Spin-Hamiltonian parameters and tetragonal distortion due to the Jahn–Teller effect for Cu2+ centres in trigonal Zn(BrO3)·6H2O crystal

The spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants ⁶⁵A_// and ⁶⁵A_⊥) for the tetragonal Cu²⁺ centres in trigonal Zn(BrO₃)·6H₂O crystal are calculated from the complete diagonalization (of energy matrix) method (CDM) based on the cluster approach. In the CDM, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM and the contributions to the spin-Hamiltonian parameters from both the spin-orbit coupling parameter of central d⁹ ion and that of ligand ion are included. The calculated spin-Hamiltonian parameters of Zn(BrO₃)·6H₂O: Cu²⁺ show good agreement with the experimental values and the tetragonal elongation (characterized by ΔR=R_// ? R _⊥, where R_// and R _⊥ represent the metal-ligand distances parallel with and perpendicular to the C₄ axis) due to the static Jahn–Teller effect is obtained from the calculations. The results are discussed.     

The 4 A 2→2 E transitions of 2[Cr(en)3Cl3]KCl. 6H2O in strong magnetic fields

The Zeeman effect of the R absorption lines for the pure compound 2[Cr(en)₃Cl₃]KCl.6H₂O has been measured photographically, using a strong pulsed magnet with fields of up to 200 000 gauss at 77 K. The results indicate g _∥ (⁴ A ₂) = 1·82 , g _⊥(⁴ A ₂) = 1·90 with g _∥(ē) = -1·82 and g _∥ (2ā) = 1·82. The uncertainties are of the order of ± 0·05.     

Snyder''s quantized space-time and de Sitter special relativity

There is a one-to-one correspondence between Snyder’s model in de Sitter space of momenta and the dS-invariant special relativity as well as a minimum uncertainty-like relation. This indicates that physics at the Planck length ℓ _P and the scale R = (3/Λ)^1/2 should be dual to each other and there is in-between gravity of local dS-invariance characterized by a dimensionless coupling constant g = ℓ _P /R ∼ 10⁻⁶¹.      

Effective Action in Multidimensional (Super)Gravities and Spontaneous Compactification (Quantum Aspects of Kaluza-Klein Theories)

The review of modern status of problem of quantum effects in Kaluza-Klein theories is given. The effective action (EA) in multidimensional (super)gravities (SG's) on the compactified background is investigated. The standard gauge dependent EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄ × S₁, where R₄ is 4-dimensional space, S₁ is one-dimensional sphere is calculated. Gauge and parametrization independent Vilcovisky-De Witt EA in d=5 Einstein gravity and d=5 R²-gravity on the background R₄×S₁ at zero and non-zero temperature is obtained. We have found that there are no physically acceptable self-consistent solutions of the form R₄×S₁ at the one-loop level in d=5 Einstein gravity. We calculated also EA for arbitrary multidimensional SG on the background R₄×T_d-n where T_d is d-dimensional torus as expansion on the curvature and its derivatives. The mechanizm of induced of four-dimensional gravity with zero Λ-term is proposed. The Vilcovisky-De Witt EA in d=5 SG's on the background R₄×S₁ at non-zero temperature is obtained. The three gauge parameter dependent off-shell EA in N=2, d=5 gauged SG on R₄⁰×S₁ where R₄⁰ is flat four-dimensional space is calculated. The expression for vacuum energy for bosonic string with torus compactification is presented. Vacuum energy for superstrings with supersymmetry broken as the result of choice of boundary conditions on background R₄×T₆ is calculated.     

Absorption and resonance Raman spectroscopy of the 1Bu state of trans‐1,3,5‐hexatriene including vibronic coupling

The vibronic coupling between the first excited S₁ (2¹A_g) and the second excited S₂ (1¹B_u) singlet electronic states in spectroscopy of trans‐1,3,5‐hexatriene molecule is investigated on the basis of a model consisting of two electronic states coupled by two vibrational modes. Employing a perturbation theory that treats the intramolecular couplings in a perturbative manner, the absorption and resonance Raman cross sections and excitation profiles of this molecule are calculated using the time‐correlation function formalism. The non‐Condon corrections are included in evaluation of cross sections. The multidimensional time‐domain integrals that arise in these calculations have been evaluated for the case in which S₀ (1¹A_g) S₂ (1¹B_u) electronic transition takes place between displaced and distorted harmonic potential energy surfaces. The calculated spectra are in good agreement with the experimental ones. Copyright © 2011 John Wiley & Sons, Ltd.     

