The analytical treatment of magnetic properties of three-layer ferrimagnetic superlattice

The Hamiltonian of the magnetic superlattice with three-layer unit cell was treated within the Boson formalism. The Boson Green’s functions (BGFs) were derived and it was shown that the system for BGFs splits into two sets which lead to the energies with opposite signs, although the energies of elementary excitations are strictly only the positive ones. However, when corresponding energies are used, the correlation functions calculated from both sets are the same. All the physically relevant quantities: total energy of the system, ground state energy, layer magnetization and zero-point (quantum) fluctuations are derived analytically by using both sets, showing that they lead to the same expressions. The Hamiltonian was also diagonalized by the so-called “u-v” transformation of the operators. It is shown that in spite of formal independence of the approaches, there exists a close relationship between BGF and “u-v” transformations.     

Photoassociative spectroscopy of the long-range state

The photoassociative spectroscopy of the Cs₂ 0 g ^- long-range molecular state dissociating into the asymptote is performed, using cold cesium atoms in a vapor-cell magneto-optical trap (MOT). Vibrational levels from v =0 to v =132 are identified, and their rotational structure is well resolved up J =8 for levels below v =74. These data are analyzed in terms of the Rydberg-Klein-Rees (RKR) procedure, and correspond to 99.6% of an effective potential curve with a minimum at ? and a cm^-1 depth. Both ab initio calculations and simple model estimations predict a double-well structure for this potential curve, which cannot be reproduced presently by the RKR approach but which is confirmed by the presence of giant structures in the spectrum. The 1_u()long-range state is also observed for the first time in Cs₂.     

4 Ag ↔2 Eg Transition of Mn4+ in Cs2TiF6: MnF6 2-

We report and interpret the ⁴ A_2g ?² E_g absorption, emission, linear dichroism, MCD and MCE of the MnF₆ ^2- octahedra at sites of D_3d symmetry in single crystals of Cs₂TiF₆. The spectra show many sharp features but a simplified calculation using cubic basis functions successfully accounts for all of the major features and much of the detailed structure. The electronic levels are not split by the trigonal field in first order but trigonal distortion splits the three-fold degenerate v ₆(t_2u ) vibration of the octahedron into a two-fold degenerate v ₆(e_u ) and a non-degenerate v ₆(a_1u ) vibration and these two vibrational modes give rise to the features 213 cm^-1 and 246 cm^-1 from the zero-phonon line respectively. Similarly the v ₄(t_1u ) vibration is split into a v ₄(a_2u ) and v ₄(e_u ) vibration and give the features at 313 cm^-1 and 340 cm^-1 respectively.

Several transitions involving two or more quanta of vibration are clearly seen in the emission and MCE spectrum. At an energy shift of greater than 700 cm^-1 from the zero-phonon transition these features are found to consist of progressions in the v ₁(a_1g ) breathing mode and the v ₂(e_g ) two-fold degenerate Jahn-Teller active mode. This structure can again be explained, with one exception, in terms of a calculation which assumes cubic basis functions. The exception is the reversal in sign of the MCE at a frequency v ₆(e_u ) + v ₂(e_g ) compared with that at v ₆(e_u ) which is not fully understood.     

Vibrational Spectra of Benzylidene Aniline,O-Hydroxybenzylidene O-Hydroxyaniline and its Complexes with Cu(II) and NI(II) Metal Ions

Abstract

The FTIR and FT Raman spectra of benzylidene aniline, and o-hydroxybenzylidene o-hydroxyaniline compounds in the solid state in the wavenumber (1800-200 cm^?1) are recorded. An assignment for nearly all fundamentals are proposed. Comparison of the spectra of trans stilbene and benzylidene aniline reveals that v N-Ph stretch for the latter compound is situated at 1368 cm^?1 in the IR spectra with medium intensity. for o-hydroxybenzylidene o-hydroxyaniline, the stretching modes v N-Ph, and v C-Ph are observed at 1356 and 1226 cm^?1 respectively. the two v O-Ph are observed as intense bands in the IR spectra at 1245 and 1278 cm^?1, respectively. the FTIR spectra of the o-hydroxybenzylidene o-hydroxyaniline complexes with Cu(II) and Ni(II) metal ions are also recorded and assigned.     

The Relativistic Composite-Velocity Reciprocity Principle

Gyrogroup theory [A. A. Ungar, Found. Phys. 27, 881–951 (1997)] enables the study of the algebra of Einstein's addition to be guided by analogies shared with the algebra of vector addition. The capability of gyrogroup theory to capture analogies is demonstrated in this article by exposing the relativistic composite-velocity reciprocity principle. The breakdown of commutativity in the Einstein velocity addition of relativistically admissible velocities seemingly gives rise to a corresponding breakdown of the relativistic composite-velocity reciprocity principle, since seemingly (i) on one hand, the velocity reciprocal to the composite velocity uv is –(uv) and (ii) on the other hand, it is (–v)(–u). But (iii) –(uv)(–v)(–u). We remove the confusion in (i), (ii), and (iii) by employing the gyrocommutative gyrogroup structure of Einstein's addition and, subsequently, present the relativistic composite-velocity reciprocity principle with the Thomas rotation that it involves.     

