 vertices represent distortions to D_4h tetragonal bipyramid isomers, the 8 face midpoints represent distortions to D_3d trigonal antiprism isomers, and the 12 edge midpoints represent lower symmetry rhombic D_2h intermediates. In the case of Jahn-Teller T ? h distortions of regular I_h icosahedra, the corresponding top-rep becomes a regular icosahedron in which the 12 vertices represent distortions to pentagonal D_5d isomers, the 20 face midpoints represent distortions to trigonal D_3d isomers, and the 30 edge midpoints represent D_2h intermediates. A 4-dimensional analogue of the tetrahedron (i.e. the 4-simplex) can be used as a top-rep for the G ? g problem and the H ? g component of the H ? (g + 2h) problem for JT distortions of regular icosahedra. In this case the 5 vertices and the 10 edge midpoints correspond to T_h isomers and D_3d intermediates, respectively.     

Structural and spectroscopic properties of small Pun （n= 2-5） molecules

The equilibrium structures and the electronic, spectroscopic and thermodynamic properties of small Pu_n (n=2-5) molecules are systematically investigated using the methods of general gradient approximation (GGA) of density functional theory (DFT). The results show that the bond length of the lowest-energy structure of Pu₂ is 2.578 AA. The ground state structure of Pu₃ is a triangle with D_3h symmetry, whereas for Pu₄, the ground state structure is a square (D_4h) and the spin polarization of 16 for molecule Pu₅ with square geometry (D_4h) is the most stable structure. For the ground state structures, the vibrational spectra as well as thermodynamic parameters are worked out. In addition, the values for the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) along with the energy gap of all the Pu_2-5 structures are presented. The relevant structural and chemical stabilities are predicted.     

Corrigendum

Theoretical calculations of g-tensor components for the spin–orbit quartet, which arises as the ground state in three-coordinate d⁹ complexes and low-spin d⁷ complexes of D_3h symmetry, have been made on the assumption that the spin–orbit interaction is commensurable with the electron-vibrational interaction. The calculations were carried out within the framework of crystal field theory using representations of the hole formalism. The analytical expressions for g-tensor components were obtained limited to first-order terms. It was shown that the account of the electron–vibrational interaction in the excited quartet only provides three-axial anisotropy for the g-tensor. It was shown that the g-tensor rotates in the plane of the three-coordinate structure with consensual motion of the atoms. The resulting expressions for the g-factor components are in good agreement with experimental data. Being universal for a wide range of contributions of the vibronic and spin–orbit interactions, these expressions essentially fill the gap in studying structures of coordination compounds.     

The fine structure levels and spin-singlet contributions to zero-field-splitting parameters of Cr2+ ion in CdGa2S4

A theoretical investigation is reported of the fine structure levels and the spin-singlet contributions to zero-field-splitting (ZFS) parameters for Cr²⁺ ion in CdGa₂S₄ crystals. Firstly, the complete energy matrix including all spin states for a 3d ⁴ ion in tetrahedral D _2d symmetry is constructed according the double-group chain in the strong-field scheme. Then, by diagonalizing the complete energy of electron–electron interactions, the crystal field and the spin–orbit coupling for the Cr²⁺ (3d ⁴) ion in CdGa₂S₄ crystal, the fine structure levels and the spin-singlet contributions to ZFS parameters a, D and F are calculated. The results show that the spin-singlet contribution to D is negligible, but the contributions to a and F are very important. So, to obtain more accurate ZFS parameters for 3d ⁴ ions in the tetrahedral crystals, all spin states should be considered.     

Study on the local structure and EPR spectroscopy of compressed CuX4 (X = N,S, Cl and Br) tetrahedral cluster

The spin Hamiltonian parameters g and A for copper(II) in CuX₄ (X = N, S, Cl and Br) tetrahedrons are theoretically investigated within a uniform model by utilizing the perturbation method and cluster approach for 3d⁹ ions suffering D_2d symmetry in view of host structures and angular distortions in terms of a single parameter β. For all the studied polymers, the isotropy of g tensors g_av and the hyperfine structure constant component A_‖ are found, respectively, to undergo an increasing and decreasing trend with the enlarging average X–Cu–X angle β, while the obtained cubic crystal field parameter D_q and isotropic Fermi contact constant κ are experiencing a declining and growing tendency with the rising Cu–X bond length, respectively. The critical angle β_c is concluded locating in the range of 109.471°–120° in which the g-isotropy value would reach the maximum, while the hyperfine structure factor might vanish that needs to be verified in future X-ray and EPR experiments. This work would be beneficial to the establishment of complete EPR and structure diagram for CuX₄ complexes and the synthesis of new compounds possessing novel physical and chemical properties.     

