The rich chemistry of [Zn2Cp*2]: trapping three different types of zinc ligands in the PdZn7 complex [Pd(ZnCp*)4(ZnMe)2{Zn(tmeda)}

The synthesis, structural characterization, and bonding situation analysis of a novel, all-zinc, hepta-coordinated palladium complex [Pd(ZnCp*)(4)(ZnMe)(2){Zn(tmeda)}] (1) is reported. The reaction of the substitution labile d(10) metal starting complex [Pd(CH(3))(2)(tmeda)] (tmeda = N,N,N',N'-tetramethyl-ethane-1,2-diamine) with stoichiometric amounts of [Zn(2)Cp*(2)] (Cp* = pentamethylcyclopentadienyl) results in the formation of [Pd(ZnCp*)(4)(ZnMe)(2){Zn(tmeda)}] (1) in 35% yield. Compound 1 has been fully characterized by single-crystal X-ray diffraction, (1)H and (13)C NMR spectroscopy, IR spectroscopy, and liquid injection field desorption ionization mass spectrometry. It consists of an unusual [PdZn(7)] metal core and exhibits a terminal {Zn(tmeda)} unit. The bonding situation of 1 with respect to the properties of the three different types of Zn ligands Zn(R,L) (R = CH(3), Cp*; L = tmeda) bonded to the Pd center was studied by density functional theory quantum chemical calculations. The results of energy decomposition and atoms in molecules analysis clearly point out significant differences according to R vs L. While Zn(CH(3)) and ZnCp* can be viewed as 1e donor Zn(I) ligands, {Zn(tmeda)} is best described as a strong 2e Zn(0) donor ligand. Thus, the 18 valence electron complex 1 nicely fits to the family of metal-rich molecules of the general formula [M(ZnR)(a)(GaR)(b)] (a + 2b = n ≥ 8; M = Mo, Ru, Rh; Ni, Pd, Pt; R = Me, Et, Cp*).     

Multiple boron-boron bonds in neutral molecules: an insight from the extended transition state method and the natural orbitals for chemical valence scheme

We have analyzed the character of B═B and B≡B bonds in the neutral molecules of general form: LHB═BHL (2-L) and LB≡BL (3-L), for various ancillary ligands L attached to the boron center, based on a recently developed method that combines the extended transition state scheme with the theory of natural orbitals for chemical valence (ETS-NOCV). In the case of molecules with the B═B bond, 2-L, we have included L = PMe(3), PF(3), PCl(3), PH(3), C(3)H(4)N(2)═C(NHCH)(2), whereas for molecules containing the B≡B connection, 3-L, the following ligands were considered L = CO, PMe(3), PCl(3), (Me(2)NCH(2)CH(2)O)(2)Ge. The results led us to conclude that use of phosphorus ligands leads to strengthening of the B═B bond by 6.4 kcal/mol (for 2-PMe(3)), by 4.4 (for 2-PF(3)) and by 9.2 (for 2-PH(3)), when compared to a molecule developed on the experimental basis, 2-C(3)H(4)N(2) (ΔE(total) = -118.3 kcal/mol). The ETS scheme has shown that all contributions, that is, (i) orbital interaction ΔE(orb), (ii) Pauli repulsion ΔE(Pauli), and (iii) electrostatic stabilization ΔE(elstat), are important in determining the trend in the B═B bond energies, ΔE(total). ETS-NOCV results revealed that both σ(B═B) and π(B═B) contributions are responsible for the changes in ΔE(orb) values. All considered molecules of the type LB≡BL, 3-L, exhibit a stronger B≡B bond when compared to a double B═B connection in 2-L (|ΔE(total)| is lower by 11.8-42.5 kcal/mol, depending on the molecule). The main reason is a lower Pauli repulsion contribution noted for 3-CO, 3-PMe(3), and 3-PCl(3) molecules. In addition, in the case of 3-PMe(3) and 3-PCl(3), the orbital interaction term is more stabilizing; however, the effect is less pronounced compared to the drop in the Pauli repulsion term. In all of the systems with double and triple boron-boron bonds, the electronic factor (ΔE(orb)) dominates over the electrostatic contribution (ΔE(elstat)). Finally, the strongest B≡B connection was found for 3-Ge [L = (Me(2)NCH(2)CH(2)O)(2)Ge], predominantly as a result of the strongest σ- and π-contributions, despite the highest destabilization originating from the sizable bulkiness of the germanium-containing ligand. The data on energetic stability of multiple boron-boron bonds (relatively high values of bond dissociation energies |ΔE(total)|), suggest that it should be possible to isolate experimentally the novel proposed systems with double B═B bonds, 2-PMe(3), 2-PF(3), 2-PCl(3), and 2-PH(3), and those with triple B≡B connections, 3-PMe(3), 3-Ge, and 3-PCl(3).     