Stilbene-Like Molecules as Fluorescent Probes Applied for Monitoring of Polymerization Process

2-(p-N,N-dimethylaminostyryl)benzoxazole (OS), 2-(p-N,N-dimethylaminostyryl)-benzothiazole (SS) and 2-(p-N,N-dimethylaminostyryl)naphtiazole (PS) were prepared and their absorption and fluorescence spectra were measured in various solvents at room temperature. On the basis of the solvatochromic behavior the ground state (μ_g) and excited state (μ_e) dipole moments of these pN,N-dimethylaminostyryl derivatives were evaluated. The dipole moments (μ_g and μ_e) were estimated from solvatochromic shifts of absorption and fluorescence spectra as function of the dielectric constant (ɛ) and refractive index (n) of applied solvents. The absorption spectra only slightly are affected by the solvent polarity in contrast to the fluorescence spectra that are highly solvatochromic and display a large Stokes shift. The analysis of the solvatochromic behavior of the fluorescence spectra as function of Δf (ɛ, n) revealed that the emission occurs from a high polarity excited state. The large dipole moment change along with the strongly red-shifted fluorescence, as the solvent polarity is increased, demonstrate the formation of an intramolecular charge transfer state (ICT). Compounds under the study were used as fluorescence probes for monitoring the kinetics of polymerization. The study on the changes in fluorescence intensity and spectroscopic shifts of studied compounds were carried out during thermally initiated polymerization of methyl methacrylate (MMA) and during photoinitiated polymerization of 2-ethyl-2-(hydroxymethyl)propane-1,3-diol triacrylate (TMPTA).     

Laser absorption spectroscopy of the A1Σu+-X1Σg+(v′, v″) bands of Na2

Laser absorption spectra of the band system A¹Σ_u⁺-X¹Σ_g⁺(v′,v″) of Na₂ in the range between 16835 and 16960 cm^?1 are analyzed. The spectra are free of first-order-Doppler broadening at low internal temperature. Rotational and vibrational assignments of 10 bands are reported. Rotational and vibrational levels, especially the (22, 1) band, are found to be perturbed by the b³Π_u state. The band origins and line frequencies calculated from previously reported constants do not reproduce the observed values. The disagreement between the calculated and observed values is discussed. More accurate constants are needed to predict the line locations.     

Density functional theory calculations of photophysical properties of linear 2, 7-carbazole derivatives as solar cell materials

A theoretical study has been performed to explore the optical and electronic properties on a series of linear 2, 7-carbazole derivative (PCDTBT) by introducing vinyl (v) as linkage and/or benzene (B) as end-capped group for solar cell materials. The PBE0/6-31G(d) method was employed to calculate the frontier molecular orbital (FMO) and energy gap of all derivatives. The values of energy gap change less than 0.28?eV depending on v as linkage and/or B as end-capped group. The absorption spectra was evaluated using the TD-PBE0/6-31?+?G(d,p) level on the basis of the optimized geometries. The absorption spectrum has a red shift along with the increasing of molecular chain. The results of ionization potential (IP), electron affinity (EA), and reorganization energy (λ) reveal that, v as linkage and/or B as end-capped group both lead to the increase of charger transfer rates for PCDTBT. Moreover, v as linkage and/or B as end-capped group have slight effects on the stability property of PCDTBT.     

High-resolution FTIR spectra of CH2 = CClF in the 930-1050 cm−1 region

The gas-phase infrared spectra of natural CH₂ = CClF have been measured in the v ₆ and 2v ₁₂ band regions (930–1050 cm^?1) by high-resolution Fourier transform spectroscopy at room temperature. 1-Chloro-1-fluoroethylene is a planar asymmetric rotor (κ = ?0.54) belonging to the symmetry point group C_s and the vibrations investigated of symmetry species A′ give rise to a/b-hybrid bands with contributions of comparable intensity from both the components.

The rovibrational analysis of the fine structure led to the identification of 1894 (J ? 73, K_a ? 20) and 718 (J ? 53, K_a ? 8) transitions for the v ₆ and 2v ₁₂ bands of the ³⁵Cl isotopic species, respectively. Using the Watson's A-reduction Hamiltonian in the I^r representation a set of accurate spectroscopic parameters for both the excited states u ₆ = 1 and u12 = 2 of ³⁵Cl has been obtained for the first time. Transitions of ³⁷Cl isotopomer could also be assigned in the Q branch region of the 2v ₁₂ overtone; the determined band origin shift of 0.782 cm^?1 towards the lower wavenumbers led to describing the v ₁₂ fundamental as a vibration mainly involving the CFCl bending motion.     

