The problem of the structure (state of helium) in small He<Subscript><Emphasis Type="Italic">N</Emphasis></Subscript>-CO clusters

A second-order perturbation theory, developed for calculating the energy levels of the He-CO binary complex, is applied to small He _N -CO clusters with N = 2−4, the helium atoms being considered as a single bound object. The interaction potential between the CO molecule and HeN is represented as a linear expansion in Legendre polynomials, in which the free rotation limit is chosen as the zero approximation and the angular dependence of the interaction is considered as a small perturbation. By fitting calculated rotational transitions to experimental values it was possible to determine the optimal parameters of the potential and to achieve good agreement (to within less than 1%) between calculated and experimental energy levels. As a result, the shape of the angular anisotropy of the interaction potential is obtained for various clusters. It turns out that the minimum of the potential energy is smoothly shifted from an angle between the axes of the CO molecule and the cluster of θ = 100° in He-CO to θ = 180° (the oxygen end) in He₃-CO and He₄-CO clusters. Under the assumption that the distribution of helium atoms with respect to the cluster axis is cylindrically symmetric, the structure of the cluster can be represented as a pyramid with the CO molecule at the vertex.     

Density functional theory study on the structural and electronic properties of Ag-adsorbed (MgO)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters

Equilibrium geometries, charge distributions, stabilities and electronic properties of the Ag-adsorbed (MgO) _n (n = 1–8) clusters have been investigated by density functional theory (DFT) with generalized gradient approximation (GGA) for exchange-correlation functional. The results show that hollow site is energetically preferred for n⩾4, and the incoming Ag atoms tend to cluster on the existing Ag cluster. The Mulliken populations indicate that the interaction between the Ag atom and Magnesia clusters is mainly induced by a weak atomic polarization. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of Magnesia clusters is minor. Furthermore, the investigations on the first energy difference, fragmentation energies and electron affinities show that the Ag(MgO)₄ and Ag(MgO)₆ are the most stable among studied clusters. Supported by the Startup Fund of High-level Personal for Shihezi University (Grant No. RCZX200747)     

Temperature determination of (CF<Subscript>3</Subscript>I)<Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> clusters in a beam by time-of-flight measurements of IR-laser excited SF<Subscript>6</Subscript> molecules sublimating from the surface of clusters

The method is described and the experimental results are presented on the temperature determination of the (CF₃I) _N clusters in a beam (N ⩽ 10² is a number of monomers in a cluster) using SF₆ molecules from intersecting molecular beam as probe thermometers. The SF₆ molecules are captured by clusters in the crossed cluster and molecular beams and, after a certain time, sublimate from the surface of clusters carrying information on the velocity and temperature (internal energy) of clusters. Using time-of-flight (TOF) method the kinetic energy (velocity) of sublimated SF₆ molecules was measured and the temperature of clusters was determined to be T _cl = (88 ± 15) K.     

Electronic structure of crystal-forming fulborenes B<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>N<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

A general approach is formulated to the design of crystal-forming fullerene-like clusters X _n Y _n from which zeolite-like covalent crystals based on IV-IV, III-V, and II-VI binary semiconductor compounds with diamond-like sp ³ bonds can be constructed and synthesized by means of copolymerization through faces. A number of the smallest sized crystal-forming boron nitride clusters are constructed, such as the B₁₂N₁₂, B₁₆N1₆, B₁₈N₁₈, B₂₄N₂₄, B₃₆N₃₆, and B ₆₀N₆₀ fulborenes. The optimized configurations, electronic structures, charge transfers, band gaps, total energies, cohesive energies, and electron density maps of the clusters are calculated using the spin-restricted Hartree-Fock method in the 6–31G basis set. Comparative calculations of the B₆₀N₆₀ fulborene with the use of the density functional theory method have demonstrated that the spin-restricted Hartree-Fock method in the 6–31G basis set is optimum from the standpoint of the accuracy and efficiency.     

Electron paramagnetic resonance of spin-variable metallomesogens [Fe<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>]<Emphasis Type="Italic">X</Emphasis> (<Emphasis Type="Italic">X</Emphasis> = PF<Subscript>6</Subscript>, SCN)

Significant differences in the manifestation of spin-crossover properties of the mesogen compounds [FeL ₂]X with oxysalicylidene-N′-ethyl-N-ethylenediamine ligands L and anions X = PF₆⁻ and SCH⁻ have been found by means of electron paramagnetic resonance. The electron paramagnetic resonance data and the quantum-chemical calculation within the density functional theory enables us to establish that the observed specific features are associated with the incorporation of the SCH⁻ ion into the first coordination sphere of the Fe(III) ion. The role of the transition of the material to the liquid-state phase in the formation of a low-dimensional (two-dimensional) structure with stronger intermolecular interactions has been revealed.     

