Dimethyltin Dichloride-Dibenzyl Sulfoxide, a Compound Crystallizing with Seven Molecules in the Asymmetric Unit

Dimethyltin dichloride-dibenzyl sulfoxide,((CH3)2SnCl2·O=S(CH2C6H5)2),crystallizes in the orthorhombic space group P212121 with a superstructure of dimensions a = 11.9290(1),b = 19.50490(1),c = 55.7390(6) ; Z = 28. The geometry of the five-coordinated tin atom in each of the seven independent adduct molecules is a square pyramid that is displaced towards a cis-trigonal bipyramid; the extent of displacement along the Berry pseudorotation pathway ranges from 20 to 45%.     

Synthesis and characterization of novel "3 + 2" oxorhenium complexes, ReO[SNO][NN

The present paper deals with the synthesis and structural characterization of novel neutral oxorhenium(V) complexes of the general formula ReO[SNO][NN]. The simultaneous action of the tridentate SNO ligand, N-(2-mercaptoacetyl)glycine (1), and the bidentate NN ligand, N-phenylpyridine-2-aldimine (2), on ReOCl3(PPh3)2 leads to the formation of two isomers 4a and 4b of the general formula ReO[SNO][NN], as a result of the different orientations of the NN ligand. In both cases, the SNO donor atoms of the tridentate ligand occupy the three positions in the equatorial plane of the distorted octahedron, whereas the oxo group is always directed toward one of the apical positions. In the first isomer, 4a, the imino nitrogen of the NN ligand occupies the fourth equatorial position and the pyridine type nitrogen is directed trans to the oxo group, while in the second isomer, 4b, the imino nitrogen of the NN ligand occupies the apical position trans to the oxo group and the pyridine type nitrogen completes the equatorial plane of the distorted octahedron. The [SNO][NN] mixed-ligand system was applied in the synthesis of the oxorhenium complex 5 in which the 1-(2-methoxyphenyl)piperazine moiety, a fragment of the true 5-HT1A antagonist WAY 100635, has been incorporated in the NN bidentate ligand (NN is N-{3-[4-(2-methoxyphenyl)piperazin-1-yl]propyl}pyridine-2-aldimine). In this case, high-performance liquid chromatography and NMR showed the existence of one isomer, 5, in which the pyridine nitrogen is trans to the oxo core, as demonstrated by crystal structure analysis.     

Oxorhenium(V) and oxotechnetium(V) [NN][S]3 complexes of 2-phenylbenzothiazole derivatives

The reaction of 2-(2'-pyridyl)benzothiazole, [NN], with the ReO(V)(3+) and TcO(V)(3+) cores in the presence of thiophenols, [S] (RC(6)H(4)SH, R = H, 4-CH(3), 4-OCH(3)), as coligands led to the isolation of hexacoordinated complexes of the MO[NN][S](3) type (M = Re, Tc). In all cases, two geometric mer isomers were formed, as evidenced by NMR spectroscopy and confirmed by X-ray crystallography. In both isomers, the coordination geometry about the metal ion is a distorted octahedral defined by the two nitrogen atoms of the bidentate ligand, the three sulfur atoms of the monodentate thiols, and the oxygen atom of the oxo group. The apical positions of the octahedron are occupied by the oxygen of the oxo group and, in one of the isomers, the nitrogen of the pyridyl moiety of 2-(2'-pyridyl)benzothiazole, while, in the second isomer, the imine nitrogen of 2-(2'-pyridyl)benzothiazole. The complexes are stable, neutral, and lipophilic. Complete (1)H and (13)C NMR assignments are reported for all complexes. The synthetic reaction was also successfully transferred at the technetium-99m tracer level by ligand exchange reaction using (99m)Tc-glucoheptonate as precursor in the presence of 2-(2'-pyridyl)benzothiazole and 4-CH(3)C(6)H(4)SH. The structure of the technetium-99m complex was established by high-performance liquid chromatographic comparison with the analogous oxotechnetium and oxorhenium complexes. The 2-(2'-pyridyl)benzothiazole ligand serves as a preliminary model for 2-(4-aminophenyl)benzothiazole, which possesses interesting properties for the development of technetium and rhenium radiopharmaceuticals for tumor imaging and/or radiotherapy as well as in vivo diagnosis of Alzheimer's disease.     

Length spectra and the Teichmüller metric for surfaces with boundary

We consider some metrics and weak metrics defined on the Teichmüller space of a surface of finite type with nonempty boundary, that are defined using the hyperbolic length spectrum of simple closed curves and of properly embedded arcs, and we compare these metrics and weak metrics with the Teichmüller metric. The comparison is on subsets of Teichmüller space which we call “ε ₀-relative \({\epsilon}\)-thick parts”, and whose definition depends on the choice of some positive constants ε ₀ and \({\epsilon}\). Meanwhile, we give a formula for the Teichmüller metric of a surface with boundary in terms of extremal lengths of families of arcs.     

Characterizing and computing minimal cograph completions

A cograph completion of an arbitrary graph G is a cograph supergraph of G on the same vertex set. Such a completion is called minimal if the set of edges added to G is inclusion minimal. In this paper we present two results on minimal cograph completions. The first is a characterization that allows us to check in linear time whether a given cograph completion is minimal. The second result is a vertex incremental algorithm to compute a minimal cograph completion H of an arbitrary input graph G in O(|V(H)|+|E(H)|) time. An extended abstract of the result has been already presented at FAW 2008 [D. Lokshtanov, F. Mancini, C. Papadopoulos, Characterizing and computing minimal cograph completions, in: Proceedings of FAW’08-2nd International Frontiers of Algorithmics Workshop, in: LNCS, vol. 5059, 2008, pp. 147158. [1]].     

On the Geometry of the Berry-Robbins Approach to Spin-Statistics

Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed. A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support for this approach. In our work, a geometric approach to quantum indistinguishability is introduced which allows the treatment of singlevaluedness of wave functions in a global, model independent way.