Geometric critical exponent inequalities for general random cluster models

A set of new critical exponent inequalities,d(1 –1 /)2 –, dv(1 – 1/), andd> 1, is proved for a general class of random cluster models, which includes (independent or dependent) percolations, lattice animals (with any interactions), and various stochastic cluster growth models. The inequalities imply that the critical phenomena in the models are inevitably not mean-field-like in the dimensions one, two, and three.The present work was reported at the 56th Statistical Mechanics Meeting (Rutgers, December 1986).     

A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.     

C(2×2)S/Fe(001)吸附体系的SCF-Xa-MS研究

采用SCF-X_α-MS方法, 对于C(2×2)S/Fe(001)吸附体系, 选择Fe_5S和Fe_9S两种原子簇模型, 研究了该吸附体系的电子结构、吸附成键特征及其相互作用图象。结果表明, S吸附于Fe(001)单晶表面具有较强的定域性质, S原子与底物Fe原子之间的吸附相互作用主要表现为S(3p)-Fe(4s,3d)之间的轨道相互作用。通过对表面吸附键长的优化, 其结果与X.S.Zhang等的ARPEFS的实验结果一致。     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Tantalum Clusters in Oxidic Matrices — Synthesis,Crystal Structure and Magnetic Properties of Eu1.83Ta15O32

The mixed‐valent oxotantalate Eu_1.83Ta₁₅O₃₂ was prepared from a compressed mixture of Ta₂O₅ and the metals in a sealed Ta ampoule at 1400 °C. The crystal structure was determined by means of single crystal X‐ray diffraction: space group R3¯, a = 777.2(6) pm and c = 3523.5(3) pm, Z = 3, 984 symmetrically independent reflections, 83 variables, R_F = 0.027 for I > 2σ (I). The structure is isotypic to Ba₂Nb₁₅O₃₂. The salient feature is a [Ta(+8/3)₆O₁₂ⁱO₆^a] cluster consisting of an octahedral Ta₆ core bonded to 12 edge‐bridging inner and six outer oxygen atoms. The clusters are arranged to slabs which are sandwiched by layers of [Ta(+5)₃O₁₃] triple octahedra. Additional Ta(+5) and Eu(+2) atoms provide the cohesion of these structural units. Twelve‐fold coordinated Eu(+2) atoms are situated on a triply degenerate position 33 pm displaced from the threefold axis of symmetry. A depletion of the Eu(+2) site from 6 to 5.5 atoms per unit cell reduces the number of electrons available for Ta‐Ta bonding from 15 to 14.67 electrons per cluster. Between 125 and 320 K Eu_1.83Ta₁₅O₃₂ is semi‐conducting with a band gap of 0.23 eV. The course of the magnetization is consistently described with the Brillouin function in terms of a M_mol/(N_Aμ_B) versus B/T plot in the temperature range 5 K — 320 K and at magnetic flux densities 0.1 T — 5 T. At moderate flux densities (< 1 T) the magnetic moment agrees fairly well with the expected value of 7.94 μ_B for free Eu (2+) ions with 4f⁷ configuration in ⁸S_7/2 ground state. Below 5 K, anisotropic magnetization measurements at flux densities B < 1 T point to an onset of an antiferromagnetic ordering of Eu spins within the layers and an incipient ferromagnetic ordering perpendicular to the layers.     

Linear scaling local correlation approach for solving the coupled cluster equations of large systems

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.     

Hydrogen analysis in solid samples by utilizing He metastable atoms induced by TEA CO2 laser plasma in He gas at 1 atm

A TEA CO₂ laser (350 mJ–1.5 J, 10.6 μm, 200 ns, 10 Hz) was focused onto a metal sub-target under He as host gas at 1 atmospheric pressure with a small amount of impurity gas, such as water and ethanol vapors. It was found that the TEA CO₂ laser with the help of the metal sub-target is favorable for generating a strong, large volume helium gas breakdown plasma at 1 atmospheric pressure, in which the helium metastable-excited state was then produced overwhelmingly. While the metal sub-target itself was never ablated. The helium metastable-excited state produced after the strong helium gas breakdown plasma was considered to play an important role in exciting the atoms. This was confirmed by the specific characteristics of the detected H emission, namely the strong intensity with low background, narrow spectral width, and the long lifetime. This technique can be used for gas and solid samples analysis. For nonmetal solid analysis, a metal mesh was introduced in front of the nonmetal sample surface to help initiation of the helium gas breakdown plasma. For metal sample, analysis can be carried out by combining the TEA CO₂ laser and an Nd–YAG laser where the Nd–YAG laser is used to ablate the metal sample. The ablated atoms from the metal sample are then sent into the region of helium gas breakdown plasma induced by the TEA CO₂ laser to be excited through the helium metastable-excited state. This technique can be extended to the analysis of other elements, not limited only to hydrogen, such as halogens.     

Two 3D supramolecular polymers constructed from an amino acid and a high-nuclear Ln6Cu24 cluster node

The first successful attempt to construct 3D supramolecular frameworks with high-nuclear 3d-4f heterometallic clusters as a node is reported. The self-assembly of Ln3+, Cu2+ and amino acid in solution leads to the formation of two polymers, 35-nuclear complex [Sm6Cu29] 1 with a primitive cubic net-like structure and 36-nuclear complex [Nd6Cu30] 2 with a face-centred cubic network type structure. Glycine and L-proline, respectively, were used as ligands. It should be noted that 2 has a chiral framework. X-ray structure analyses show that 1 crystallizes in the triclinic P1 space group (a=19.6451(8), b=20.4682(8), c=20.7046(8) A, alpha=89.453(1), beta=66.290(1), gamma=68.572(1) degrees, V=7003.0(5) A3 and Z=1) and 2 belongs to the cubic P2(1)3 space group (a=b=c=32.4341(3) A, V=34 119.7(5) A3 and Z=4). Both complexes utilize Ln6Cu24 octahedral clusters as nodes and trans-Cu(amino acid)2 groups as bridges. Electrical conductivity measurements reveal that both polymers behave as semiconductors.     

<Emphasis Type="Italic">Ab initio</Emphasis> study of small coinage metal telluride clusters Au<Subscript>n</Subscript>Te<Subscript>m</Subscript> (<Emphasis Type="Italic">n,m</Emphasis> = 1, 2)

The geometries of the most stable isomers of gold telluride systems AuTe, Au₂Te, and AuTe₂ are determined using the MP2 method. The aspect of gold—telluride interaction, the electron correlation, and relativistic effects on geometry and stability are investigated at the MP2 and CCSD(T) theoretical levels. The results show that the electron correlation and relativistic effects are responsible not only for gold—gold attraction but also for additional gold—telluride interaction. The gold—telluride interaction is strong enough to modify the known pattern of bare gold clusters. Both effects are essential for determining the geometry and relative stability of this type of systems.