The <Emphasis Type="Italic">k</Emphasis>-domatic number of a graph

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-dominating set of the graph G is a subset D of V (G) such that every vertex of V (G)-D is adjacent to at least k vertices in D. A k-domatic partition of G is a partition of V (G) into k-dominating sets. The maximum number of dominating sets in a k-domatic partition of G is called the k-domatic number d _k (G). In this paper, we present upper and lower bounds for the k-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number d(G) = d ₁(G).      

Fe valence state at the surface of the Fe0.5Cu0.5Cr2S4 spinel

Here we present X‐ray absorption measurements of a vacuum cleaved Fe_0.5Cu_0.5Cr₂S₄ single crystal. Measurements at different positions on the cleaved sample surface clearly reveal a difference between the valence state of the Fe ions in the sur‐ face layers and the valency of the Fe ions present in the bulk. These results confirm the findings of recent measurements outlined previously. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tetrahalidometallate(II) Ionic Liquids with More than One Metal: The Effect of Bromide versus Chloride

Fifteen N-butylpyridinium salts – five monometallic [C₄Py]₂[MBr₄] and ten bimetallic [C₄Py]₂[M_0.5^aM_0.5^bBr₄] (M=Co, Cu, Mn, Ni, Zn) – were synthesized, and their structures and thermal and electrochemical properties were studied. All the compounds are ionic liquids (ILs) with melting points between 64 and 101 °C. Powder and single-crystal X-ray diffraction show that all ILs are isostructural. The electrochemical stability windows of the ILs are between 2 and 3 V. The conductivities at room temperature are between 10⁻⁵ and 10⁻⁶ S cm⁻¹. At elevated temperatures, the conductivities reach up to 10⁻⁴ S cm⁻¹ at 70 °C. The structures and properties of the current bromide-based ILs were also compared with those of previous examples using chloride ligands, which illustrated differences and similarities between the two groups of ILs.     

Coordination and Redox Isomerization in the Reduction of a Uranium(III) Monoarene Complex

Synthetic studies on the redox chemistry of trivalent uranium monoarene complexes were undertaken with a complex derived from the chelating tris(aryloxide)arene ligand (^Ad,MeArO)₃mes^3?. Cyclic voltammetry of [{(^Ad,MeArO)₃mes}U^III] ( 1 ) revealed a nearly reversible and chemically accessible reduction at ?2.495 V vs. Fc/Fc⁺—the first electrochemical evidence for a formally divalent uranium complex. Chemical reduction of 1 indicates that reduction induces coordination and redox isomerization to form a uranium(IV) hydride, and addition of a crown ether results in hydride insertion into the coordinated arene to afford uranium(IV) complexes. This stoichiometric reaction sequence provides structural insight into the mechanism of arene functionalization at diuranium inverted sandwich complexes.     

Aldehyde‐Assisted Ruthenium(II)‐Catalyzed CH Oxygenations

Versatile ruthenium(II) complexes allow for site‐selective C? H oxygenations with weakly‐coordinating aldehydes. The challenging C? H functionalizations proceed with high chemoselectivity by rate‐determining C? H metalation. The new method features an ample substrate scope, which sets the stage for the step‐economical preparation of various bioactive heterocycles.     

Molybdenum and tungsten structural differences are dependent on ndz(2)/(n + 1)s mixing: comparisons of (silox)3MX/R (M = Mo, W; silox = (t)Bu3SiO)

Treatment of trans-(Et 2O) 2MoCl 4 with 2 or 3 equiv of Na(silox) (i.e., NaOSi (t) Bu 3) afforded (silox) 3MoCl 2 ( 1-Mo) or (silox) 3MoCl ( 2-Mo). Purification of 2-Mo was accomplished via addition of PMe 3 to precipitate (silox) 3ClMoPMe 3 ( 2-MoPMe 3), followed by thermolysis to remove phosphine. Use of MoCl 3(THF) 3 with various amounts of Na(silox) produced (silox) 2ClMoMoCl(silox) 2 ( 3-Mo). Alkylation of 2-Mo with MeMgBr or EtMgBr afforded (silox) 3MoR (R = Me, 2-MoMe; Et, 2-MoEt). 2-MoEt was also synthesized from C 2H 4 and (silox) 3MoH, which was prepared from 2-Mo and NaBEt 3H. Thermolysis of WCl 6 with HOSi ( t )Bu 3 afforded (silox) 2WCl 4 ( 4-W), and sequential treatment of 4-W with Na/Hg and Na(silox) provided (silox) 3WCl 2 ( 1-W, tbp, X-ray), which was alternatively prepared from trans-(Et 2S) 2WCl 4 and 3 equiv of Tl(silox). Na/Hg reduction of 1-W generated (silox) 3WCl ( 2-W). Alkylation of 2-W with MeMgBr produced (silox) 3WMe ( 2-WMe), which dehydrogenated to (silox) 3WCH ( 6-W) with Delta H (double dagger) = 14.9(9) kcal/mol and Delta S (double dagger) = -26(2) eu. Magnetism and structural studies revealed that 2-Mo and 2-MoEt have triplet ground states (GS) and distorted trigonal monopyramid (tmp) and tmp structures, respectively. In contrast, 2-W and 2-WMe possess squashed-T d (distorted square planar) structures, and the former has a singlet GS. Quantum mechanics/molecular mechanics studies of the S = 0 and S = 1 states for full models of 2-Mo, 2-MoEt, 2-W, and 2-WMe corroborate the experimental findings and are consistent with the greater nd z (2) /( n + 1)s mixing in the third-row transition-metal species being the dominant feature in determining the structural disparity between molybdenum and tungsten.     

