Intensity of singlet-triplet transitions in C<Subscript>60</Subscript> fullerene calculated on the basis of the time-dependent density functional theory and taking into account the quadratic response

The singlet-singlet and triplet-triplet absorption spectra of C₆₀ fullerene are calculated using the density functional method and taking into account the theory of linear and quadratic responses. The B3LYP density functional and the 6–31G and 3–21G atomic basis sets are used. The calculations are performed using the D_2h and D_5d symmetry groups, although the real symmetry of the ground state is described by the I _h symmetry group. The matrix elements of the operator of the spin-orbit coupling are calculated and the probabilities of some singlet-triplet transitions are estimated. Taking into account the data in the literature on vibronic interactions of vibrations of the t_1u, t_2u, g _u , and h _u symmetry species, the radiative lifetime of the 1³T_2g → 1¹A _g phosphorescence was estimated to be 45 s. The fact that this time proved to be considerably greater than the experimentally observed total lifetime of the triplet testifies to a fast nonradiative deactivation of the lowest triplet state of C₆₀ fullerene and agrees with a low phosphorescence intensity. The zero-field splitting of some triplets and the intensities of magnetic dipole transitions are discussed.     

The oxidation of fullerenes (C<Subscript>60</Subscript>, C<Subscript>70</Subscript>) with various oxidants under ultrasonication

The reaction of C₆₀, under ultrasonication, with various oxidants, such as 3-chloroperoxy benzoic acid (Fluka 99%), 4-methyl morpholine N-oxide (Aldrich 97%), chromium (VI) oxide (Aldrich 99.9%), and the oxone® monopersulfate compound, causes the oxidation of fullerenes at room temperature. The FAB-MS spectra and HPLC profile confirmed that the products of fullerene oxidation were [C₆₀(O)_n] (n=1～3 or n=1). C₇₀ also reacted, under ultrasonication, with various oxidants, but the reaction rate of C₇₀ was lower than that of C₆₀.     

Rotation of the inner shell in a C<Subscript>20</Subscript>@C<Subscript>80</Subscript> nanoparticle

The stability of a C₂₀@C₈₀ nanoparticle and the rotation of its inner shell are studied theoretically within the tight-binding approximation. It is found that the C₂₀ skeleton in the free state is described by space group D_3d; in the case where C₂₀ is placed into the C₈₀(I _h ) fullerene field, the space group of C₂₀ is raised to I _h due to isomerization. The total energy surface of the C₂₀@C₈₀ compound is scanned over two rotation angles. Based on an analysis of the surface relief and energy isoline map, orientational melting of the nanoparticle is predicted. A nanoparticle gyroscope—C₂₀ rotating in the field of C₈₀ at a certain relative orientation and energy supply—is also predicted to exist.     

Experimental Study and Analysis of Absorption Spectra of Ni<Superscript>2+</Superscript> Ions in Nickel Orthoborate Ni<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>2</Subscript>

The results of studies of the absorption spectra of nickel orthoborate Ni₃(BO₃)₂ in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni²⁺ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C_2h and C₂, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion ³A_2g (³F) to the sublevels of the ³T_2g (³F), ³T_1g (³F) and ³T_1g (³P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.     

X-ray emission and X-ray photoelectron spectroscopic studies of fullerene fluoride C<Subscript>60</Subscript>F<Subscript>24</Subscript>

The structure of the fullerence fluoride C₆₀F₂₄ of the T _h symmetry contains two types of chemically different carbon atoms, namely, atoms of isolated double bonds and atoms of CF groups. X-ray photoelectron and x-ray emission spectroscopic studies of C₆₀F₂₄ revealed a difference in the widths of the x-ray bands corresponding to these types of atoms. Nonempirical quantum-chemical calculations performed for C₅₉NF ₂₄ ⁺ ions with a hole in the C 1s core level of the fullerence fluoride showed that the difference in the bandwidths may be due to the fact that the vibrational states of the system are different when 1s electrons are removed from chemically nonequivalent atoms.     