The magnetic circular dichroism spectra of matrix-isolated benzene

The magnetic circular dichroism (MCD) spectra of the ¹ B _2u ←¹ A _1g transition of benzene in nitrogen and argon matrices at 20 K have been measured in order to obtain a spectrum devoid of hot bands and complicating rotational structure. The spectrum is dominated by three progressions of B terms, two of positive sign and one of negative. One positive progression and the negative one can be definitely assigned to the e_2g modes v ₆ and v ₉ respectively, whilst the other positive progression may be the e _2g mode v ₈. This is in marked contrast with the absorption spectra of the same matrices which reveal only a single progression built upon v ₆. The MCD spectra are nicely accounted for in terms of a magnetic mixing between the ¹ B _1u and ¹ B _2u states, the electric dipole intensity arising from the mixing in of a ¹ E _1u state via e _2g vibrational modes.     

Conformational and Electronic Interaction Studies of P-Substituted α-Phenoxyacetones

The v_co analysis of p-substituted α-phenoxy-acetones X-θ-O-CH₂-C(O)-Me (1-6) indicates the existence of the cislgauche rotational isomerism. The nearly constant increase in the cislgauche population ratios for the whole series, on going from carbon tetrachloride to acetonitrile, and the small sensitivity of the carbonyl frequency shifts (Δv_c) for the cis rotamer, on going from electron-attracting to electron-donating substituents, are interpreted as an interplay of the Field (F) and the Inductive (-I) Effects, which originates an almost constant carbonyl bond order, and suggests that the cis rotamers have almost the same energy in the whole series. The decrease in the cislgauche population ratios, in all solvents, and the deshielding effects on the carbonyl carbon atom, and on the methylene carbon atom in a weaker extent, observed in the ¹³C NMR spectra, on going from electron-attracting to electron-donating substituents, are discussed in terms of φ*CO/ⁿO orbital and Ar^δ+ -O^δ- — C^δ+ =O^δ- Coulombic interactions, which stabilize the gauche rotamers of the investigated compounds.     

Hyperfine structure in the BΠ0u state of Br2 and the influence of the perturbing 1u state

Using Doppler-free polarization spectroscopy, the hyperfine structure of the B-X system of ⁷⁹Br₂ was measured for the levels B³Π_0⁺u, v′ = 16–28, and X¹Σ_g⁺, v″ = 1, 2. Besides the nuclear electric quadrupole coupling, the magnetic spin-rotation interaction was analyzed, which varies strongly with the vibrational energy of the electronically excited state. This behavior originates from a perturbing repulsive state Ω = 1_u, the potential of which can be estimated in this way.     

boldmath B3Σu-–X3Σg- transition in selenium dimer: ab initio multireference configuration interaction calculations

Theoretical investigation of low-lying electronic states and B³Σ_u^-–X³Σ_g^- transition properties of selenium dimer using size-extensivity singly and doubly excitation multireference configuration interaction theory with nonrelativistic all-electron basis set and relativistic effective core potential plus its split valence basis set is presented in this paper. The spectroscopic constants of ten low-lying Λ-S bound states have been obtained and compared with experiments. Spin-orbit calculations for coupling between B³Σ_u^- sates and repulsive ¹Π_u, ⁵Π_u states have been made to interpret the predissociation mechanisms of the B³Σ_u^- state. The lifetimes of B³Σ_u^- (v=0～6) have been calculated with scalar relativistic effects included or excluded, respectively, and reasonably agree with experimental values.     

EPR Study of Single Crystals of PROXYLs

Electron paramagnetic resonance study of the single crystals of two PROXYLs, trans-2,5-bis(4-methylphenyl)-2,5-dimethylpyrrolidine-1-oxy [(±)-1] and trans-2-(4-methylphenyl)-2,5-dimethyl-5-phenylpyrrolidine-1-oxy [(±)-2] was conducted. The obtained spectra were always fitted well by a single Lorentzian. The principal g-values (g _x , g _y , g _z ) of (±)-1 and (±)-2 were determined as (2.00990, 2.00639, 2.00266) and (2.01106, 2.00742, 2.00389), respectively. The profiles of half width at half maximum (HWHM) depending on two polar angles, θ and ϕ, were measured in all directions. The angular profiles of the exchange interaction (|J ₀|) were attempted to be estimated by dividing the experimental HWHM by the calculated total second moment (M ₂ ^tot) with the crystallographic data. For (±)-1, |J ₀| along the c-axis was estimated to be much larger than that along the a- or b-axis. This suggests that (±)-1 is a one-dimensional magnet along the c-axis. Authors' address: Yohei Noda, Electron Spin Chemistry Laboratory, Department of Chemistry, Graduate School of Science, Kyoto University, 606-8502 Kyoto, Japan     

Schwinger boson mapping of SO(8) fermion model

The Schwinger representation of the SO(8) fermion pair algebra in terms ofd and quasispin vector (u, s, v) bosons is used in deriving a microscopic boson coherent state having both particle-hole and pair excitations. The coherent state is the exact boson image of the HFB variational solution. We can study the shape phase transition and pairing behaviour of the nuclear ground states using the coherent states.     