1/<Emphasis Type="Italic">N</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> countings in baryons

The 1/N _c -power countings for baryon decays and configuration mixings are determined by means of a nonrelativistic quark picture. Such countings are expected to be robust under changes in the quark masses and, therefore, valid as these become light. It is shown that excited baryons have natural widths of \(\mathcal{O}(N_c^0 )\). These dominant widths are due to the decays that proceed directly to the ground-state baryons, with cascade decays being suppressed to \(\mathcal{O}(1/N_c )\). Configuration mixings, defined as mixings between states belonging to different O(3) × SU(2N _f ) multiplets, are shown to be subleading in an expansion in \(1/\sqrt {N_c }\) when they involve the ground-state baryons, while the mixings between excited states can be \(\mathcal{O}(N_c^0 )\).     

Detection of SF<Subscript>6</Subscript> molecules sublimating from the surface of (CO<Subscript>2</Subscript>)<Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> nanoparticles in a cluster beam by the infrared multiphoton excitation method

It has been found that SF₆ molecules captured by large van der Waals clusters (CO₂) _N (where N ≥ 10² is the number of monomers in a cluster) in intersecting molecular and cluster beams sublimate from the surface of clusters after a certain time and carry information on the velocity and temperature (internal energy) of clusters. Experiments have been carried out for detecting these molecules by means of a pyroelectric detector and the infrared multiphoton excitation method. The multiphoton absorption spectra of molecules sublimating from the surface of clusters have been obtained. The temperature of the (CO₂) _N nanoparticles in the cluster beam has been estimated using these spectra and comparing them with the infrared multiphoton absorption spectra of SF₆ in the initial molecular beam.     

Features of structure and properties of Na<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>C<Subscript>60</Subscript> (<Emphasis Type="Italic">n</Emphasis> = 2, 3) fullerides synthesized in toluene

The structure and electron properties of Na _n C₆₀ (n = 2, 3) sodium fullerides synthesized from simple compounds in toluene were studied. It was shown that Na₂C₆₀ fulleride forms a face-centered cubic lattice at temperatures above 300 K. As the temperature is lowered, the phase transition to a structure with a simple cubic lattice takes place. The temperature dependences of the properties of Na₃C₆₀ with a more complex structure exhibit features that are presumably due to sodium atom redistribution in the Na₃C₆₀ fulleride lattice and the formation of sodium ion clusters.     

Polynomial Realization of <Emphasis Type="Italic">s</Emphasis>l<Subscript><Emphasis Type="Italic">q</Emphasis></Subscript>(2) and Fusion Rules at Exceptional Values of <Emphasis Type="Italic">q</Emphasis>

Representations of the sℓ_q(2) algebra are constructed in the space of polynomials of real (complex) variable for q^N=1. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated.     

The Effect of the Complexation of <Emphasis Type="Italic">p-N,N</Emphasis>-Dimethylaminobenzoic Acid and <Emphasis Type="Italic">p-N,N</Emphasis>-Dimethylaminobenzonitrile with LaCl<Subscript>3</Subscript> on Spectral-luminescent Parameters of Fluorophores

The LE band fluorescence enhancement of p-N,N-dimethylaminobenzoic acid (DMABA) and p-N,N-dimethylaminobenzonitrile (DMABN) was found in aprotic acetonitrile and butyronitrile at the addition of LaCl₃. The corresponding ICT fluorescence band remains unchanged. This enhancement is explained by the decrease of the internal conversion rate constant in a coordination complex with LaCl₃. The formation of the coordination complex between DMABA and LaCl₃ in ethanol is accompanied by the efficient fluorescence quenching in LE and ICT bands, in parallel with the enhancement of ICT/LE emission ratio. The experimental data are well described by the proposed kinetic schemes.     

A reanalysis of finite temperature <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

We revise the SU(N _c ), N _c =3,4,6, lattice data on pure gauge theories at finite temperature by means of a quasi-particle approach. In particular, we focus on the relation between the effective mass of the quasi-particle and the order of the deconfinement transition, the scaling of the interaction measure with N²_c -1N^{2}_{c} -1, the role of gluon condensate, and the screening mass.     

On the Sutherland Spin Model of <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> Type and Its Associated Spin Chain

 The B _N hyperbolic Sutherland spin model is expressed in terms of a suitable set of commuting Dunkl operators. This fact is exploited to derive a complete family of commuting integrals of motion of the model, thus establishing its integrability. The Dunkl operators are shown to possess a common flag of invariant finite-dimensional linear spaces of smooth scalar functions. This implies that the Hamiltonian of the model preserves a corresponding flag of smooth spin functions. The discrete spectrum of the restriction of the Hamiltonian to this spin flag is explicitly computed by triangularization. The integrability of the hyperbolic Sutherland spin chain of B _N type associated with the dynamical model is proved using Polychronakos's ``freezing trick'. Received: 14 February 2002 / Accepted: 19 June 2002 Published online: 10 December 2002 RID="*" ID="*" Corresponding author. E-mail: artemio@fis.ucm.es RID="**" ID="**" On leave of absence from Institute of Mathematics, 3 Tereschenkivska St., 01601 Kyiv-4 Ukraine Communicated by L. Takhtajan     

Ordering of nonstoichiometric hexagonal compounds <Emphasis Type="Italic">M</Emphasis><Subscript>2</Subscript><Emphasis Type="Italic">X</Emphasis>: A sequence of special figures

