On the rate of convergence of the sum of the sample extremes

Summary Let X ₁, X ₂,..., X _n be independent random variables having a common distribution in the domain of normal attraction of a completely asymmetric stable law with characteristic exponent }(0,1) and support bounded below. Let X _n:n X _n:n ^-1...X _n:1 denote the ordered sample. We obtain the rate of convergence of n ^-1/ (X _n:n +...+X _{n:n-k n+1} ) to the stable limit law as both n and k _n ». As a consequence we obtain a representation of the sum X _n:n +...+X _{n:n-k n+1} .     

Ab initio calculation of the NH(3sigma-)-NH(3sigma-) interaction potentials in the quintet, triplet, and singlet states

We present the ab initio potential-energy surfaces of the NH-NH complex that correlate with two NH molecules in their 3sigma- electronic ground state. Three distinct potential-energy surfaces, split by exchange interactions, correspond to the coupling of the S(A) = 1 and S(B) = 1 electronic spins of the monomers to dimer states with S = 0, 1, and 2. Exploratory calculations on the quintet (S = 2), triplet (S = 1), and singlet (S = 0) states and their exchange splittings were performed with the valence bond self-consistent-field method that explicitly accounts for the nonorthogonality of the orbitals on different monomers. The potential surface of the quintet state, which can be described by a single Slater determinant reference function, was calculated at the coupled cluster level with single and double excitations and noniterative treatment of the triples. The triplet and singlet states require multiconfiguration reference wave functions and the exchange splittings between the three potential surfaces were calculated with the complete active space self-consistent-field method supplemented with perturbative configuration interaction calculations of second and third orders. Full potential-energy surfaces were computed as a function of the four intermolecular Jacobi coordinates, with an aug-cc-pVTZ basis on the N and H atoms and bond functions at the midpoint of the intermolecular vector R. An analytical representation of these potentials was given by expanding their dependence on the molecular orientations in coupled spherical harmonics, and representing the dependence of the expansion coefficients on the intermolecular distance R by the reproducing kernel Hilbert space method. The quintet surface has a van der Waals minimum of depth D(e) = 675 cm(-1) at R(e) = 6.6a0 for a linear geometry with the two NH electric dipoles aligned. The singlet and triplet surfaces show similar, slightly deeper, van der Waals wells, but when R is decreased the weakly bound NH dimer with S = 0 and S = 1 converts into the chemically bound N2H2 diimide (also called diazene) molecule with only a small energy barrier to overcome.     

Dithiacrown Ether Substituted Porphyrazines: Synthesis, Single-Crystal Structure, and Control of Aggregation in Solution by Complexation of Transition-Metal Ions

The synthesis of novel magnesium, copper, and metal-free porphyrazines, peripherally substituted with dithia-7-crown-2 (MPz(7)), dithia-15-crown-5 (MPz(15)), and dithia-18-crown-6 (MPz(18)) macrocycles is reported. These compounds are prepared starting from dicyanoethylene containing crown ethers 3, 2(1), and 2(2), respectively, which contain sulfur as well as oxygen heteroatoms. The "crowned" porphyrazines bind silver(I) and mercury(II) perchlorates. UV/vis spectroscopy and electron paramagnetic resonance measurements reveal that addition of the transition-metal ions leads to dimerization of the porphyrazine complexes. In the case of the dithia-18-crown-6-substituted porphyrazines, the dimers break up to form monomeric 6:1 guest-host complexes when more than 2 equiv of the metal ion is added. The single-crystal structures of the crown ether 2(2) and the porphyrazine MgPz(18) are presented. Compound C(14)H(20)N(2)O(4)S(2) (2(2)) crystallizes in the monoclinic space group P2(1)/c with a = 10.9310(13) ?, b = 19.383(3) ?, c = 8.6976(14) ?, beta = 108.898(11) degrees, V = 1743.5(5) ?(3), and Z = 4. The structure refinement converged to R = 0.0366 and R(w) = 0.0504. Compound C(56)H(82)MgN(8)O(17)S(8) (MgPz(18)) crystallizes in the triclinic space group P&onemacr; with a = 9.584(3) ?, b = 17.672(2) ?, c = 19.620(4) ?, alpha = 84.904(14) degrees, beta = 85.21(2) degrees, gamma = 89.29(2) degrees, V = 3298.4(13) ?(3), and Z = 2. The structure refinement converged to R1 = 0.0839 and wR2 = 0.2196. The electrical properties of H(2)Pz(18) have been studied by complex impedance spectroscopy. The bulk electrical conductivity of this compound is approximately 1 order of magnitude higher than that of the corresponding 18-crown-6 phthalocyanine.     

