Bis(2,2′-bipyrid­yl)bromidocopper(II) bromide bromo­acetic acid hemihydrate

In the title compound, [CuBr(C10H8N2)2]Br·BrCH2COOH·0.5H2O, the CuII ion is coordinated by four N atoms [Cu—N = 1.985 (6)–2.125 (7) Å] from two 2,2′-bipyridine ligand mol­ecules and a bromide anion [Cu—Br = 2.471 (2) Å] in a distorted trigonal-bipyramidal geometry. Short centroid–centroid distances [3.762 (5) and 3.867 (5) Å] between the aromatic rings of neighbouring cations suggest the existence of π–π inter­actions. Inter­molecular O—H⋯Br hydrogen bonds and weak C—H⋯O and C—H⋯Br inter­actions consolidate the crystal packing

Bis(3,4-dimethoxy­benzoato-κ2 O,O′)(1,10-phenanthroline-κ2 N,N′)copper(II)

The asymmetric unit of the title compound, [Cu(C9H9O4)2(C12H8N2)], contains one half-mol­ecule, the complete mol­ecule being generated by a twofold rotation axis. The CuII atom exhibits a six-coordinated distorted octa­hedral geometry with two N atoms from the phenanthroline ligand [Cu—N 2.007 (2) Å] and four O atoms from two 3,4-dimethoxy­benzoate ligands [Cu—O 1.950 (1) and 2.524 (1) Å]. The difference in Cu—O bond distances indicates a strong Jahn–Teller effect. In the crystal, C—H⋯π inter­actions result in chains of mol­ecules along the c axis

Bis(2-bromo­acetato-κ2 O,O′)(1,10-phenanthroline-κ2 N,N′)copper(II)

The two halves of the title compound, [Cu(C2H2BrO2)2(C12H8N2)], are related by twofold symmetry along the b axis through the central CuII ion. The CuII ion is coordinated by two symmetry-related N atoms from the 1,10-phenanthroline ligand and four O atoms from two 2-bromo­acetate ligands, showing a distorted octahedral geometry. Weak inter­molecular C—H⋯O inter­actions link neighbouring mol­ecules

Aqua­bis(2-iodo­acetato-κO)(1,10-phenanthroline-κ2 N,N′)copper(II)

In the title compound, [Cu(C2H2IO2)2(C12H8N2)(H2O)], the CuII ion is coordinated by two N atoms [Cu—N = 2.013 (4) and 2.024 (4) Å] from a 1,10-phenanthroline ligand and three O atoms [Cu—O = 1.940 (4)–2.261 (4) Å] from two carboxyl ligands and a water mol­ecule in a distorted square-pyramidal geometry. One iodo­acetate O atom [Cu—O = 2.775 (4) Å] completes the coordination to form a distorted octa­hedron. Inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into centrosymmetric dimers, which are further packed by π–π inter­actions between the 1,10-phenanthroline ligands into layers parallel to the ab plane. The crystal packing also exhibits short inter­molecular I⋯I contacts of 3.6772 (9) Å and weak C—H⋯O hydrogen bonds

A Tensor-Based Framework for Studying Eigenvector Multicentrality in Multilayer Networks

Centrality is widely recognized as one of the most critical measures to provide insight in the structure and function of complex networks. While various centrality measures have been proposed for single-layer networks, a general framework for studying centrality in multilayer networks (i.e., multicentrality) is still lacking. In this study, a tensor-based framework is introduced to study eigenvector multicentrality, which enables the quantification of the impact of interlayer influence on multicentrality, providing a systematic way to describe how multicentrality propagates across different layers. This framework can leverage prior knowledge about the interplay among layers to better characterize multicentrality for varying scenarios. Two interesting cases are presented to illustrate how to model multilayer influence by choosing appropriate functions of interlayer influence and design algorithms to calculate eigenvector multicentrality. This framework is applied to analyze several empirical multilayer networks, and the results corroborate that it can quantify the influence among layers and multicentrality of nodes effectively.Comment: 57 pages, 10 figure

