Limited resolution in complex network community detection with Potts model approach

According to Fortunato and Barthélemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.     

Syntheses and Crystal Structures of Two Coordination Polymers with Aromatic Dioxide as Bridge Ligands

Two coordination polymers, namely, two-dimensional complex 1 {[Cu(μ- L)1.5(ClO4)2(H2O)].(H2O)0.5}n (L = pyrazine-1,4-dioxide) and one-dimensional complex 2 [Co(μ-L)Br2(H2O)2]n, have been synthesized with pyrazine-1,4-dioxide as bridging ligands, and their crystal structures were determined by X-ray crystallography. Crystal data for complex 1: monoclinic system, space group C2/c, with a = 23.310(3), b = 12.2338(17), c = 10.6075(15) , β = 110.487(2)°, V = 2833.6(7) 3, Z = 8, C6H9Cl2CuN3O12.5, Mr = 457.60, Dc = 2.145 g/cm3, F(000) = 1832 and μ = 1.998 mm-1; and those for 2: monoclinic system, space group C2/c, with a = 11.012(3), b = 7.483(2), c = 11.451(3) , β = 101.654(4)°, V = 924.2(4) 3, Z = 4, C4H8Br2CoN2O4, Mr = 366.87, Dc = 2.637 g/cm3, F(000) = 700 and μ = 10.487 mm-1. 1 shows a two-dimensional sheet structure on the ac plane through the coordination of μ-L bridging ligands with Cu(II) ions, while 2 displays a zigzag one-dimensional chain along the c axis via the coordination of μ-L bridging ligand with Co(II) ions. Hydrogen bonds in 1 and 2 make the sheets (or chains) connect each other to form a three-dimensional structure.     

Polyol-Metall-Komplexe. 27. Bis-diolato-antimonate(III) mit Guanosin als Diol

Polyol Metal Complexes. 27. Bis-Diolato Antimonates(III ) with Guanosine as the Diol The complex anions of K₃[Sb^III(Guo1,2′,3′H_?3)₂] · 10 H₂O ( 1 ) and [Co(NH₃)₆][Sb^III(Guo1,2′,3′H_?3)₂] · 9 H₂O ( 2 ) are four-coordinate homoleptic bis(diolato)antimonate(III ) species. The guanosine trianions act as carbohydrate ligands through their cis-furanoidic ribosyl moiety, thus forming no nucleobase–metal bonds.     

Er2S[SiO4]: Ein Erbiumsulfid‐ortho‐Oxosilicat mit ungewöhnlicher Sulfidionen‐Koordination

During the reaction of cadmium sulfide with erbium and sulfur in evacuated silica ampoules pink lath‐shaped crystals of Er₂S[SiO₄] occur as by‐product which were characterized by X‐ray single crystal structure analysis. The title compound crystallizes orthorhombically in the space group Cmce (a = 1070.02(8), b = 1235.48(9), c = 683.64(6) pm) with eight formula units per unit cell. Besides isolated ortho‐oxosilicate units [SiO₄]^4?, the crystal structure contains two crystallographically independent Er³⁺ cations which are both eightfold coordinated by six oxygen and two sulfur atoms. The sulfide anions are surrounded by four erbium cations each in the shape of very distorted tetrahedra. These excentric [SEr₄]¹⁰⁺ tetrahedra build up layers according to by vertex‐ and edge‐connection. They are piled parallel to (010) and separated by the isolated ortho‐oxosilicate tetrahedra.     

Synthese und Kristallstrukturen der Phosphanimin-Komplexe MCl2(Me3SiNPMe3)2 mit M = Zn und Co,und CoCl2(HNPMe3)2

Syntheses and Crystal Structures of the Phosphaneimine Complexes MCl₂(Me₃SiNPMe₃)₂ with M = Zn and Co, and CoCl₂(HNPMe₃)₂ The molecular complexes MCl₂(Me₃SiNPMe₃)₂ (M = Zn, Co) have been prepared by the reaction of the dichlorides of zinc and cobalt with Me₃SiNPMe₃ in CH₃CN and CH₂Cl₂, respectively, whereas the complex CoCl₂(HNPMe₃)₂ has been prepared by the reaction of CoCl₂ with NaF in boiling acetonitrile in the presence of Me₃SiNPMe₃. All complexes were characterized by IR spectroscopy and by crystal structure determinations. The complexes MCl₂(Me₃SiNPMe₃)₂ crystallize isotypically. ZnCl₂(Me₃SiNPMe₃)₂: Space group P2₁2₁2₁, Z = 4, 2677 observed unique reflections, R = 0.024. Lattice dimensions at ?70°C: a = 1243.6; b = 1319.0; c = 1464.7 pm. CoCl₂(Me₃SiNPMe₃)₂: Space group P2₁2₁2₁, Z = 4, 3963 observed unique reflections, R = 0,071. Lattice dimensions at ?80°C: a = 1236.3; b = 1317.4; c = 1457.6 pm. CoCl₂(HNPMe₃)₂ · CH₂Cl₂: Space group Pbca, Z = 8, 1354 observed unique reflections, R = 0.055. Lattice dimensions at ?80°C: a = 1247.3; b = 998.4; c = 2882.4 pm. All complexes have monomeric molecular structures, in which the metal atoms are coordinated in a distorted tetrahedral fashion by the two chlorine atoms and by the nitrogen atoms of the phosphaneimine molecules.     