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g_//, g_⊥ and hyperfine structure constants A_//, A_⊥) and optical band positions for Ni⁺ ion in silver gallium selenide (AgGaSe₂) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dⁿ ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni⁺ centre in AgGaSe₂ is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dⁿ clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dⁿ ion and ligand ion should be contained.     

Availability of the thermodynamics and weak cosmic censorship conjecture for a charged AdS black hole in the large dimension limit

The thermodynamics and the weak cosmic censorship conjecture (WCCC) in a high dimensional RN ? AdS_d+?1 black hole with energy-momentum relation are investigated by absorbing a charged particle in the phase space. In the RN ? AdS_d+?1 space-time, the cosmological constant Λ is treated as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume. We use the energy-momentum relation of the absorbed particle to discuss the thermodynamics of the RN ? AdS_d+?1 black hole and to prove the WCCC in the phase space. Based on this assumption, we find that the first law and the second law of thermodynamics are satisfied in normal phase space. On the other hand, in the extend phase space, the first law is satisfied and the second law is violated. Then we study the WCCC in the phase space, we find that the WCCC is satisfied for an extreme black and a near-extreme black hole in the normal phase space. In the extend phase space, the WCCC is satisfied for an extreme black hole and unidentified for a near-extreme black hole.

     

Molecular magnetism of a linear Fe(III)-Mn(II)-Fe(III) complex. Influence of long-range exchange interaction

The magnetic properties of [L-Fe(III)-dmg₃Mn(II)-Fe(III)-L] (ClO₄)₂ have been characterized by magnetic susceptibility, EPR, and Mössbauer studies. L represents 1,4,7-trimethyl-, 1,4,7-triazacyclononane and dmg represents dimethylglyoxime. X-ray diffraction measurements yield that the arrangement of the three metal centers is strictly linear with atomic distancesd _Fe-Mn=0.35 nm andd _Fe-Fe=0.7 nm. Magnetic susceptibility measurements (3–295 K) were analyzed in the framework of the spin-Hamiltonian formalism considering Heisenberg exchange and Zeeman interaction:=J _Fe-Mn(S _Fe1+S _Fe2)S _Mn +J _Fe-Fe(S _Fe1 S _Fe2) +g_B S _total B. The spinsS _Fe1=S _Fe2 =S _Mn=5/2 of the complex are antiferromagnetically coupled, yielding a total spin ofS _total=5/2 with exchange coupling constantsF _Fe-Mn=13.4 cm^–1 andJ _Fe-Fe= 4.5 cm^–1. Magnetically split Mössbauer spectra were recorded at 1.5 K under various applied fields (20 mT, 170 mT, 4T). The spin-Hamiltonian analysis of these spectra yields isotropic magnetic hyperfine coupling withA _total/(g _{N N})=–18.5 T. The corresponding local componentA _Fe is related toA _total via spin-projection:A _total=(6/7)A_Fe. The resultingA _Fe/(g _NN)=–21.6 T is in agreement with standard values of ferric high-spin complexes. Spin-Hamiltonian parameters as obtained from Mössbauer studies and exchange coupling constants as derived from susceptibility measurements are corroborated by temperature-dependent EPR studies.     

First and second‐order Raman scattering of B6O

First and second‐order Raman spectra of B₆O and their dependence on the wavelength of the excitation line from IR (infrared) to deep UV (ultraviolet) has been studied. The first‐order Raman spectra contain 11 well‐resolved lines of the 12 expected modes 5 A_1g + 7 E_g (space group R‐3m, point group D_3d). The second‐order Raman spectra contains eight lines that are resolved only in the case of the 244‐nm excitation line. Copyright © 2009 John Wiley & Sons, Ltd.     

Studies of the optical spectra and spin-Hamiltonian parameters for the trivalent ytterbium ions in lithium yttrium fluoride crystals

In this paper, the crystal field (CF) levels and spin-Hamiltonian (SH) parameters (g factors g _∥ and g _⊥ and hyperfine structure constants A _∥ and A _⊥) of the rare-earth ion Yb³⁺ in lithium yttrium fluoride crystals are calculated under D _2d point symmetry assumption. Two main methods are used in the calculation to study the SH parameters: one is the perturbation theory method and the other is the complete diagonalization (energy matrix) method (CDM). Comparing the calculated results with the experimental data, we can see that the CDM is more effective to calculate the SH parameters. In addition, the CF J-mixing of all excited-state multiplets into the ground-state multiplet ²F_7/2 is considered. The validity of the calculated results is discussed.     