Triaqua­chlorido(1,10-phenanthroline-κ2 N,N′)cobalt(II) chloride monohydrate

In the title compound, [CoCl(C12H8N2)(H2O)3]Cl·H2O, the CoII ion is coordinated by two N atoms from the 1,10-phenanthroline ligand [Co—N = 2.125 (6) and 2.146 (6) Å], one chloride ligand [Co—Cl = 2.459 (2)Å] and three water mol­ecules [Co—O = 2.070 (5)–2.105 (5)Å] in a distorted octa­hedral geometry. Inter­molecular O—H⋯Cl and O—H⋯O hydrogen bonds form an extensive three-dimensional hydrogen-bonding network, which consolidates the crystal packing

Bis(2,2′-bipyridyl-κ2 N,N′)(nitrato-κ2 O,O′)(trifluoro­acetato-κO)cadmium(II)

In the title complex, [Cd(C2F3O2)(NO3)(C10H8N2)2], the Cd(II) ion is hepta­coordinated by two chelating 2,2′-bipyridyl ligands [Cd⋯N 2.370 (6)–2.416 (6) Å], one carboxyl­ate O atom [Cd⋯O 2.290 (6) Å] from the trifluoro­acetate ligand and two O atoms [Cd⋯O 2.386 (6), 2.633 (6) Å] from a chelating nitrate anion. The trifluoro­methyl fragment is rotationally disordered between two orientations in a 0.640 (7):0.360 (7) ratio. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds contribute to the crystal packing stability

Aqua­bis(dichloro­acetato-κO)(1,10-phenanthroline-κ2 N,N′)copper(II)

In the title complex, [Cu(C2HCl2O2)2(C12H8N2)(H2O)], the CuII ion has a distorted square-pyramidal coordination geometry. The equatorial positions are occupied by two N atoms from a 1,10-phenanthroline ligand [Cu—N = 1.994 (3) and 2.027 (3) Å] and two O atoms from dichloro­acetate ligands and a water mol­ecule [Cu—O = 1.971 (2) and 1.939 (2) Å]. One O atom from another dichloro­acetate ligand occupies the apical positon [Cu—O = 2.152 (3) Å]. Inter­molecular O—H⋯O hydrogen bonds link the mol­ecules into centrosymmetric dimers. The crystal packing also exhibits weak inter­molecular C—H⋯O hydrogen bonds, π–π inter­actions [centroid–centroid distance = 3.734 (2) Å] and short inter­molecular Cl⋯Cl contacts [3.306 (2) and 3.278 (2) Å]

Aqua­(furan-2-carboxyl­ato-κO)(furan-2-carboxyl­ato-κ2 O,O′)(1,10-phenanthroline-κ2 N,N′)copper(II) methanol hemisolvate

The asymmetric unit of the title compound, [Cu(C5H3O3)2(C12H8N2)2(H2O)]·0.5CH3OH, contains two CuII complex mol­ecules and one methanol solvent mol­ecule with the metal centres in strongly distorted octahedral coordination. The coordinated water mol­ecule is involved in inter­molecular O—H⋯O hydrogen bonding, which links the complex mol­ecules into chains propagating along the c axis. Neighbouring chains inter­act further via π–π inter­actions between the aromatic rings of 1,10-phenanthroline fragments [centroid–centroid distances = 3.726 (4) and 3.750 (4) Å]

Aqua­bis(2-chloro­acetato-κO)(1,10-phenanthroline-κ2 N,N′)copper(II)

In the title complex, [Cu(C2H2ClO2)2(C12H8N2)(H2O)], the CuII ion is five-coordinated by two N atoms [Cu—N = 2.005 (2) and 2.029 (2) Å] from the 1,10-phenanthroline ligand, two O atoms [Cu—O = 1.943 (2)–1.966 (2) Å] from two 2-chloro­acetate ligands and one water mol­ecule [Cu—O = 2.253 (2) Å] in a distorted square-pyramidal geometry. The crystal structure exhibits inter­molecular O—H⋯O hydrogen bonds, short Cl⋯Cl contacts [3.334 (1) Å] and π–π inter­actions [centroid–centroid distance 3.621 (11) Å]