Electron impact ionization of Ar n , (H2O) n , Ar n (H2O) m clusters

Signals from ions forming in a supersonic molecular beam consisting of an argon-water vapor mixture are measured as functions of the exciting electron energy in the range to 120 eV. The thresholds of electron impact excitation of (H₂O) _{n − 1}H⁺ and Ar _n (H₂O _m ⁺ clusters are determined for the first time. It is found that the proton-hydroxyl group binding energy decreases considerably both in the case of water molecule clustering and when mixed Ar _n (H₂O) _m clusters arise.     

Contrasting routes to the Kostka coefficients of λ [boxvr] n (ln)-permutational module expansions for 6n8: Applications to NMR spin clusters under SU(mn)×Ln spin symmetries

Aspects of the higher-n λ( _n) permutational modules associated with Young subgroups of various highly-branched high-n fold algebras, which are pertinent to identical spin NMR clusters, are presented for λ [boxvr] _n (or λ [boxvR] n), aRota p-tuple or number partition; the method of optimal choice for deriving the Λ_[λ′] Kostka coefficients, found in {[λ′]} sets derived from λ permutational module expansions, rests on the ordering of the λ-(shape) to the self-associated diagram(s) in the dominance hierarchy. Hence, physical insight into these cage-cluster NMR systems is developed both from these properties and from the inter-related induced symmetries of GL(n, ) and _n groups. From these associated combinatorial, mapping or scalar invariant aspects of SU(mn)× _n symmetry, one may define the [A]_n( _n) systems of [AX]_n NMR problems in a general semi-topological limit. This corresponds to a high-n _n limit in which the individual spin cluster exhibits a lack of any (intracluster) ‘magnetic equivalence’ properties.     

(HMgN3)n(n=1–5)团簇结构与性质的密度泛函理论研究

利用密度泛函理论在B3LYP/6-311G^*水平上对叠氮化合物(HMgN₃)_n(n=1–5)团簇各种可能构型进行了几何优化,预测了各团簇的最稳定结构. 并对最稳定结构的成键特性、电荷分布、振动特性及稳定性进行理论研究. 结果表明:HMgN₃团簇最稳定结构为直线型;(HMgN₃)_n(n=2,5)团簇最稳定结构为叠氮基中N原子和金属原子相连构成Mg–N–Mg结构;(HMgN₃)_n(n=3,4)团簇最稳定结构为叠氮基与Mg原子相互链接形成的环状结构. 团簇最稳定结构中金属Mg原子均显示正电性,H原子均显示负电性,叠氮基中间的N原子显示正电性、两端的N原子显示负电性,且与Mg原子直接作用的N原子负电性更强. Mg–N键和Mg–H键为典型的离子键,叠氮基内N原子之间是共价键. 团簇最稳定结构的红外光谱分为三部分,其最强振动峰均位于2258–2347 cm^-1,振动模式为叠氮基中N–N键的反对称伸缩振动. 叠氮基在团簇和晶体中结构不变,始终以直线型存在. 稳定性分析显示,(HMgN₃)₃团簇相对于其他团簇更为稳定. 关键词： 3)_n(n=1–5)团簇')" href="#">(HMgN₃)_n(n=1–5)团簇 叠氮基 密度泛函理论 结构与性质     

Analysis of irreducible representations of the group U (4) Up(2) × Un(2)

The general method of projection operators is used to construct the noncanonical nonorthogonal basis of arbitrary irreducible representation of the group U (4) in the reduction U (4) U_p(2) × U_n(2), where U_p(2)(U_n(2)) is the transformation group in the proton (neutron) spin space. The completeness of this basis is proved and the matrices of the U (4) group generators and of the Bargmann-Moshinsky operator Ω in this basis are obtained. The matrix Ω exhibits a nondegenerate spectrum of the eigenvalues which may be used as the missing quantum number.     