Effect of heating of the electronic subsystem on the thermal stability of the C<Subscript>60</Subscript> and C<Subscript>20</Subscript> fullerenes and (C<Subscript>20</Subscript>)<Subscript>2</Subscript> cluster molecule

The effect of heating of the electronic subsystem on the thermal stability of C₆₀ and C₂₀ fullerenes and a (C₂₀)₂ cluster molecule is investigated theoretically. It is demonstrated that the excitation of electrons to upper energy levels in accordance with the Fermi-Dirac distribution function does not lead to a substantial change in the activation energy E _a for decay of the C₂₀ fullerene. The stability of the C₆₀ fullerene and the (C₂₀)₂ cluster molecule likewise does not change radically. However, the inclusion of corrections associated with the finite sizes of the heat bath leads to the activation energy E _a which is in better agreement with the calculated height of the potential barrier preventing the cluster decay.     

EPR study of copper ions in Li<Subscript>2</Subscript>Ge<Subscript>7</Subscript>O<Subscript>15</Subscript> crystals

The EPR spectra of Cu²⁺ ions (² D _5/2) located at two structurally nonequivalent positions Cu1 and Cu2 in crystals of lithium heptagermanate Li₂Ge₇O₁₅ are recorded. The angular dependences of the EPR spectrum are measured in the paraelectric phase of the Li₂Ge₇O₁₅ compound (T = 300 K). The components of the g factor and the hyperfine interaction tensor A are determined, and the orientation of the magnetic axes with respect to the crystallographic basis is established. The EPR spectra are recorded in the temperature range in the vicinity of the temperature T _C = 283 K of the transition from the paraelectric phase to the ferroelectric phase. The position symmetry of the Cu1 and Cu2 centers is determined at temperatures above and below the phase transition temperature T _C . The localization of paramagnetic centers in the structure is discussed, An analysis of the results obtained demonstrates that the Cu1 and Cu2 centers in the Li₂Ge₇O₁₅ crystal lattice replace lithium ions located at two structurally nonequivalent positions with the symmetries described at temperatures above T _C by the triclinic C _i and monoclinic C ₂ point groups, respectively.     

High-pressure hydrogenated fullerenes: Optical spectra and stability of C<Subscript>60</Subscript>H<Subscript>36</Subscript> at high pressure

The optical Raman and photoluminescence (PL) spectra of the high-pressure hydrogenated fullerene C₆₀ are studied at normal conditions and at high pressure. The Raman spectrum of the most stable hydrofullerene C₆₀H₃₆ contains a large number of peaks related to various isomers of this molecule. Comparison of the experimental data with the results of calculations shows that the most abundant isomers have the symmetries S₆, T, and D_3d. The Raman spectrum of deuterofullerene C₆₀H₃₆ is similar to that of C₆₀H₃₆, but the frequencies of the C-H stretching and bending modes are shifted due to the isotopic effect. The PL spectrum of hydrofullerene C₆₀H₃₆ is shifted to higher energies by approximately 1 eV with respect to that of pristine C₆₀. The effect of hydrostatic pressure on the Raman and PL spectra of C₆₀H₃₆ has been investigated up to 12 GPa. The pressure dependence of the phonon frequencies exhibits peculiarities at approximately 0.6 and 6 GPa. The changes observed at approximately 0.6 GPa are probably related to a phase transition from the initial orientationally disordered body-centered cubic structure to an orientationally ordered structure. The peculiarity at approximately 6 GPa may be related to a pressure-driven enhancement of the C-H interaction between the hydrogen and carbon atoms belonging to neighboring molecular cages. The pressure-induced shift of the photoluminescence spectrum of C₆₀H₃₆ is very small up to 6 GPa, and a negative pressure shift was observed at higher pressure. All the observed pressure effects are reversible with pressure.     

Optical and x-ray diffraction studies of the symmetry of distorted phases of the (NH<Subscript>4</Subscript>)<Subscript>3</Subscript>ZrF<Subscript>7</Subscript> crystal

(NH₄)₃ZrF₇ single crystals were grown, and polarization-optical and x-ray diffraction studies were performed on powders and crystalline plates of various cuts over a wide temperature range. Phase transitions are revealed at temperatures T _1↑ = 280 K, T _2↑ = 279.6 K, T _3↑ = 260–265 K, and T _4↑ = 238 K on heating and at T _1↓ = 280 K, T _2↓ = 269–270 K, T _3↓ = 246 K, and T _4↓ = 235 K on cooling. The sequence of changes in symmetry is established to be as follows: O _h ⁵ (Z = 4) ? D _2h ²⁵ (Z = 2) ? C _2h ³ (Z = 2) ? C _i ¹ (Z = 108) ? monoclinic²(Z = 216).     