Theoretical study of hyperfine coupling constants and electron spin g factors for X2Σ+ diatomics from Groups 1 and 2

The ESR parameters of the cations Be⁺ ₂, Mg⁺ ₂, Ca⁺ ₂, BeMg⁺, BeCa⁺, MgCa⁺ and the mixed radicals ZBe, ZMg, ZCa (Z = Li, Na, K), all having a X ²Σ⁺ _u(1σ² _g1σ_u)/X ²Σ⁺(1σ²2σ) ground state, have been studied theoretically. The A _iso and A _dip constants have been calculated with UHF, CISD, MP2, B3LYP, PW91PW91 wavefunctions, and 6–311+G(2df) basis sets. The electron spin g factors (magnetic moment μ_s) have been evaluated from correlated (MRDCI) wavefunctions, using a Hamiltonian based on Breit-Pauli theory with perturbation expansions up to second order, and 6–311 + G(2d) basis sets. As expected for s-rich radicals, the hyperfine spectra are governed by the A _iso terms. Both Δg∥ and Δg⊥ values are negative, but Δg∥ lies close to zero. For Δg⊥, the coupling with 1 ²Π_(u) dominates the sum-over-states expansions. Although the singly occupied MOs (SOMO) are mostly of s character, the |Δg⊥| are relatively large, up to 5200 ppm for cationic, and up to 7850 ppm for neutral radicals. These large values are caused by low excitation energies and high magnetic transition moments, the latter due to the fact that the σ?(s-s) SOMO has the same nodal properties as a pσ orbital. Of the radicals considered here, an ESR spectrum is available only for Mg⁺ ₂. Our theoretical A _iso of ?287 MHz reproduces well the matrix result (-291 MHz). Calculated values of ?10 ppm for Δg∥ and of ?1280 ppm for Δg⊥ give an average 〈Δg〉 = ?860 ppm that lies within the experimental range of ?600(±300) ppm in Ne, and of ?1300(±500) ppm in Ar matrices.     

The X2Π and A2Σ+ states of FH+, ClH+ and BrH+: theoretical study of their g -factors and fine/hyperfine structures

Theoretical calculations on the fine, hyperfine and Zeeman (g-factor) parameters are reported for the X²Π and A²Σ⁺ states of FH⁺, ClH⁺ and BrH⁺. The fine-structure constants [spin–orbit (A), Λ-doubling (p, q) and spin–rotation constants (γ _Π, γ _Σ)] are evaluated up to second order (via SO/L couplings with several excited states) using a multireference configuration interaction (MRCI) method, a Breit–Pauli Hamiltonian and 6-311++(2d,2pd) basis sets. Hyperfine constants of magnetic and electric type [Frosch–Foley (a, b, c, d) and nuclear quadrupole (eQq ₀, eQq ₂)] are studied with density functional methods and various basis sets. Magnetic dipole moments (parameterized via g-factors) are calculated in second order like the fine structure constants. The situation is somewhat complex for X²Π since no less than five different g’s have to be evaluated in second order. In general, our results are in good agreement with those reported in the literature, mostly limited to the ground state. Our calculations confirm that, at equilibrium, all second-order properties are dominated by the couplings between the electronic states X and A.     

X‐ray photon correlation spectroscopy in systems without long‐range order: existence of an intermediate‐field regime

Successful X‐ray photon correlation spectroscopy studies often require that signals be optimized while minimizing power density in the sample to decrease radiation damage and, at free‐electron laser sources, thermal impact. This suggests exploration of scattering outside the Fraunhofer far‐field diffraction limit d²/λR, where d is the incident beam size, λ is the photon wavelength and R is the sample‐to‐detector distance. Here it is shown that, in an intermediate regime d²/λ > Rdξ/λ, where ξ is the structural correlation length in the material, the ensemble averages of the scattered intensity and of the structure factor are equal. Similarly, in the regime d²/λ > Rdξ(τ)/λ, where ξ(τ) is a time‐dependent dynamics length scale of interest, the ensemble‐averaged correlation functions g₁(τ) and g₂(τ) of the scattered electric field are also equal to their values in the far‐field limit. This broadens the parameter space for X‐ray photon correlation spectroscopy experiments, but detectors with smaller pixel size and variable focusing are required to more fully exploit the potential for such studies.     