Structural mechanisms of proton conduction in MemHn(XO4)(m + n)/2 crystals

Investigations of K₃H(SO₄)₂ samples, which belong to the family of Me _m H _n (XO₄)_{(m + n)/2} (Me = K, Cs, Rb, NH₄; X = S, Se, As) crystals, revealed temperature anomalies in the dielectric and optical properties and in the heat capacity upon phase transitions. X-ray diffraction studies confirmed that K₃H(SO₄)₂ crystals undergo a structural phase transition from the monoclinic phase to the trigonal phase C2/c → R m and that the high proton conductivity in the high-temperature phases of crystals belonging to this family is due to the formation of a qualitatively new system of hydrogen bonds. Original Russian Text ? A.A. Simonov, I.P. Makarova, V.V. Grebenev, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 8, pp. 1477–1479.     

Discrete series of unitary irreducible representations of the Uq(u(3, 1)) and Uq(u(n, 1)) noncompact quantum algebras

The structure of all discrete series of unitary irreducible representations of the U _q (u(3, 1)) and U _q (u(n, 1)) noncompact quantum algebras are investigated with the aid of extremal projection operators and the q-analog of the Mickelsson-Zhelobenko algebra Z(g, g′) _q . The orthonormal basis constructed in the infinite-dimensional space of irreducible representations of the U _q (u(n, 1)) ⊇ U _q (u(n)) algebra is the q-analog of the Gelfand-Graev basis in the space of the corresponding irreducible representations of the u(n, 1) ⊇ u(n) classical algebra.     

α(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order α(Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through α(Q²) we find , with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

SO q (n+1,n−1) as a real form of SO q (2n,ℂ)

Quantum pseudo-orthogonal groups SO _q (n+1,n–1) are defined as real forms of quantum orthogonal groups SO _q (n+1,n–1) by means of a suitable antilinear involution. In particular, the casen=2 gives a quantized Lorentz group.     

Lower bounds for eigenvalues of the Dirac operator on n-spheres with SO(n)-symmetry

In this paper we derive estimates for the eigenvalues of the Dirac operator and their multiplicity on manifolds diffeomorphic to Sⁿ with an isometric SO(n)-action. Especially we prove a new lower bound for the first eigenvalue and show an example, where this new bound coincides in the limit with the known upper bounds.     

Density functional theory study of neutral AlS_n(n=2-9) clusters

This paper investigates the geometrical structures and relative stabilities of neutral AlS n(n = 2-9) using the density functional theory.Structural optimisation and frequency analysis are performed at the B3LYP/6-311G(d) level.The ground state structures of the AlS n show that the sulfur atoms prefer not only to evenly distribute on both sides of the aluminum atom but also to form stable structures in AlS n clusters.The structures of pure S n are fundamentally changed due to the doping of the Al atom.The fragmentation energies and the second-order energy differences are calculated and discussed.Among neutral AlS n(n = 2-9) clusters,AlS 4 and AlS 6 are the most stable.     

Scaling contributions to the free energy in the 1/n expansion of O(n) nonlinear sigma models in d-dimensions

Within the 1/N expansion of O(N) nonlinear σ models for d≤4 it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to O(1/N). For critical dimensions d=2+2/n the Abe-Hikami anomaly is recovered, while for d=2 the removal of the spin-wave term is justified.     

Magnetotransport and magnetotunneling in single-layer, two-layer, and three-layer Bi2Sr2Can−1CunOz (n=1,2,3) single crystals

In continuous magnetic fields H up to 28 T, we have studied the out-of-plane transport properties and tunneling characteristics of high-quality nondoped single crystals of the Bi-cuprate family: Bi₂Sr₂CuO_6+δ (Bi2201), Bi₂Sr₂CaCu₂O_8+δ (Bi2212) and Bi₂Sr₂Ca₂Cu₃O_10+δ (Bi2223) grown by an identical method. For all compounds the out-of-plane magnetotransport ρ_c(H) is negative in the temperature region where ρ_c(T) shows in the normal state a semiconducting-like temperature dependence. The negative magnetoresistance of ρ_c corresponds to the suppression of the semiconducting temperature dependence of ρ_c(T) which is found to be isotropic. For the Bi2201 compound, where the normal state can be reached in the available magnetic fields (28 T), a nearly complete suppression of the low-temperature upturn in ρ_c(T) is observed in the highest magnetic fields with a tendency towards a metallic behavior down to the lowest temperatures (0.4 K). Using the break-junction technique, especially for the Bi2212 and Bi2232 compounds, a clear superconducting gap structure can be observed. Both for temperatures above the critical temperature and for magnetic fields above the upper critical field, a pseudogap structure remains present in the tunneling spectra. The applied magnetic fields yield a stronger suppression of the superconducting state compared to that of the normal-state gap structures as manifested in ρ_c(T) transport and tunneling.     