Molecular dynamics calculation of the dielectric constant

Molecular dynamics (MD) simulations of an isolated dipolar system (made of Stockmayer molecules) has been performed. A two dimensional system has been adopted, using a ‘2-D electrostatics’ dipolar interaction.

The isolated system was a disc in vacuo. The autocorrelation function (ACF) of the moment of the disc was extracted from our runs, together with the ACF of the moment of a small inner disc (‘microscopic’ or ‘multimolecular’ ACF). Comparison of these two ACF has allowed us to compute the response function of the annulus between the two discs. The behaviour of the latter was that predicted by the theory of Fatuzzo and Mason. It is thus shown, for the first time, that one can obtain, by numerical simulation of a few hundred molecules, reliable values of the complex permittivity of highly polar fluids, despite the long range character of the dipolar interaction.

Its behaviour is surprisingly realistic when compared with that of real 3-D polar liquids.

Monomolecular ACF have also been extracted from the MD runs. They recall that of the Itinerant Oscillator model, the long time behaviour of <u(0). u(t)> being diffusive, but shorter-lived than that of the multimolecular ACF. Compared to the free rotation, the monomolecular orientational correlation time dt (u(0). u(t)> cannot be explained quantitatively using the theory of dielectric friction derived from the Onsager reaction field. Finally a comparison between this monomolecular correlation time and the multimolecular one is made: Models linking the ratio of these two times to the Kirkwood g _K factor are examined.     

Trajectory attractor of a reaction-diffusion system with a series of zero diffusion coefficients

We study a reaction-diffusion system of N equations with k nonzero and N − k zero diffusion coefficients. More exactly, the first k equations of the system contain the terms a _i Δu _i − f _j (u, v), i = 1, …, k, with the diffusion coefficient a _i > 0. The right-hand sides of the other N − k equations contain only nonlinear interaction functions −h _j (u, v), j = k + 1, …, N, with zero diffusion. Here u = (u ₁, …, u _k ) and v = (υ _k+1, …, υ _N ) are unknown concentration vectors. Under appropriate assumptions on the interaction functions f(·) and h(·), we construct the trajectory attractor of this reaction-diffusion system. We also find the trajectory attractors , δ = (δ ₁, …, δ _k ), for the analogous reaction-diffusion systems having the terms δ _j Δυ _j − h _j (u, v), j = k + 1, …, N, with small diffusion coefficients δ _j ⩾ 0 in the last N − k equations. We prove that the trajectory attractors converge to (in an appropriate topology) as δ → 0+. Dedicated to the memory of Vladimir Borovikov Partially supported by the Russian Foundation for Basic Research (projects nos. 08-01-00784 and 07-01-00500).     

Absolute Position of the D′2g(P2) Ion-Pair State of I2 Determined by Perturbation-Facilitated Optical-Optical Double Resonance

We have reexamined the sequential two-photon absorption of I₂ from the X¹Σ_g⁺ ground state to the lowest D′2_g(³P₂) ion-pair state using the high vibrational level of the B³Π(0_u⁺) state as an intermediate. The double resonance transition to the D′2_g(³P₂) state was found to occur through the B³Π(0_u⁺)-b′2_u coupled state by hyperfine interaction, which permits to mix the different J levels of different electronic states. We elucidated the B³Π(0_u⁺)-b′2_u coupling schemes in the intermediate states. The double resonance spectra recorded for the D′2_g(³P₂) state in the range v=0-30 were used to determine the absolute energy of the D′2_g(³P₂) state. The molecular parameters of the D′2_g(³P₂) state obtained in this study are Y₀₀=40 388.783(2), Y₁₀=103.956 46(57), Y₂₀=−0.207 717(51), Y₃₀=2.199(13)×10⁻⁴, Y₀₁=0.020 528 18(62), and Y₁₁=−5.1753(48)×10⁻⁵ (all in cm⁻¹ and σ in parentheses). An RKR potential curve constructed using these constants is reported. Combined with the data on the D′2_g(³P₂)-A′³Π(2_u) transition from Zheng et al. (J. Chem. Phys.96, 4877 (1992)), we can locate the A′³Π(2_u) v=0 state at 10 096.444(6) cm⁻¹ above the ground state.