An ensemble of figures required for the analysis of the atomic-vacancy ordering in nonstoichiometric compounds M ₂ X _y (M ₂ X _y ▭_{1 − y} ) with an L′3 hexagonal structure has been determined by the order-parameter functional method. It has been demonstrated reasoning from the crystal lattice geometry that, in order to describe M ₂ X _y compounds with an L′3 structure, it is necessary to use the basis cluster in the form of a trigonal prism consisting of six sites of the nonmetal lattice with a metal atom at the center. The overlapping figures that, together with the basis cluster, form a sequence of special figures uniquely describing the L′3 structure have been found. The equilibrium conditions for disorder-order transformations in nonstoichiometric compounds M ₂ X _y have been determined in the general form.     

On the degeneracy of <Emphasis Type="Italic">SU</Emphasis>(3)<Subscript><Emphasis Type="Italic">k</Emphasis></Subscript> topological phases

The ground state degeneracy of an SU(N) _k topological phase with n quasiparticle excitations is a relevant quantity for quantum computation, condensed matter physics, and knot theory. It is an open question to find a closed formula for this degeneracy for any N >2. Here we present the problem in an explicit combinatorial way and analyze the case N = 3. While not finding a complete closed-form solution, we obtain generating functions and solve some special cases.     

Optical characteristics of nickel and boron carbonitride films in Si(100)/Ni/BC<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>N<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> structures

The optical characteristics of nickel films deposited on Si(100) substrates by vacuum thermal evaporation have been studied. The thickness and optical constants of the films are determined using monochromatic zero ellipsometry, while the inverse problems are solved within the three-layer optical model of the samples. It is shown that thermal annealing leads to a change in the optical constants of nickel films in the heating-temperature range of 500–900°C. Boron carbonitride layers deposited on silicon substrates with a nickel sublayer are analyzed within multilayer optical models, which make it possible to determine the refractive index and absorption coefficient distributions along the thickness of the synthesized Si(100)/Ni/BC _x N _y structure.     

Fragmentation of sputtered Si<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>O<Stack><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript><Superscript>+</Superscript></Stack> clusters: Release kinetic and dissociation energies

The spectra of kinetic energies of positive Si _n O _m ⁺ cluster ions (n = 2–5, m = 2–7) have been measured using a double focusing ion microanalyzer with reverse geometry at instants 10⁻⁵ to 10⁻⁴ s after emission. The dissociation energies have been determined within the evaporative ensemble model and the theory of unimolecular decay reactions. The results obtained are compared with the binding energies of neutral Si _n O _m clusters.     

Reduction of silver nanoparticles onto graphene oxide nanosheets with <Emphasis Type="Italic">N</Emphasis>,<Emphasis Type="Italic">N</Emphasis>-dimethylformamide and SERS activities of GO/Ag composites

Silver nanoparticles (Ag NPs) have been homogeneously deposited onto graphene oxide (GO) nanosheets by an optimal method, in which N,N-dimethylformamide (DMF) as a co-dispersant of GO and reductant of sliver ions is added to an aqueous suspension of GO and AgNO₃. GO nanosheets are uniformly covered by Ag NPs with a narrow size distribution and inter-particle gap. Raman signals of GO are greatly enhanced after deposition owing to the charge transfer interaction of GO with Ag NPs. The GO/Ag composite can be further utilized as an effective surface-enhanced Raman scattering (SERS) active substrate. Several new Raman bands and frequency shifts are clearly observed in using 4-aminothiophenol (4-ATP) as a Raman probe on GO/Ag compared to the normal Raman spectrum of solid 4-ATP. The Raman enhancement arises from a major electromagnetic effect and a minor chemical effect.     

Orientation ordering of N<Subscript>2</Subscript> molecules in vertically aligned CN<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> nanotubes

Arrays of vertically aligned nitrogen-doped carbon (CN _x ) nanotubes have been synthesized by decomposition of aerosol mixture of acetonitrile and ferrocene at 850°C. Nitrogen concentration in the outer shells of the CN _x nanotubes was found from X-ray photoelectron spectroscopy (XPS) data to reach ∼6%. The XPS N 1s spectra and N 1s near-edge X-ray absorption fine structure (NEXAFS) spectra identified three chemical forms of nitrogen in the CN _x nanotube arrays: pyridine-like, graphitic, and molecular nitrogen. The π ^* resonance of molecular nitrogen showed clear polarization dependence that indicates predominant orientation of N₂ molecules along the nanotubes axis. The estimated range of the polar angle distribution of the N₂ molecules orientation in the CN _x nanotube array amounts to 15°.     

<Emphasis Type="Italic">SU</Emphasis>(3)-Instantons and <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>,<Emphasis Type="Italic">Spin</Emphasis>(7)-Heterotic String Solitons

Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. A formula for the Riemannian scalar curvature is obtained. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimension 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in G₂ arises from our considerations and Hitchin’s flow equations, which seems to be new. Compact examples of SU(3),G₂ and Spin(7) instanton satisfying the anomaly cancellation conditions are presented.