Spin-spin and spin-other-orbit effects of optical spectra and the spin-Hamiltonian parameters for Cr ions in MgO crystals

An extended complete diagonalization method/microscopic spin-Hamiltonian (CDM/MSH) program has been developed, which is applicable for d³ ions at sites of tetragonal symmetry type I (C_4v, D_2d, D₄, D_4h) and trigonal symmetry type I (C_3v, D₃, D_3d). The Hamiltonian includes the spin-spin (SS) and spin-other-orbit (SOO) magnetic interactions besides the spin-orbit (SO) magnetic interaction usually taken into account. Utilizing the extended CDM/MSH program, the optical spectra, the spin-Hamiltonian (SH) parameters of the ground state ⁴B₁, and the splitting δ(²E) of the first excited ²E state for Cr³⁺ (3d³) ions at C_4v symmetry sites in MgO crystals have been successfully investigated. It is found that although the SO magnetic interaction is the most important one, the contributions to the SH parameters and the optical spectra from the SS and SOO magnetic interactions for Cr³⁺:MgO crystals are appreciable and should not be omitted, especially reaching 27.8% for the zero field splitting parameter D.     

Electronic structure of copper in zinc oxide

Copper influences the electrical and optical properties of zinc oxide to a high degree. Previously this has been explained within the frame of a model assuming Cu⁺⁺ ions to be substitutional for divalent zinc. The observation of additional signals in the Electron Spin Resonance spectrum, however, proved this assumption to be wrong. Satisfying quantitative agreement with experiment is obtained assuming neutral copper atoms at an interstitial site having 3d⁹ 4s² electron configuration and a²D_3/2 ground state. The infrared absorption bands as well as the spin lattice relaxation mechanism give further confirmation of Cu _i ⁰ .     

Relativistic pseudo-Jahn-Teller effect in the square-planar molecules with a central atom

We consider the relativistic multi-mode pseudo-Jahn-Teller effect (²E_u + ²A_2u) × (b_ig + b_2g + e_u) for square-planar molecular complexes with a heavy central atom and the odd number of electrons.

All 32 elements of the double spin group D_4h are determined in the form of space-matrix operators. The 6 × 6 vibronic matrix is derived in the quadratic (with respect to the normal coordinates) approximation for the contributions of electrostatic (non-relativistic) Hamiltonian and in linear approximation for contribution of spin-orbital coupling. Vibronic matrix is represented on the basis of double-value irreducible representations of the symmetry group D_4h     

High‐resolution stimulated Raman spectroscopy and analysis of line positions and assignments for the ν2 and ν3 bands of 13C2H4

High‐resolution stimulated Raman spectra of¹³C₂H₄ in the regions of the ν₂ and ν₃ Raman active modes have been recorded at two temperatures (145 and 296 K) based on the quasi continuous‐wave (cw) stimulated Raman spectrometer at Instituto de Estructura de la Materia IEM‐CSIC in Madrid. A tensorial formalism adapted to X₂Y₄ planar asymmetric tops with D_2h symmetry (developed in Dijon) and a program suite called D_2hTDS (now part of the XTDS/SPVIEW spectroscopic software) were proposed to analyze and calculate the high‐resolution spectra. A total of 103 and 51 lines corresponding to ν₂ and ν₃ Raman active modes have been assigned and fitted in wavenumber with a global root mean square deviation of 0.54 × 10⁻³ and 0.36 × 10⁻³ cm⁻¹, respectively. Due to the fact that the Raman scattering effect is weak, we did not perform in this contribution the line intensities analysis. Copyright © 2016 John Wiley & Sons, Ltd.     

Research on the defect structure and g factors for the tetragonal (CrO4)3− impurity center in ZrSiO4: Cr5+ crystal

ABSTRACT

The EPR g factors g// and g⊥ for the tetragonal (CrO₄)^3? impurity center in ZrSiO4: Cr⁵⁺ crystal are studied from the high-order perturbation formulas based on the two-mechanism (the crystal field and charge-transfer mechanisms) model. The studies indicate that differing from the tetragonally-elongated host (SiO4)^4- tetrahedron, the dominant defect structure of the substitutional (CrO₄)^3? tetrahedron is tetragonally- compressed with the ground state |d_z² due to the Jahn-Teller distortion. Furthermore, the agreement of g factors between calculation and experiment requires a small admixture of the first excited state |d_x²_?y² to the ground state |d_z² due to the vibrational motion of ligands, which leads a compressed (CrO₄)^3? tetrahedron to become a twinkling elongated one, These results are discussed.     