Solvent solute interactions probed by picosecond transient Raman spectroscopy:S 1 1,4-diphenyl-1,3-butadiene in the linear alkanes

We present theS ₁ Raman spectra of 1,4-DiPhenyl-1,3-Butadiene (DPB) in a series of linear alkanes (pentane, hexane, heptane, octane, decane, and dodecane). Bands assignable to both the 1¹ B _u and 2¹ A _g states are present, suggesting that the state we are observing in solution is a mixed state with both 1¹ B _u and 2¹ A _g character. The relative intensities of several bands associated with C_oC_o stretching motions in the 2¹ A _g and 1¹ B _u states change systematically through the solvent series. The relative intensity changes reflect a changing distribution ofs-trans conformers inS ₁ DPB as the solvent is varied. We suggest that the distribution ofs-trans conformers inS ₁ DPB controls the nature of the mixing between the 2¹ A _g and 1¹ B _u states and that the distribution of conformers is controlled by the solvent viscosity. Changes in the peak position and bandwidth of the phenyl C=C stretch with delay reflect vibrational relaxation processes inS ¹ DPB. We observe anomolous behavior in pentane that we attribute to the effect of the solvent structure on the ability of DPB to exchange energy with pentane.     

Defect Structure and EPR Parameters of the Cu2+Center in MNB Ternary Glasses

The electron paramagnetic resonance (EPR) parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) for 15MgO-15Na₂O-69B₂O₃ (MNB):Cu²⁺ ternary glasses were calculated based on the high-order perturbation formulae of 3d⁹ ion in a tetragonal symmetry. From the calculations, the defect structures of MNB:Cu²⁺ ternary glasses were obtained and a negative sign for A _// and A_⊥ for the Cu²⁺ center is suggested in the discussion.     

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g _//, g ⊥ and hyperfine structure constants ⁶³ A _//, ⁶³ A ⊥, ⁶⁵ A _//, ⁶⁵ A ⊥) for Cu²⁺ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d ⁹ ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the ² T ₂ term. It appears that, for exact calculations of SH parameters of d ⁹ ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the ² T ₂ term. The local structures of Cu²⁺ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu²⁺ and GaN : Cu²⁺ are obtained from the calculations. The results are discussed.     

Studies of local phase transition behavior for Co2+ in CsCaCl3 crystals from EPR data

In this paper, we establish the calculation formulas ofg factorsg _∥,g _⊥ and the hyperfine structure constantsA _∥,A _⊥ for 3d⁷ ions in tetragonal octahedral field from a cluster approach. In these formulas, besides the configuration interaction, the covalency effect due to the admixture between d electrons of 3d⁷ ion and the p electrons of ligands is considered. The parameters used in these formulas (except the core polarization constantsk in the calculation ofA _i) can be obtained from optical spectra of the studied crystal. From these formulas, the local release (or elongation) factork, which is introduced to characterize the release effect of impurity-ligand bond along C₄ axis at the cubic to tetragonal phase transition, is estimated for CsCaCl₃:Co²⁺ crystal by calculating the electronic paramagnetic resonance (EPR) parametersg _i andA _i . These EPR parameters are therefore explained reasonably and the results are discussed.     

Theoretical investigation of the spin-Hamiltonian parameters and optical spectra for the doped Cu2+ in ZnCdO nanopowder

The spin-Hamiltonian (SH) parameters (g factors g_||, g_⊥ and hyperfine structure constants A_||, A_⊥) and d–d transitions for ZnCdO:Cu²⁺ are calculated based on the perturbation formulas for a 3d⁹ ion in tetragonally elongated octahedra. Good agreement between the calculated results (four SH parameters and three optical absorption bands) and the experimental results can be obtained. Since the SH parameters are sensitive to the local structure of a paramagnetic impurity center, the tetragonal distortion (characterized by the relative elongation ratio ρ ≈ 3.5% along the C₄ axis) of the impurity center due to the Jahn–Teller effect is also acquired from the calculations. The negative and positive signs of hyperfine structure constants A_|| and A_⊥ for ZnCdO:Cu²⁺, respectively, are also suggested in the discussions.     

Theory of the ionization of ethane

Ab initio molecular orbital studies on C₂H₆ ⁺ support an assignment of ² A _1g (D _3d point group symmetry) for the ground state of this cation. This differs from the prediction of Koopmans' theorem which suggests a ² E_g state for vertical ionization. Approximate force constants and vibrational frequencies are calculated for the ethane cation in the ² A _1g state and are found to be consistent with the vibrational progression observed in the experimental photoelectron spectrum.     

Defect structure of Cu2+ center in K2SO4‒Na2SO4‒ZnSO4 glasses

The spin Hamiltonian parameters (g factors g _//, g _⊥ and hyperfine structure constants A _//, A _⊥) of Cu²⁺ in K₂SO₄?Na₂SO₄?ZnSO₄ glasses are calculated from the high-order perturbation formulas of 3d⁹ ion in tetragonal octahedral sites. The calculated results are in agreement with the observed values. Since the EPR parameters are sensitive to the local structure of a paramagnetic impurity center, the defect structure of Cu²⁺ center in K₂SO₄?Na₂SO₄?ZnSO₄ glasses is estimated. The validity of results is discussed.