Ab initio calculations and mass spectrometric determination of the gas-phase proton affinities of 4,4'-disubstituted 2,2'-bipyridines

The gas-phase proton affinities of 4,4'-di(R)-2,2'-bipyridines (R: H, Br, Cl, NO(2), Me) were determined by mass spectrometric measurements and by ab initio calculations at the HF/6-31G and MP2/6-31G levels of theory. The energy barriers for rotation about the central C-C bond were also studied computationally. Two minima were found for both unprotonated and protonated species, the global minima being at the trans planar and cis planar conformations, respectively. Local minima for the unprotonated compounds were at the cis nonplanar conformation and for the protonated compounds at the trans nonplanar. Two different proton affinity values were calculated for each compound by employing different conformations for the protonated species. The computational values were in good agreement with the experimental proton affinities. Substituents affect the proton affinity according to their ability to withdraw or to donate electrons, halogen and nitro-substituted bipyridines having a lower proton affinity and methyl-substituted bipyridine having a higher proton affinity than 2,2'-bipyridine itself.     

The synthesis, structure and dynamic behaviour of disubstituted alkenylphosphine derivatives of [Rh6(CO)16

A series of [Rh(6)(CO)(16)] substituted derivatives containing Ph(2)P(alkenyl) ligands has been synthesized starting from the [Rh(6)(CO)(16-x)(NCMe)(x)](x= 1, 2) clusters and Ph(2)P((CH(2))(n)CH=CH(2))(n= 2, 3) phosphines. It was shown that the terminal alkenyl substituents in these phosphines easily undergo isomerization in the coordination sphere of the hexarhodium complexes to give the allyl -CH(2)CH=C(H)R (R = Me and Et) fragments coordinated through the double bond of the rearranged organic moieties. The solid-state structure of two clusters, [Rh(6)(CO)(14)(mu2,kappa3-Ph(2)PCH(2)CH=C(H)CH(3))](4) and [Rh(6)(CO)(14)(mu2,kappa3-Ph(2)PCH(2)CH=C(H)CH(2)CH(3))](8), was established by X-ray crystallography. Solution structures of the products obtained were also characterized by IR and NMR ((1)H, (31)P, (1)H-(1)H COSY and (1)H-(1)H NOE) spectroscopy. It was shown that 4 and 8 exist in solution as mixtures of three isomers (A, B and C), which differ in the conformation of the coordinated allyl fragment. A similar (two species, A and B) equilibrium was found to occur in the solution of the [Rh(6)(CO)(14)(mu2,kappa3-Ph(2)PCH(2)CH=CH(2))](2) cluster. The dynamic behaviour of 2, 4 and 8[Rh(6)(CO)(14)(mu2,kappa3-Ph(2)PCH=CH(2))] has been studied using VT (31)P and (1)H-(1)H NOESY NMR spectroscopy, rate constants and activation parameters of the (A<-->B) isomerization processes were determined. It was shown that the most probable mechanism of this isomerization involves a dissociative [Rh6(CO)(14)(kappa1-Ph(2)P(alkenyl))] intermediate and re-coordination of the double bond to the same metal atom where the process started from. The conversion of the A and B species in and into the third isomer very likely occurs through the transfer of an allyl hydrogen atom onto the rhodium skeleton to give eventually cis conformation of the coordinated allyl fragment.     

Comparison theorems for hyperbolic type metrics

The connection between several hyperbolic type metrics is studied in subdomains of the Euclidean space. In particular, a new metric is introduced and compared to the distance ratio metric.     

Structural Principles of Polyhedral Allotropes of Phosphorus

We derive the structural principles of polyhedral allotropes of phosphorus, introducing three distinct families of black phosphorus nanostructures. The predicted tetrahedral, octahedral, and icosahedral phosphorus cages can also be considered as phosphorus fullerenes. Phosphorus cages up to P₈₈₈ are systematically investigated by quantum chemical methods, and their thermodynamic stabilities are compared with the experimentally known allotropic forms of phosphorus. The tetrahedral cages are thermodynamically favored over the octahedral and icosahedral structures, although large octahedral structures become nearly as stable as the tetrahedral ones. The stability trends of the studied polyhedral families can be rationalized on the basis of their structural characteristics. The phosphorus polyhedra can be further stabilized by fitting smaller structures inside larger ones, resulting in multilayered, bulk‐like cages. The synthesis of the predicted black phosphorus nanostructures is suggested to be viable from the thermodynamic point of view, and several approaches for their experimental preparation can be envisaged.     

Supramolecular luminescent gold(I)-copper(I) complexes: self-assembly of the Au(x)Cu(y) clusters inside the [Au3(diphosphine)3]3+ triangles

The reactions between diphosphino-alkynyl gold complexes (PhC2Au)PPh2(C6H4)(n)PPh2(AuC2Ph) (n = 1, 2, 3) with Cu(+) lead to formation of the heterometallic aggregates, the composition of which may be described by a general formula [{Au(x)Cu(y)(C2Ph)2x}Au3{PPh2(C6H4)(n)PPh2}3](3+(y-x)) (n = 1, 2, 3; x = (n + 1)(n + 2)/2; y = n(n + 1)). These compounds display very similar structural patterns and consist of the [Au(x)Cu(y)(C2Ph)2x](y-x) alkynyl clusters "wrapped" in the [Au3(diphosphine)3](3+) triangles. The complex for n = 1 was characterized crystallographically and spectrally, the larger ones (n = 2, 3) were investigated in detail by NMR spectroscopy. Their luminescence behavior has been studied, and a remarkably efficient emission with a maximum quantum yield of 0.92 (n = 1) has been detected. Photophysical experiments demonstrate that an increase of the size of the aggregates leads to a decrease in photostability and photoefficiency. Computational studies have been performed to provide additional insight into the structural and electronic properties of these supramolecular complexes. The theoretical results obtained are in good agreement with the experimental data, supporting the proposed structural motif. These studies also suggest that the observed efficient long-wavelength luminescence originates from metal-centered transitions within the heterometallic Au-Cu core.     

Intrinsic Geometry and Boundary Structure of Plane Domains

Siberian Mathematical Journal - Given a&nbsp;nonempty compact set $ E $ in a proper subdomain $ Omega $ of the complex plane, we denote the diameter of $ E $ and the distance from $ E $ to the...     

On Borel equivalence relations in generalized Baire space

We construct two Borel equivalence relations on the generalized Baire space κ ^κ , κ ^<κ ?=?κ >?ω, with the property that neither of them is Borel reducible to the other. A small modification of the construction shows that the straightforward generalization of the Glimm-Effros dichotomy fails.     

On Belinskii conformality in countable sets of points

The local behavior of plane quasiconformal mappings is investigated. In particular, generalizing the well-known Reich-Walczak problem, we study the possibility for a quasiconformal mapping to be conformal in the sense of Belinskii at a prescribed point or in a prescribed set of points when the modulus of the complex dilatation is a fixed measurable function. The notion of the Belinskii conformality is related to the conception of asymptotical rotations by Brakalova and Jenkins.