Silver(I) and copper(I) complexes supported by fully fluorinated 1,3,5-triazapentadienyl ligands

Synthesis of the perfluorinated 1,3,5-triazapentadiene [N{(CF(3))C(C(6)F(5))N}(2)]H and the use of its conjugate base as a supporting ligand for the isolation of silver(i) and copper(i) complexes are reported. Some of the related chemistry involving [N{(C(3)F(7))C(C(6)F(5))N}(2)](-) (that has bulkier -C(3)F(7) groups on the 1,3,5-triazapentadienyl ligand backbone) is also presented. X-ray crystallographic data show a wide variety of structures ranging from intermolecular, hydrogen-bonded chain structure for [N{(CF(3))C(C(6)F(5))N}(2)]H with a twisted W-shaped N(3)C(2) core, monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Ag(CN(t)Bu)(2) and [N{(C(3)F(7))C(C(6)F(5))N}(2)]Ag(CN(t)Bu)(2) where the κ(1)-bonded triazapentadienyl ligand bonding to the metal fragment via the central nitrogen atom, monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Ag(PPh(3))(2) and [N{(C(3)F(7))C(C(6)F(5))N}(2)]Ag(PPh(3))(2) that feature κ(1)-bonded triazapentadienyl ligand bonding to the metal fragment via one of the terminal nitrogen atoms, to that of the monomeric [N{(CF(3))C(C(6)F(5))N}(2)]Cu(CN(t)Bu)(2) containing a κ(2)-bonded triazapentadienyl ligand and a U-shaped NCNCN ligand backbone. The isocyanide adducts show relatively high ν(CN) values in the IR spectra.     

On a refinement of Craig’s lattices

Let p be an odd prime. A family of (p−1)-dimensional over-lattices yielding new record packings for several values of p in the interval [149…3001] is presented. The result is obtained by modifying Craig’s construction and considering conveniently chosen Z-submodules of Q(ζ), where ζ is a primitive pth root of unity. For p≥59, it is shown that the center density of the (p−1)-dimensional lattice in the new family is at least twice the center density of the (p−1)-dimensional Craig lattice.     

A note on geodesic connectedness of Gödel type spacetimes

In this note we reduce the problem of geodesic connectedness in a wide class of Gödel type spacetimes to the search of critical points of a functional naturally involved in the study of geodesics in standard static spacetimes. Then, by using some known accurate results on the latter, we improve previous results on the former.     

Assessment of the electronic structure of 2,2'-pyridylpyrrolides as ligands

The ligand class 2,2'-pyridylpyrrolide is surveyed, both for its structural features and its electronic structure, when attached to monovalent K, Cu, Ag, Au, and Rh. The influence of pyrrolide ring substituents is studied, as well as the question of push/pull interaction between the pyridyl and pyrrolide halves. The π donor ability of the pyrrolide is found to be less than that of an analogous phenyl. However, in contrast to the phenyl analog, the HOMO is pyrrolide π in character for pyridylpyrrolide complexes of copper and rhodium, while it is conventionally metal localized for planar, d(8) rhodium pyridylphenyl. Monovalent three-coordinate copper complexes show great deviations from Y-shaped toward T-shaped structures, including cases where the pyridyl ligand bonds only weakly.     

Domination problems for strictly singular operators and other related classes

We survey recent results on domination properties of strictly singular operators and related operator ideals, as well as Banach–Saks operators, Narrow operators and p-summing operators.     

Schottky barrier formation in the low metal coverage limit

A theoretical discussion of the state of the art in the field of Schottky barrier formation is presented. The thin metal layer limit is analyzed for Al and In on GaAs(110), and the adsorption sites are determined as a function of the metal coverage. Intrinsic and extrinsic charge neutrality levels are also discussed for the In-case.