Synthesis,Structure and Reactivity of PH‐Phosphoraneiminato‐ and Iminophosphoraneiminato Group 4 Transition‐Metal Complexes

The versatile coordination chemistry of the well‐investigated phosphoraneiminato‐ligand R₃PN^— ( I ) was extended by the successive introduction of protons to the phosphorus atom. The position of the resulting equilibrium between the NH‐phosphanylamido‐ [R₂P‐NH^—] and the PH‐phosphoraneiminato‐form [R₂HP=N^—] is affected by the Lewis acidity of the coordinated metal fragment. Experimental studies on complexes with various substitution patterns at the group 4 metal center R₂HP=N[M] ( II ) were unambiguously confirmed by DFT‐calculations. The isolation of group 4 PH‐dihydrido‐phosphoraneiminato‐complexes RH₂P‐N[M] ( III ) is prevented by the low thermodynamic stability of the target molecules, also supported by the results of ab initio calculations. However, an access to the by then unknown transition‐metal substituted iminophosphanes RP=N[M] ( IV ) was verified for the first time. Within extensive studies on the coordination chemistry of bis(imino)phosphoranes RP(=NR′)(=NR″), several species of group 4 complexes R(R′N=)P=N[M] ( V ) were isolated and structurally characterized. In this case, investigations on the NH/PH‐tautomerism were performed exclusively on theoretical level, because the required educts are experimentally non‐accessible due to their kinetic instability.     

Copper phosphonates with dinuclear and layer structures: a structural and magnetic study

Hydrothermal reactions of copper (II) nitrate with 1-hydroxycyclohexanephosphonic acid [C₆H₁₀(OH)PO₃H₂] or Δ¹-cyclohexenephosphonic acid [C₆H₉PO₃H₂] have resulted in three new copper phosphonates, namely, Cu(C₆H₁₀(OH)PO₃)(H₂O)₂ (1), Cu(C₆H₁₀(OH)PO₃) (2) and Cu(C₆H₉PO₃)(H₂O) (3). Compound 1 has a dinuclear structure in which two {CuO₅} square pyramids are bridged by two {CPO₃} tetrahedra through corner sharing. The dimers are connected through intermolecular hydrogen bonds, forming supramolecular layers. Both compounds 2 and 3 show layer structures typical for metal mono-phosphonates, in which the inorganic metal-containing layers are separated by cyclohexane or cyclohexene groups. The magnetic studies show that ferromagnetic interactions are mediated between copper centers in compound 1. In compounds 2 and 3, antiferromagnetic interactions are dominant.     

C59H3N异构体的结构与稳定性的理论研究

分别用MNDO,AM1和PM3三种半经验方法对C59HN所有1-2,1-4和1-6氢加成物C59H3N的异构体进行几何构型全优化,结合频率分析及HF/6-31G单点能计算,确定了各异构体的基态结构及其相对稳定性,计算结果表明,C59HN氢加成物的立体选择性规律与C60和C60H2的不同,最稳定异构体不是1-2加成物,而是1-4加成的6,18-或12,15-异构体,次稳定异构体为1-2加成物,三种半经验方法计算得到的两者能量差为13～15kJ/mol,N原子取代碳笼骨架C原子后,改变了碳笼氢加成物的立体选择性规律.     

C28X4（X=H,Cl）,CX4（X=H,Cl）的结构和电子光谱的理论研究

用ＩＮＤＯ法对Ｃ２８Ｘ４（Ｘ＝Ｈ，Ｃｌ）和ＣＸ４（Ｘ＝Ｈ，Ｃｌ）进行几何构型优化，得到Ｔｄ对称性的构型Ｃ２８Ｘ４有４种键、４种不等同原子，基态为稳定的闭壳层分子，以此构型为基础计算了上述分子的电子光谱，并预测Ｃ２８Ｘ４的电子光谱。     

Covalent Structures of Phosphorus: A Comprehensive Theoretical Study

Starting from earlier work by Baudler we introduce a chemical heuristic for the systematic deduction and classification of covalent partial structures of phosphorus in polycyclic phosphanes, phosphorus-rich polycyclic phosphides, and allotropes of phosphorus except the black forms. This approach is used to direct ab initio techniques (which also confirm the rules) in the quest for as yet unknown forms of molecular or macromolecular phosphorus. Based on calculated stabilities of systematically generated structural alternatives we rationalize the stabilities of Hittorf's phosphorus and of molecular P₄, confirm the possible existence of at least one other crystalline allotropic form of phosphorus, and provide insight into the probable structure of amorphous red phosphorus. In total, the combined approach of chemical heuristics and large scale ab initio calculations presented in this work supplies a coherent chemical understanding of covalent polyphosphorus structures.