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.     

Molecular structure and nanosecond optical limiting property of a typical silver cubane-like cluster containing tetraselenotungstate

A typical silver cubane-like heteroselenometallic cluster, (μ₃-WSe₄)Ag₃(PPh₃)₃Cl·0.5SePPh₃, was synthesized from reaction of [Et₄N]₂[WSe₄] and Ag(PPh₃)₂(NO₃) in CH₂Cl₂ solution and structurally characterized by X-ray crystallography. The compound crystallizes in the trigonal space group R3 with a=16.258(4), b=22.80(3) Å, V=5217(7) ų, and Z=3. The structure contains a strongly distorted cubane-like {WAg₃Se₃Cl} core. The coordination geometries of the W center and each Ag atom are tetrahedral. The mean W-Ag separation is 3.010(3) Å. Optical nonlinearity of this cubane-like cluster was studied. Large optical limiting effect with threshold of 0.45 J/cm² was observed with the laser pulses of 7 ns at 532 nm.     

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。     

金属羰基化合物的结构对氧原子转移反应速率的影响

本文研究了氧化三甲胺Ｍｅ３ＮＯ与羰基簇合物Ｍ４（ＣＯ）１２－ｎＬｎ（Ｍ＝Ｃｏ，Ｉｒ；ｎ＝１，２；Ｌ＝磷配体）的氧转移反应动力学，讨论了反应机理。反应符合二级速率方程：ｒ＝Ｋ２［Ｍｅ３ＮＯ］［Ｍ４（ＣＯ）１２－ｎＬｎ］Ｍ４（ＣＯ）１２－ｎＬｎ的氧转移反应活性呈现如下顺序：中心元素不同时Ｃｏ４（ＣＯ）１２－ｎＬｎ＜Ｉｒ４（ＣＯ）１２－ｎＬｎ；取代配体不同时Ｍ４（ＣＯ）１２－ｎ（Ｐ（ＯＭｅ）３）ｎ＞Ｍ４     

几个金属卤素簇的合成与性能研究

The hydrothermal reaction of CuBr2 and CuBr with phen·H2O （phen= 1,10-phenanthroline） in a molar ratio of 1：1：1.5 gave birth to the first copper-halo cationic cluster [Cu2^Ⅱ Cu2^Br4 （phen）4 ] ^2＋（1） with tetranuclear anionic cluster [Cu4Br6]^2-. Changing the precursors or their molar ratios, two mononuclear complexes [Cu（phen）2Br]Br·H2O （2） and [Ni（phen）3][CuCl2]2 （3） as well as two unusual copper-halo chains found in polymers [Cu2Br2（phen）]∞ （4） and [Cu^ⅡCu3^ⅠBr2Ⅰ3 （phen）2 ]∞ （5） were obtained. The （Cu2Br2）∞ chain of 4 looks like a linearar ray of hexagons based on fused Cu3Br3 units, and the linear （Cu3Ⅰ3Br^-）∞ chain of 5 is an alternate combination of the rhombic Cu2I2 cores and the Cu4I4Br2^2- units. In addition, the hydrothermal reaction of CuBr2 with NA（NA=nicotinic acid） or INA （INA =isonicotinic acid） resulted in the syntheses of two compounds [CuBr（NA）] （6） and [CuBr（INA）]∞（7） containing staircase chain. Among them the third-order non-linear optical properties of 2, 5, 6 and 7 were investigated and all exhibit the reverse saturable absorption （α2〉0） and self-defocusing performance （n2〈0）.     

Preparative and electrochemical investigations on the electron sponge behavior of cobalt telluride clusters: CO substitution in [Co11Te7(CO)10]n- ions (n=1, 2) by PMe2Ph and crystal structure of [Co11Te7(CO)5(PMe2Ph)5

The reaction of the cluster salts [Cp(2*) Nb(CO)(2)](n)[Co(11)Te(7)(CO)(10)] (Cp*=C(5)Me(5); n=1, 2) with excess PMe(2)Ph gave the neutral, dark brown clusters [Co(11)Te(7)(CO)(6)(PMe(2)Ph)(4)] (5) and [Co(11)Te(7)(CO)(5)(PMe(2)Ph)(5)] (6) with 147 metal valence electrons. The new compounds were characterized by IR spectroscopy, elemental analyses, and mass spectrometry. The molecular structure of 6 was determined by X-ray crystallography. Like its precursor anion, it consists of a pentagonal-prismatic [Co(11)Te(7)] core, but with a ligand sphere composed of five CO and five PMe(2)Ph ligands. Detailed electrochemical studies of both reactions reveal that a stepwise substitution of CO ligands in the initial cluster anions takes place leading to intermediate [Co(11)Te(7)(CO)(10-m)(PMe(2)Ph)(m)](n-) ions (m=1-5; n=1, 2). Each of these intermediates is distinguished by at least one oxidation and two reduction waves, giving rise to a total of 21 redox couples and 27 electroactive species. The electron sponge character of the new compounds is particularly pronounced in 5, which exhibits charges n between +1 and -4 corresponding to metal valence electron counts of between 146 and 151.     

On the calculation of expectation values and transition matrix elements by coupled cluster method

Summary Finite order expressions are derived for expectation values and transition matrix elements within the framework of the coupled cluster method.     

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.