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Crystallographic and magnetic properties of TbCrO4 at low temperature (x-ray and neutron experiments)

The TbCrO₄ zircon-like compound was investigated by X-ray and neutron diffraction experiments in the 4.2–300 K temperature range. It first undergoes a second order phase transition at about 48 K from a tetragonal symmetry: Ia₁/4amd(D¹⁹_4h) to an orthorhombic one: F₂₂₂ (D²⁴_2h). The local symmetry of the Tb³⁺ site is lowered from D_2d to D₂. At 22.8 K, TbCrO₄ undergoes a transition from a paramagnetic phase to a collinear ferromagnetic spin arrangement in the basal plane which is in good agreement with the F₂₂₂ space group. The Tb³⁺ and Cr⁵⁺ magnetic moments are 7.64 and 0.97μ_B respectively.     

C42+的几何构型和Jahn Teller效应

用从头计算法QCISD/6-311G得到了C₄²⁺分子的10种不同的几何构型,其中包括C_s,C_∞v,C_2v,D_2h,D_∞h,D_4h,D_2d,C_3v等不同的构型.计算表明C₄²⁺的T_d构型不能稳定存在,详细讨论了T_{d 关键词： 几何构型 4}²⁺')" href="#">C₄²⁺ Jahn Teller效应     

EPR studies of rhodium in LiH and LiD single crystals

EPR studies of rhodium in LiD and LiH single crystals reveal an axial rhodium complex with the unpaired electron in a 4d_x²?y² molecular orbital and with 5% of the spin density transferred to the planar ligands.     

XAFS investigations of copper(II) complexes with tetradentate Schiff base ligands

X‐ray absorption fine structure spectra have been investigated at the K‐edge of copper in copper(II) salen/salophen complexes: [Cu(salen)] (1), [Cu(salen)CuCl₂].H₂O (2), [Cu(salophen)] (3) and [Cu(salophen) CuCl₂].H₂O (4), where salen^2? = N,N′‐ethylenebis (salicylidenaminato); salophen^2? = o‐phenylenediaminebis(salicylidenaminato). Complexes 1 and 3 are supposed to have one type of copper centers (called (Cu1)) and complexes 2 and 4 two types of copper centers (called (Cu1) and (Cu2)) having different coordination environments and geometries. A theoretical model has been generated using the available crystallographic data of complex 1 and it has been used for analysis of the extended X‐ray absorption fine structure (EXAFS) data of the four complexes to obtain the structural parameters for (Cu1) center. For this center, the obtained Cu–Cu distance (3.2 Å) verifies the binuclear nature of all the complexes. For determining the coordination geometry around (Cu2) center in 2 and 4, a theoretical model has been generated using the crystal structure of a Cu(II) complex, [Cu(C₁₆H₁₂N₂O₂Cl₂)]. This theoretical model has been fitted to the EXAFS data of 2 and 4 to obtain the structural parameters for (Cu2) center. The present analysis shows that (Cu1) center has square pyramidal geometry involving 2N and 3O donor atoms, whereas (Cu2) center has distorted tetrahedral geometry with 2O and 2Cl donor atoms. The values of the chemical shifts and presence of typical Cu(II) X‐ray absorption near‐edge spectroscopy features suggest that copper is in the +2 oxidation state in all these complexes. The intensity of ls → 3d pre‐edge feature has been used to investigate the geometry and binuclear nature of the complexes. Copyright © 2012 John Wiley & Sons, Ltd.     

Easily attainable new approach to mass yield ferrocenyl Schiff base and different metal complexes of ferrocenyl Schiff base through convenient ultrasonication‐solvothermal method

A new alternative approach with crucial mass yield and high reaction rates is proposed for the synthesis of ferrocenyl Schiff bases using an ultrasonication‐solvothermal method. Equimolar condensation of ferrocenecarboxaldehyde and 2‐aminophenol interact with each other, giving 1‐(1‐[2‐hydroxyphenyl‐2‐imino]methyl)‐ferrocene (FcOH). Furthermore, this ligand forms 1:1 complexes with cobalt(II), nickel(II), copper(II), and palladium(II) ions. From the different spectral data, it is found that metal ions coordinate with ligands through the azomethine group and the deprotonated oxygen of the phenol groups. Moreover, FcOH and their complexes were characterized by elemental analysis, Fourier transform infrared, ¹H nuclear magnetic resonance, and UV‐visible spectrophotometry. The spectral data of FcOH and its metal complexes were discussed in connection with the structural changes due to complexation. Meanwhile, the information about geometric structures can be concluded from the electronic spectra and the magnetic moments. Plainly, electron spin resonance spectra of the Cu(II) complex revealed d_x2?y2 as a ground state, suggesting a square planar geometry around the Cu(II) center. The direct optical band gap energy E_g values of cobalt, nickel, copper, and palladium complexes of FcOH are found to be 3.7, 3.9, 4.6, and 3.65 eV, respectively. 1‐(1‐[2‐Hydroxyphenyl‐2‐imino]methyl)‐ferrocene and its metal complexes were screened for antibacterial activity. The results depict that the metal complexes were found to be more strongly antibacterial than the guardian Schiff base ligand (FcOH) against one or more bacterial species. The minimum inhibitory concentrations of antimicrobial properties of the purified compound were determined using the broth microdilution method.     