Photoionization of the Xe atom and Xe@C<Subscript>60</Subscript> molecule

Photoionization of the Xe atom and Xe@C₆₀ molecule have been studied usingthe random phase approximation with exchange (RPAE) method. The Xe atom was described byrelaxed orbitals including overlap integrals. The C₆₀ fullerene has beenrepresented by an attractive short range spherical well with potentialV(r), given byV(r) =  ?V ₀ forr _i  < r < r _o ,otherwise V(r) = 0 wherer _i andr _o are respectively, the inner and outerradii of the spherical shell. The time independent Schrödinger equation was solved usingboth regular and irregular solutions and the continuous boundary conditions atr _i andr _o . The results demonstrate improvementto previous calculations for both the Xe atom and Xe@C₆₀ molecule and comparevery well with the recent experimental data.     

Manifestation of a strong quadrupole interaction and peculiarities in the SERS and SEHRS spectra of 4,4'-bipyridine

The paper analyzes Surface Enhanced Raman Scattering (SERS) and Surface Enhanced Hyper Raman Scattering (SEHRS) spectra of 4,4'-bypiridine molecule for two possible geometries, which are described by D ₂ and D _2h symmetry groups. It is pointed out on appearance of sufficiently strong lines, caused by vibrations with the unit irreducible representation for both possible configurations. Appearance of these lines in the SEHRS spectrum points out the existence of a strong quadrupole light-molecule interaction. In addition one observes the lines, caused by vibrations both with the unit irreducible representations A or A _g and the irreducible representation B ₁ or B _1u . The last ones describe transformational properties of the d _z component of the dipole moment, which is perpendicular to the surface. This property of the spectrum is caused by peculiarity of the geometry of the molecule, which consists of two benzene rings, which are weakly connected with each other. The linear combinations of the vibrations of the rings create two nearly degenerated symmetric and anti symmetrical states, which cannot be identified in the experimental spectra. The result is in a full agreement with the dipole-quadrupole theory of SERS and SEHRS.     

Effect of annealing temperature on the structural reorganization of Eu<Superscript>3+</Superscript> optical centers in Al<Subscript>2</Subscript>O<Subscript>3</Subscript>-Eu<Subscript>2</Subscript>O<Subscript>3</Subscript>-BiOF gel films

The dependence of the structural reorganization of Eu³⁺ optical centers in Al₂O₃-Eu₂O₃-BiOF films on the annealing temperature has been investigated. It is shown by the methods of crystal field theory and computer simulation that the increase in the annealing temperature from 700 to 1100 °C leads to removal of bismuth from Eu-O-Bi complex centers with the C _3V symmetry in the Al₂O₃ structure and the change in symmetry from D ₃ to O _h for a large fraction of EuAlO₃ centers.     

Harmonic analysis of coefficients of free energy decomposition in the polarization of a Rb<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystal

Landau–Devonshire decomposition coefficients W_C in a series with respect to P_C are determined via harmonic analysis of experimental free energy coordinates W_C of a Rb₂ZnCl₄ crystal, depending on its polarization P_C. The number of terms needed in W_C decomposition is determined for quantitative evaluation of the measured data.     

Study of third-and fifth-order nonlinear optical processes in thin C<Subscript>60</Subscript> films

The nonlinear refraction in thin films of fullerene C₆₀ (100 nm) is studied by the Z-and RZ-scan methods using the second harmonic of a picosecond Nd:YAG laser (λ = 532 nm, τ = 55 ps). The combined effect of n₂ (self-focusing of laser radiation) and n₄ (self-defocusing) is analyzed. Mechanisms responsible for the nonlinear refraction in films are discussed.     

