Azido-, hydroxo-, and oxo-bridged copper(II) dimers: spin population analysis within broken-symmetry, density functional methods

Within the general context of homometallic spin-coupled Cu(II) dimers, we propose to relate the antiferromagnetic part of the exchange coupling constant, J _AF, to the quantity ΔP ²(Cu), the difference of copper squared spin populations as calculated for the high-spin (i.e. triplet) and broken-symmetry spin states, through J _AF≈−UΔP ²(Cu), where U is interpreted as the covalent–ionic term. This proportionality is illustrated for three “bare” Cu(II) dimers (i.e. without peripheral ligation, so as to enhance the antiferromagnetic contribution) bridged by azido, hydroxo, or oxo groups. This provides an alternative quantifier of the exchange phenomenon to that usually used, i.e. Δ², the square of the singly occupied molecular orbital splitting in the triplet state. Moreover, and quite interestingly, the quantity ΔP ²(Cu) can become negative (i.e. induce ferromagnetism) without apparently affecting the proportionality relation. Received: 17 September 1999 / Accepted: 9 March 2000 / Published online: 21 June 2000     

Simultaneous reversible addition fragmentation chain transfer and ring‐opening polymerization

The simultaneous ring‐opening polymerization (ROP) of ε‐caprolactone (ε‐CL) and 2‐hydroxyethyl methacrylate (HEMA) polymerization via reversible addition fragmentation chain transfer (RAFT) chemistry and the possible access to graft copolymers with degradable and nondegradable segments is investigated. HEMA and ε‐CL are reacted in the presence of cyanoisopropyl dithiobenzoate (CPDB) and tin(II) 2‐ethylhexanoate (Sn(Oct)₂) under typical ROP conditions (T > 100 °C) using toluene as the solvent in order to lead to the graft copolymer PHEMA‐g‐PCL. Graft copolymer formation is evidenced by a combination of size‐exclusion chromatography (SEC) and NMR analyses as well as confirmed by the hydrolysis of the PCL segments of the copolymer. With targeted copolymers containing at least 10% weight of PHEMA and relatively small PHEMA backbones (ca. 5,000–10,000 g mol^?1) the copolymer grafting density is higher than 90%. The ratio of free HEMA‐PCL homopolymer produced during the “one‐step” process was found to depend on the HEMA concentration, as well as the half‐life time of the radical initiator used. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3058–3067, 2008     

Global G-Manifold Reductions and Resolutions

The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.     

A major index for matchings and set partitions

We introduce a statistic pmaj(P) for partitions of [n], and show that it is equidistributed with cr₂, the number of 2-crossings, over all partitions of [n] with given sets of minimal block elements and maximal block elements. This generalizes the classical result of equidistribution for the permutation statistics inv and maj.     

Linked partitions and linked cycles

The notion of noncrossing linked partition arose from the study of certain transforms in free probability theory. It is known that the number of noncrossing linked partitions of [n+1] is equal to the n-th large Schröder number r_n, which counts the number of Schröder paths. In this paper we give a bijective proof of this result. Then we introduce the structures of linked partitions and linked cycles. We present various combinatorial properties of noncrossing linked partitions, linked partitions, and linked cycles, and connect them to other combinatorial structures and results, including increasing trees, partial matchings, k-Stirling numbers of the second kind, and the symmetry between crossings and nestings over certain linear graphs.     

Microstrain in hydroxyapatite carbon nanotube composites

Synchrotron radiation diffraction data were collected from hydroxyapatite–carbon nanotube bioceramic composites to determine the crystallite size and to measure changes in non‐uniform strain. Estimates of crystallite size and strain were determined by line‐profile fitting of discrete peaks and these were compared with a Rietveld whole‐pattern analysis. Overall the two analysis methods produced very similar numbers. In the commercial hydroxyapatite material, one reflection in particular, (0 2 3), has higher crystallite size and lower strain values in comparison with laboratory‐synthesized material. This could indicate preferential crystal growth in the [0 2 3] direction in the commercial material. From the measured strains in the pure material and the composite, there was a degree of bonding between the matrix and strengthening fibres. However, increasing the amount of carbon nanotubes in the composite has increased the strain in the material, which is undesirable for biomedical implant applications.     

Vector-valued perturbed equilibrium problems

The goal of this paper is to prove some general vector-valued perturbed equilibrium principles and some existence results of vector equilibrium points for bifunctions satisfying a new natural notion of lower semi-continuity. We obtain these results by going through a new concept of approximative equilibrium point.     

α‐Tetraphosphorus Trichalcogenide Diamides and Imides containing both Sulfur and Selenium

Reaction of a mixture of bicyclic phosphorus sulfide selenide iodides α‐P₄S_nSe_3−nI₂ (n = 0–3) with PrⁱNH₂ and Et₃N gave corresponding diamides α‐P₄S_nSe_3−n(NHPrⁱ)₂ (n = 0–3) and imides α‐P₄S_nSe_3−n(μ‐NPrⁱ) (n = 2–3), identified in solution by ³¹P NMR. In one isomer of α‐P₄S₂Se(μ‐NPrⁱ), the C₂ symmetry of imides such as α‐P₄S₃(μ‐NPrⁱ) was broken, allowing relative assignment of ²J NMR couplings to the PNP bridge and the PSP bridge opposite to it. The coupling through the sulfur bridge was found to be reduced to ca. zero, in contrast to previous assumptions for this class of compounds. Ab initio models were calculated at the MPW1PW91/svp level for the sulfide selenide imides and for a selection of bond rotamers of the diamides, and at the MPW1PW91/LanL2DZ(d) level for the sulfide selenide diiodides. Different skeletal isomers were prevalent for the mixed chalcogenide diamides than for the diiodides, showing that exchange of chalcogen between skeletal positions took place in the amination reaction even at room temperature. Similar differences to those observed were predicted by the models, suggesting that equilibrium was attained.