Dynamical and symmetry groups of the SU(2) Kepler problem

It is well known that the MIC–Kepler problem, an extension of the three-dimensional Kepler problems, admits the same dynamical and symmetry groups as the Kepler problem. This paper aims to study dynamical and symmetry groups of the SU(2) Kepler problem, where the SU(2) Kepler problem is defined to be the dynamical system reduced from the eight-dimensional conformal Kepler problem through an SU(2) symmetry and turns out to be an extension of the five-dimensional Kepler problem. It is shown that the SU(2) Kepler problem admits a dynamical group SO^*(8) and that the phase space of the SU(2) Kepler problem is symplectomorphic with a co-adjoint orbit of SO^*(8), on which the Kirillov–Kostant–Souriau form is defined. It is further shown that the subgroups, SU(4), SU^*(4), and Sp(2)×_SR⁵, of SO^*(8) provide the symmetry groups, SU(4)/Z₂SO(6), SU^*(4)/Z₂SO₀(1,5), and (Sp(2)×_SR⁵)/Z₂SO(5)×_SR⁵, of the SU(2) Kepler problem with negative, positive, and zero energies, respectively, where ×_S denotes a semi-direct product. Furthermore, constants of motion for the SU(2) Kepler problem are found together with their Poisson brackets. The symmetry Lie algebra formed by constants of motion is shown to be isomorphic with so(6)su(4), so(1,5)su^*(4), or so(5)_SR⁵sp(2)_SR⁵, depending on whether the energy is negative, positive, or zero, where _S denotes a semi-direct sum. These Lie algebras are subalgebras of so^*(8)so(2,6).     

WnNim(n+m=8)团簇的极性和光谱性质的理论研究

采用密度泛函理论(DFT)中的B3LYP方法,在LANL2DZ基组水平上对WnNim(n+m=8)团簇的各种可能构型进行了几何参数全优化,得到了它们的基态构型;并对基态构型的偶极距、极化率、红外光谱和拉曼光谱性质进行了分析,结果表明:团簇WnNim(n+m=8)都具有极性,富W团簇非线性光学效应强,容易被外加场极化;振动频率主要分布在0-350 cm-1范围内,团簇W4Ni4因其振动方式的特殊性,红外光谱和拉曼光谱在频率421.971 cm-1处,都有明显强峰;团簇W5Ni3因其结构的高对称性在振动光谱中出现多处共振现象.     

Structures and electronic properties of Mo2nNn（n=1-5）:a density functional study

The lowest-energy structures and the electronic properties of Mo2nNn(n=1-5) clusters have been studied by using the density functional theory(DFT) simulating package DMol 3 in the generalized gradient approximation(GGA).The resulting equilibrium geometries show that the lowest-energy structures are dominated by central cores which correspond to the ground states of Mo n(n = 2,4,6,8,10) clusters and nitrogen atoms which surround these cores.The average binding energy,the adiabatic electron affinity(AEA),the vertical electron affinity(VEA),the adiabatic ionization potential(AIP) and the vertical ionization potential(VIP) of Mo2nNn(n=1-5) clusters have been estimated.The HOMO-LUMO gaps reveal that the clusters have strong chemical activities.An analysis of Mulliken charge distribution shows that charge-transfer moves from Mo atoms to N atoms and increases with cluster size.     