Rise of the fullerene yield in an arc discharge under the action of gas flow in a hollow electrode

When a turbulent gas flow and a hollow electrode are combined in a discharge chamber, a synergetic effect is observed: the weight of the deposit decreases by five to six times and fullerene-containing soot dissolves completely (without precipitation) in benzene. The mass spectra of the synthesis products contain the lines of C₆₀, C₇₀, and C_{74 + 2n} (n = 0–40) fullerenes. This indicates a 100% yield of the fullerene mixture. As a result, the output of the fullerene synthesis process increases by a factor of more than 10.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Anomalous thermal stability of metastable C<Subscript>20</Subscript> fullerene

The results of computer simulation of the dynamics of fullerene C₂₀ at different temperatures are presented. It is shown that, although it is metastable, this isomer is very stable with respect to the transition to a lower energy configuration and retains its chemical structure under heating to very high temperatures, T ≈ 3000 K. Its decay activation energy is found to be E _a ≈ 7 eV. Possible decay channels are studied, and the height of the minimum potential barrier to decay is determined to be U = 5.0 eV. The results obtained make it possible to understand the reasons for the anomalous stability of fullerene C₂₀ under normal conditions.     

Specific features of optical absorption in rare-earth orthoaluminate DyAlO<Subscript>3</Subscript>

Polarization spectra of optical absorption of the 4f-4f transition ⁶ H _15/2 → ⁶ F _3/2 in the rare-earth orthoaluminate DyAlO₃ are theoretically and experimentally studied at the temperature T=78 K. It is shown that the nontrivial character of the anisotropy of the polarization absorption spectra at low temperatures can be explained by the J-J mixing of excited multiplets of the 4f ⁹ configuration of Dy³⁺ ions in a low-symmetry crystal field of the orthoaluminate structure. The energy and wave functions of the Stark sublevels within the excited ⁶ F _5/2 multiplet in the 4f ⁹ configuration of the Dy³⁺ rare-earth ion in the crystal field of C _s symmetry are numerically calculated.     

Pressure dependence of the superconducting state parameters of a binary Ca<Subscript>70</Subscript>Mg<Subscript>30</Subscript> metallic glass superconductor

Theoretical computation of the pressure dependence of superconducting state parameters of a binary Ca₇₀Mg₃₀ metallic glass has been performed using the model potential formalism. Explicit expressions have been derived for the volume dependence of the electron-phonon coupling strength λ and the Coulomb pseudopotential μ*, considering the variation of the Fermi momentum k _F and Debye temperature θ_D with volume. Well-known Ashcroft’s empty core model pseudopotential and five different types of the local-field correction functions, namely, Hartree, Taylor, Ichimaru-Utsumi, Farid et al. and Sarkar et al. have been used for obtaining pressure dependence of transition temperature T _C and the logarithmic volume derivative Φ of the effective interaction strength N ₀ V for the metallic glass superconductor. It has been obtained that T _C of Ca₇₀Mg₃₀ metallic glass decreases rapidly with increasing pressure up to 60% decrease in the volume, for which the μ* and Φ curves show a linear nature. The superconducting phase disappears at about 60% decrease in the volume.     

Pressure-induced antiferromagnetism in La<Subscript>0.75</Subscript>Ca<Subscript>0.25</Subscript>MnO<Subscript>3</Subscript> manganite

The crystal and magnetic structures of La_0.75Ca_0.25MnO₃ manganite are studied under high pressures up to 4.5 GPa in the temperature range 12–300 K by the neutron diffraction method. At normal pressure and temperature T _C = 240 K, a ferromagnetic state is formed in La_0.75Ca_0.25MnO₃. At high pressures P ≥ 1.5 GPa and at temperatures T < T _N ≈ 150 K, a new A-type antiferromagnetic state appears. A further increase in pressure leads to an increase in the volume fraction of the antiferromagnetic phase, which coexists with the initial ferromagnetic phase. The effect of high pressure causes a considerable increase in T _C with the slope dT _C /dP ≈ 12 K/GPa. Calculations performed in the framework of the double exchange model with allowance for the electron-phonon interaction make it possible to explain this pressure dependence of T _C on the basis of experimental data.