Twofold 2-perfect bowtie systems with an extra property

A bowtie is a closed trail whose graph consists of two 3-cycles with exactly one vertex in common. A 2-fold bowtie system of order n is an edge-disjoint decomposition of 2K _n into bowties. A 2-fold bowtie system is said to be 2-perfect provided that every pair of distinct vertices is joined by two paths of length 2. It is said to be extra provided these two paths always have distinct midpoints. The extra property guarantees that the two paths x, a, y and x, b, y between every pair of vertices form a 4-cycle (x, a, y, b), and that the collection of all such 4-cycles is a four-fold 4-cycle system. We show that the spectrum for extra 2-perfect 2-fold bowtie systems is precisely the set of all n ?? 0 or 1 (mod 3), ${n\,\geqslant\,6}$ . Additionally, with an obvious definition, we show that the spectrum for extra 2-perfect 2-fold maximum packings of 2K _n with bowties is precisely the set of all n ?? 2 (mod 3), ${n\,\geqslant\,8}$ .     

On the Uniqueness of the Density for the Invariant Measure in an Infinite Hyperbolic Iterated Function System

Periodica Mathematica Hungarica - We consider a regular infinite hyperbolic iterated function satisfying a property which guarantees that the associated Frobenius-Perron operator ? is almost...     

Geometry and ergodic theory of non-recurrent elliptic functions

We explore the class of elliptic functions whose critical points all contained in the Julia set are non-recurrent and whose ω-limit sets form compact subsets of the complex plane. In particular, this class comprises hyperbolic, subhyperbolic and parabolic elliptic maps. Leth be the Hausdorff dimension of the Julia set of such an elliptic functionf. We construct an atomlessh-conformal measurem and show that theh-dimensional Hausdorff measure of the Julia set off vanishes unless the Julia set is equal to the entire complex plane ℂ. Theh-dimensional packing measure is positive and is finite if and only if there are no rationally indifferent periodic points. Furthermore, we prove the existence of a (unique up to a multiplicative constant) σ-finitef-invariant measure μ equivalent tom. The measure μ is shown to be ergodic and conservative, and we identify the set of points whose open neighborhoods all have infinite measure μ. In particular, we show that ∞ is not among them. The research of the first author was supported in part by the Foundation for Polish Science, the Polish KBN Grant No 2 PO3A 034 25 and TUW Grant no 503G 112000442200. She also wishes to thank the University of North Texas where this research was conducted. The research of the second author was supported in part by the NSF Grant DMS 0100078. Both authors were supported in part by the NSF/PAN grant INT-0306004.     

Microwave-assisted synthesis of spherical monodispersed magnesium fluoride

Spherical monodispersed magnesium fluoride has been obtained using the microwave-assisted precipitation technique from magnesium nitrate and ammonium fluoride solutions. Studies aimed at optimizing synthesis conditions from the point of view of preparing spherical MgF₂ particles of possibly high monodispersity were performed. Spherical MgF₂ particles of 0.25-0.36 μm in diameter have been obtained with relative standard deviation from the average value ranging from 7 to 15%. It has been established that a certain optimal range of Mg(NO₃)₂ and NH₄F concentrations exists that enables a highly monodispersed MgF₂ to be prepared. The range is narrow (0.01-0.03 mol dm⁻³) for both precursors. Spherical MgF₂ particles have been characterized by SEM, XRD, DTG/DTA and FTIR techniques.     

Synthesis of some new mesoionic heterocycles

The synthesis of various substituted 1-hydroxy-2-chloroacetyl-6-thia-10b-aza-2a-azoniaaceanthrylene hydroxide inner salt, 1-hydroxy-6-thia-10b-aza-2a-azoniaaceanthrylene hydroxide inner salt, 1-hydroxy-2-piperidinoacetyl-6-thia-10b-aza-2a-azoniaaceanthrylene hydroxide inner salt is described. The ir is also included.     

Photochemical reduction of transition metal substituted heteropoly anions in nonpolar solutions

Photochromism of [SiW11O39Ni(X)]6- as a tetraheptylammonium salt in various solvents under broadband UV light is observed in the presence of alcohols. The reaction proceeds faster with benzyl alcohol than with ethanol. Benzaldehyde is identified as the oxidized product of benzyl alcohol. Photochemistry is a reliable means to produce stable reduced transition metal substituted heteropoly tungstates in nonpolar media, where they hold promise as multielectron reduction catalysts. Preliminary reactivity toward CO2 reduction is demonstrated.     

How Points Escape to Infinity Under Exponential Maps

We investigate the finer fractal structure of the set of pointsescaping to infinity under iteration of an arbitrary exponentialmap. Providing exact formulas, we show how sensitively the Hausdorffdimension depends on the rate of growth of canonical Devaney–Krychcodes.