Synthesis and luminescence properties of lead-halide based organic–inorganic layered perovskite compounds (CnH2n+1NH3)2PbI4 (n=4, 5, 7, 8 and 9)

This paper describes the synthesis and characterization of organic–inorganic layered perovskite compounds, (C_nH_2n+1NH₃)₂PbI₄ (n=4, 5, 7, 8 and 9). The effect of the number of carbon atoms on luminescence properties has been examined. Thin films of microcrystalline (C_nH_2n+1NH₃)₂PbI₄ fabricated by spin-coating are highly oriented, with the c-axis perpendicular to the substrate surface. Temperature-dependent optical absorption spectra reveal that (C_nH_2n+1NH₃)₂PbI₄ films (n=4, 7, 8 and 9) show the structural phase transitions. The excitonic structures of (C_nH_2n+1NH₃)₂PbI₄ vary with the number of carbon atoms of the alkyl chain length. At low temperatures below 100 K, the lowest-energy free-exciton band of (C_nH_2n+1NH₃)₂PbI₄ (n=7, 8 and 9) split into three fine-structure levels. In contrast to (C_nH_2n+1NH₃)₂PbBr₄ films, (C_nH_2n+1NH₃)₂PbI₄ (n=7, 8 and 9) shows no triplet exciton emission, but it shows the Stokes-shifted emission from bound excitons.     

The n = 0 replica limit of U(n) and models

Recently the replica limit n = 0 of the U(n) and models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and . This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and and draw consequences for these functions in this limit.     

A unified treatment of the groups SO(4) and SO(3,1)

The irreducible representations of the group SO(4) in which the SO(3) subgroup is reduced are studied by an explicit construction of the operators and the basis in the spinor representation. The basis function which is formally identical with that for the coupling of two angular momentaj ₁ andj ₂ is expressible in terms of a hypergeometric function and strongly resembles the one for the irreducible representations of the groups SO(3,1). For the Lorentz group, the bases for the unitary representations which require unphysical values ofj ₁ andj ₂ are found to be analytic continuation of those for SO(4). The realization of the unitary irreducible representations of the group SO(4) in the Hilbert space of these functions leads, for appropriate unphysical values ofj ₁,j ₂, to the Gelfand-Naimark formula for the principal and complementary series of the representations of SO(3;1). The matrix elements for finite transformations of SO(4) and SO(3,1) can be evaluated, in this approach, in a unified manner by using standard properties of the hypergeometric function. These turn out to be a finite sum of₃ F ₂-functions which, as expected, are polynomials for SO(4) and infinite series for SO(3,1). A number of special matrix elements are calculated from the general formula and these agree with the results obtained previously.The authors are deeply indebted to Professor S.Dutta Majumdar fo many important suggestions and clarifications.     

The analytical potential energy function of flue gas SO2（X1A1）

The equilibrium structure of flue gas SO2 is optimized using the density functional theory （DFT）/B3P86 method and CC-PV5Z basis. The result shows that it has a bent （C2v, X1A1） ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics （AMIIS）, the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie＋c6 （M-S＋c6） potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 （X1A1） molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 （XIA1）, such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

Acoustical and excess properties of {1-hexanol + n-hexane, or n-octane, or n-decane} at (298.15, 303.15, and 308.15) K

Densities (ρ) and speeds of sound (u) for the binary mixtures of 1-hexanol with n-hexane, n-octane and n-decane have been measured over the entire composition range at 298.15, 303.15 and 308.15 K. The dynamic viscosities (η) for these systems have been measured at 298.15 K. From experimental data, excess molar volumes (V_m^E), molar isentropic compressibility (K_s,m), excess molar isentropic compressibility (K_s,m^E), deviation in speed of sound (u^D) from their ideal values (u^id) in an ideal mixture, and excess free volumes (V_f^E) have been calculated. The excess functions have also been correlated with the Redlich–Kister polynomial equation. The viscosity data have been analysed in terms of some semi-empirical equations. The theoretical values of speed of sound (u) and isentropic compressibility (κ_S) have also been estimated using the Prigogine–Flory–Patterson (PFP) theory with the van der Waals (vdW) potential energy model and the results have been compared with experimental values. The effect of chain-length of n-alkanes as well as the temperature on the excess properties has also been studied.