Chelating and bridging diphosphinoamine (PPh2)(2)N(Pr-i) complexes of copper(I)

The ligand bis(diphenylphosphino) isopropylamine (dppipa) has been shown to be a versatile ligand sporting different coordination modes and geometries dictated by copper(I). Most of the molecular structures were confirmed by X-ray crystallography. It is found in a chelating mode, in a monomeric complex when the ligand to copper ratio is 2:1. A tetrameric complex is formed when low ratios of ligand to metal (1: 2) were used. But with increasing ratios of ligand to metal (1: 1 and 2: 1), a trimer or a dimer was obtained depending on the crystallization conditions. Variable temperature P-31{H-1} NMR spectra of these complexes in solution showed that the Cu-P bond was labile and the highly strained 4-membered structure chelate found in the solid state readily converted to a bridged structures. On the other hand, complexes with the ligand in a bridging mode in the solid state did not form chelated structures in solution. The effect of adding tetra-alkylammonium salts to solutions of various complexes of dppipa were probed by P-31{H-1} NMR and revealed the effect of counter ions on the stability of complexes in solution. (C) 2008 Elsevier B.V. All rights reserved.

Chelating and bridging bis(diphenylphosphino)aniline complexes of copper(I)

The ligand bis(diphenylphosphino)aniline (dppan) has been shown to be a versatile ligand sporting different coordination modes and geometries as dictated by copper(I) and the counter ion. The molecular structures of its Cu(I) complexes were characterized by X-ray crystallography. The ligand was found in a chelating mode and monomeric complexes were formed when the ligand to copper ratio was 2: 1 and the anion was non-coordinating. However, with thiocyanate as the counter anion, the ligand was found to adopt two different modes, with one ligand chelating and the other acting as a monodentate ligand. With CuX (X = Cl, Br), dppan formed a tetrameric complex when the ligand and metal were reacted in the ratio of 1:1. But reactions containing ligand and metal in the ratios of 1: 2 or 2: 1, resulted in the formation of a mixture of species in solution. Crystallization however, led to the isolation of the tetrameric complex. Variable temperature P-31{H-1} NMR spectra of the isolated tetramers did not show the presence of chelated structures in solution. Tetra-alkylammonium salts were added to solutions of various complexes of dppan and studied by P-31{H-1} NMR to probe the effect of anions on the stability of complexes in solution. The Cu-dppan complexes were robust and did not interconvert with other structures in solution unlike the bis(diphenylphosphino) isopropylamine complexes. (C) 2011 Elsevier B.V. All rights reserved.

Subexponential Algorithm for d-Cluster Edge Deletion: Exception or Rule?

The correlation clustering problem is a fundamental problem in both theory and practice, and it involves identifying clusters of objects in a data set based on their similarity. A traditional modeling of this question as a graph theoretic problem involves associating vertices with data points and indicating similarity by adjacency. Clusters then correspond to cliques in the graph. The resulting optimization problem, Cluster Editing (and several variants) are very well-studied algorithmically. In many situations, however, translating clusters to cliques can be somewhat restrictive. A more flexible notion would be that of a structure where the vertices are mutually ``not too far apart'', without necessarily being adjacent. One such generalization is realized by structures called s-clubs, which are graphs of diameter at most s. In this work, we study the question of finding a set of at most k edges whose removal leaves us with a graph whose components are s-clubs. Recently, it has been shown that unless Exponential Time Hypothesis fail (ETH) fails Cluster Editing (whose components are 1-clubs) does not admit sub-exponential time algorithm STACS, 2013]. That is, there is no algorithm solving the problem in time 2 degrees((k))n(O(1)). However, surprisingly they show that when the number of cliques in the output graph is restricted to d, then the problem can be solved in time O(2(O(root dk)) + m + n). We show that this sub-exponential time algorithm for the fixed number of cliques is rather an exception than a rule. Our first result shows that assuming the ETH, there is no algorithm solving the s-Club Cluster Edge Deletion problem in time 2 degrees((k))n(O(1)). We show, further, that even the problem of deleting edges to obtain a graph with d s-clubs cannot be solved in time 2 degrees((k))n(O)(1) for any fixed s, d >= 2. This is a radical contrast from the situation established for cliques, where sub-exponential algorithms are known.