Über eine universelle Ultramikrobestimmung des Schwefels in organischen Substanzen. I

Zusammenfassung Eine Methode zur Bestimmung von Schwefelmengen bis zu 20g in organischen Substanzen wird beschrieben. Das Verfahren ermöglicht die bei Mikroverfahren übliche Analysengenauigkeit.Der durch Reduktion mittels Sn(II)-Phosphat in konz. Phosphorsäure gebildete Schwefelwasserstoff wird mit Natronlauge in einer Cd(II)-Sulfatlösung titriert. Phosphor, Stickstoff, Halogene und die meisten Metalle stören nicht. Eine Blindwertkorrektur ist notwendig. Einige Berechnungen erläutern die Methode.

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Summary A method is described for determining amounts of sulfur up to 20g in organic substances. The precision that is usual in the analyses by the micromethods can be expected from this procedure. The hydrogen sulfide produced by reduction with Sn(II) phosphate in conc. phosphoric acid is titrated with sodium hydroxide in a Cd(II)-sulfate solution. Phosphorus, nitrogen, halogens and most metals do not interfere. A blank value correction is essential. The method is illustrated by several calculations.

     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Mechanism of homogeneously and heterogeneously catalysed Meerwein-Ponndorf-Verley-Oppenauer reactions for the racemisation of secondary alcohols

The mechanism of hydrogen transfer from alcohols to ketones, catalysed by lanthanide(III) isopropoxides or zeolite Beta has been studied. For the lanthanide catalysed reactions, (S)-1-phenyl-(1-(2)H(1))ethanol and acetophenone were used as case studies to determine the reaction pathway for the hydrogen transfer. Upon complete racemisation all deuterium was present at the 1-position, indicating that the reaction exclusively takes place via a carbon-to-carbon hydrogen transfer. Zeolite Beta with different Si/Al ratios was applied in the racemisation of (S)-1-phenylethanol. In this case the racemisation does not proceed via an oxidation/reduction pathway but via elimination of the hydroxy group and its re-addition. This mechanism, however, is not characteristic for all racemisation reactions with zeolite Beta. When 4-tert-butyl cyclohexanone is reduced with this catalyst, a classical MPV reaction takes place exclusively. This demonstrates that zeolite Beta has a substrate dependent reaction pathway.     

On the Effect of Secondary Nucleation on Deracemization through Temperature Cycles

Herein, the pivotal role of secondary nucleation in a crystallization-enhanced deracemization process is reported. During this process, complete and rapid deracemization of chiral conglomerate crystals of an isoindolinone is attained through fast microwave-assisted temperature cycling. A parametric study of the main factors that affect the occurrence of secondary nucleation in this process, namely agitation rate, suspension density, and solute supersaturation, confirms that an enhanced stereoselective secondary nucleation rate maximizes the deracemization rate. Analysis of the system during a single temperature cycle showed that, although stereoselective particle production during the crystallization stage leads to enantiomeric enrichment, undesired kinetic dissolution of smaller particles of the preferred enantiomer occurs during the dissolution step. Therefore, secondary nucleation is crucial for the enhancement of deracemization through temperature cycles and as such should be considered in further design and optimization of this process, as well as in other temperature cycling processes commonly applied in particle engineering.     

Nucleation of Organic Crystals—A Molecular Perspective

The outcome of synthetic procedures for crystalline organic materials strongly depends on the first steps along the molecular self‐assembly pathway, a process we know as crystal nucleation. New experimental techniques and computational methodologies have spurred significant interest in understanding the detailed molecular mechanisms by which nuclei form and develop into macroscopic crystals. Although classical nucleation theory (CNT) has served well in describing the kinetics of the processes involved, new proposed nucleation mechanisms are additionally concerned with the evolution of structure and the competing nature of crystallization in polymorphic systems. In this Review, we explore the extent to which CNT and nucleation rate measurements can yield molecular‐scale information on this process and summarize current knowledge relating to molecular self‐assembly in nucleating systems.     

Quantum-chemical study of the interface formed by carboxylic species on TiO<Subscript>2</Subscript> nanoparticles. 1. Nanoparticle surface

The current paper presents results of a quantum-chemical study of the surface structure of nanoparticles of both rutile and anatase crystallographic modifications. Different stages of the surface relaxation are discussed. Water adsorption is considered. The calculations were performed in the spd-basis by using semi-empirical quantum-chemical codes, both sequential and parallel. The results are mainly addressed to the study of the interface formed by titania nanoparticles and a set of carboxylated species, namely, benzoic, bi-isonicotinic acids as well as tris-(2,2′-dcbipyridine) Fe(II) complex placed on the surface of either rutile or anatase polymorphs.This revised version was published online in August 2005 with a corrected issue number.