Magnetic circular and linear dichroism in cubic high spin d5 complex

Magneto-optical parameters useful for the interpretation of magnetic circular dichroism (MCD) and magnetic linear dichroism (MLD) spectra of high spin d⁵ complexes in tetrahedral or octahedral crystalline fields have been calculated. Two possible intensity borrowing mechanisms—one involving spin-orbit (s.o.) interaction of the ground sextet with the excited quartet states and the other involving the s.o. interaction of an excited charge transfer sextet with the excited quartet states—have been considered for electric dipole transitions in T_d symmetry and for magnetic dipole transitions in O_h symmetry. Of the numerous other mechanisms which may induce electric dipole oscillator strength in O_h symmetry complexes, eight (those in involving odd parity T _1u or T _2u states vibronically induced via t _1u or t _2u vibrational modes) have been investigated in detail. In each of these mechanisms, parameters have been calculated for transitions to all individual s.o. components of all excited quartet states. It is shown how the MCD and MLD techniques, if used in combination, may provide specific information on the mechanism of intensity borrowing and on the spectroscopic assignments of individual s.o. components.     

A cellular ligand-field model for l-l spectral intensities

The intensity distributions in the ‘d-d’ spectra of three planar CuCl^2- ₄ chromophores are reproduced quantitatively within the theoretical model described in the preceding paper. Intensity for these species, namely bis(1-methyl-4-oxo-3,3-diphenylhexyldimethylammonium)tetrachlorocopper(II), bis(2-iminol-1-methy-4-imidazolidinium)tetrachlorocopper(II) and bis(N-methylphenylethylammonium)-tetrachlorocopper(II), is deemed to arise dynamically via the bending vibrations. Fair reproduction of experimental absorbances is achieved using the b _2u mode alone, this being known to be the softest vibration in these systems. The roles of spin-orbit coupling and small departures from D _4h symmetry are discussed. Nearly perfect reproduction of experiment is obtained with addition of small contributions from the e_u bend. The intensity distribution in the ‘d-d’ spectrum of the pseudo-tetrahedral chromophore, bis(N-benzylpiper-azinium)tetrachlorocopper(II), is reproduced quantitatively within the ‘static’ model described in part I of this series. Comparisons between the parameter values obtained from the ‘static’ analysis with those from the ‘dynamic’ analysis for the planar chromophores suggest that dynamic modelling with both b _2u and e_u modes is the more physically persuasive. The efficacy of the model in part IV is critically reviewed in this first application.     

ESR study of some Cu(II)-oxazepam complexes

The CuL₂X₂ (L = 7-chlor-l,3-dihydro-3-hydroxi-5-phenyl-2H-l,4-benzodiazepin-2-one, also known as oxazepam, X = Cl, Br) complexes were prepared and investigated by ESR (electron spin resonance) method. Powder ESR spectra of CuL₂X₂ compounds at room temperature show the presence of monomeric species having an axial symmetry with a small rhombic distortion. In case of compounds with Cl there is a superposition of two nonequivalent mononuclear species, one with ad_{x² - y²} d_{x^2 - y^2 } ground state and another with ad_z² d_{z^2 } ground state. In pyridine (Py) and dimethylformamide (DMF) solutions the monomeric species prevail. Two different monomeric species, one with pseudotetrahedral (T_d) and the other with elongated tetrahedral-octahedral symmetry, were evidenced in DMF solutions adsorbed on NaY zeolite. In Py-DMF solutions two monomeric species were also identified. Dimeric species appear in DMF and Py solutions adsorbed on NaY zeolite through the coordination of two Cu(II) ions at the same keto-oxygen from one oxazepam molecule.     

具有D4h对称性构型的C2+4分子的Jahn-Teller效应与能级分裂

依据量子理论与配位场理论,利用群论和对称性分析的方法探讨了C²⁺₄分子在具有D_4h对称性构型时,E×(b_1g+b_2g)系统的Jahn-Teller效应中的相关问题.研究了C²⁺₄分子的电子态与声子态的对称性及其活跃声子态,讨论了系统声子间的耦合与CG系数,构建了E×(b_1g+b_{2g 关键词： 2+4分子')" href="#">C²⁺4分子 对称性 能级分裂 Jahn-Teller畸变}