Interaction of mixed-donor macrocycles containing the 1,10-phenanthroline subunit with selected transition and post-transition metal ions: metal ion recognition in competitive liquid-liquid solvent extraction of Cu(II), Zn(II), Pb(II), Cd(II), Ag(I), and Hg(II)

Two new mixed aza-thia crowns 5-aza-2,8-dithia[9]-(2,9)-1,10-phenanthrolinophane (L(4)) and 2,8-diaza-5-thia[9]-(2,9)-1,10-phenanthrolinophane (L(7)) have been synthesized and characterized. The coordination behavior of L(4) and L(7) toward the metal ions Cu(II), Zn(II), Pb(II), Cd(II), Hg(II), and Ag(I) was studied in aqueous solution by potentiometric methods, in CD3CN/D2O 4:1 (v/v) by (1)H NMR titrations and in the solid state. The data obtained were compared with those available for the coordination behavior toward the same metal ions of structurally analogous mixed donor macrocyclic ligands L(1)-L(3), L(5), L(6): all these contain a phenanthroline subunit but have only S/O/N(aromatic) donor groups in the remaining portion of the ring and are, therefore, less water-soluble than L(4) and L(7). The complexes [Cd(NO3)2(L(5))], [Pb(L(7))](ClO4)2 x 1/2MeCN, [Pb(L(4))](ClO4)2 x MeCN, and [Cu(L(7))](ClO4)2 x 3/2MeNO2 were characterized by X-ray crystallography. The efficacy of L(1)-L(7) in competitive liquid-liquid metal ion extraction of Cu(II), Zn(II), Cd(II), Pb(II), Ag(I), and Hg(II) was assessed. In the absence of Hg(II), a clear extraction selectivity for Ag(I) was observed in all systems investigated.     

The CK2 alpha/CK2 beta interface of human protein kinase CK2 harbors a binding pocket for small molecules

The Ser/Thr kinase CK2 (previously called casein kinase 2) is composed of two catalytic chains (CK2 alpha) attached to a dimer of noncatalytic subunits (CK2 beta). CK2 is involved in suppression of apoptosis, cell survival, and tumorigenesis. To investigate these activities and possibly affect them, selective CK2 inhibitors are required. An often-used CK2 inhibitor is 5,6-dichloro-1-beta-D-ribofuranosylbenzimidazole (DRB). In a complex structure with human CK2 alpha, DRB binds to the canonical ATP cleft, but additionally it occupies an allosteric site that can be alternatively filled by glycerol. Inhibition kinetic studies corroborate the dual binding mode of the inhibitor. Structural comparisons reveal a surprising conformational plasticity of human CK2 alpha around both DRB binding sites. After local rearrangement, the allosteric site serves as a CK2 beta interface. This opens the potential to construct molecules interfering with the CK2 alpha/CK2 beta interaction.     

Even-electron ions: a systematic study of the neutral species lost in the dissociation of quasi-molecular ions

The collision-induced dissociations of the even-electron [M + H](+) and/or [M - H](-) ions of 121 model compounds (mainly small aromatic compounds with one to three functional groups) ionized by electrospray ionization (ESI) or atmospheric pressure chemical ionization (APCI) have been studied using an ion trap instrument, and the results are compared with the literature data. While some functional groups (such as COOH, COOCH(3), SO(3)H in the negative ion mode, or NO(2) in both the positive and negative ion modes) generally promote the loss of neutrals that are characteristic as well as specific, other functional groups (such as COOH in the positive ion mode) give rise to the loss of neutrals that are characteristic, but not specific. Finally, functional groups such as OH and NH(2) in aromatic compounds do not lead to the loss of a neutral that reflects the presence of these substituents. In general, the dissociation of [M + H](+) and [M - H](-) ions generated from aliphatic compounds or compounds containing an aliphatic moiety obeys the even-electron rule (loss of a molecule), but deviations from this rule (loss of a radical) are sometimes observed for aromatic compounds, in particular for nitroaromatic compounds. Thermochemical data and ab initio calculations at the CBS-QB3 level of theory provide an explanation for these exceptions. When comparing the dissociation behaviour of the even-electron [M + H](+) and/or [M - H](-) ions (generated by ESI or APCI) with that of the corresponding odd-electron [M](+) ions (generated by electron ionization, EI), three cases may be distinguished: (1) the dissociation of the two ionic species differs completely; (2) the dissociation involves the loss of a common neutral, yielding product ions differing in mass by one Da, or (3) the dissociations lead to a common product ion.