C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Fully imidized soluble polyimides based on a novel dianhydride: 2,2′-dichloro-4,4′,5,5′-benzophenone tetracarboxylic dianhydride

We have synthesized a novel dianhydride, 2,2′-dichloro-4,4′,5,5′-benzophenone tetracarboxylic dianhydride (DCBTDA). Polyimides were synthesized with DCBTDA or 3,3′,4,4′-benzophenone tetracarboxylic dianhydride (BTDA) and several relatively rigid meta- and para- substituted mononuclear diamines. The BTDA based systems were insoluble in dipolar, aprotic solvents whereas the DCBTDA based polymers displayed enhanced solubility in these solvents. The thermal stability of these polyimides was excellent as measured by 5% weight loss decomposition. The T_g's of the polymers were all above 290°C.     

Synthesis of functionalized polyhedral oligomeric silsesquioxane (POSS) macromers by microwave assisted 1,3-dipolar cycloaddition

In this paper we report the first synthesis of isoxazolidine and isoxazoline-POSS macromers by 1,3-dipolar cycloaddition reactions of vinyl- and styryl-POSS with N-methyl-C-ethoxycarbonylnitrone and ethoxycarbonyl nitrile oxide, promoted by microwave irradiation. The nature of the resulting cycloadducts has been determined by NOE experiments and supported by computational studies at PM3 and DFT B3LYP/6-31G* levels.     

Ion pair charge-transfer complexes between anionic and cationic metal-dithiolenes [M(II) = Pd,Pt

New [M(R(2)pipdt)(2)](BF(4))(2) salts [R(2)pipdt = N,N'-dialkyl-piperazine-2,3-dithione; M = Pd(II), R = Me and M = Pt(II), R = Me, Et, Pr(i)] bearing redox-active cationic dithiolene complexes have been prepared and characterized. These cations react with the redox-active [M(mnt)(2)](2-) [M = Pd(II), Pt(II); mnt = maleonitrile-2,3-dithiolate] anionic dithiolenes to form salts describable as ion pair charge-transfer complexes. X-ray crystallographic studies have shown that [M(Me(2)pipdt)(2)][M(mnt)(2)] complexes, with M = Pd(II) and Pt(II), are isomorphous. Crystal data of the Pt salt (3a): triclinic, Ponemacr; (No. 2); Z = 1; T = 293(2) K; a = 6.784(7) A, b = 8.460(6) A, c = 13.510(5) A, alpha = 100.63(2) degrees, beta = 104.04(2) degrees, gamma = 96.90(2) degrees; R1 = 0.0691 [wR2 = 0.2187 (all data)]. Structural data show that approximately square-planar [Pt(Me(2)pipdt)(2)] dications and regular square-planar [Pt(mnt)(2)] dianions form an infinite anion-cation one-dimensional stack along axis a with a Pt...Pt a/2 distance of 3.392 A and a Pt...Pt...Pt angle of 180 degrees. Anions and cations arrange themselves face-to-face so as to take on a staggered arrangement. These salts exhibit strong absorptions in the visible-near-infrared region assigned to ion pair charge-transfer transitions. A relation between the optical and thermal electron transfer in the solid state is obtained using a "Marcus-Hush model", and a solid-state electrical conductivity in agreement with expectations is observed. Vibrational spectroscopy is in agreement with the existence of charge-transfer interactions between the cationic and anionic components of the salts.     

The binding ability of iron bonded to porphodimethene: structural, magnetic, and electronic relationship to iron porphyrin complexes

The availability of the parent compound, meso-hexaethylporphodimetheneiron(II), [(Et6N4)Fe] (2), of this report results from a novel synthetic methodology that makes [Et6N4Li2] (1) easily available. The major focus is on how the axial positions, which are the key reactive sites in metalloporphyrins, and the electronic configuration of the metal can be affected by the breakdown of the aromaticity of the porphyrin skeleton and by the nonplanar conformation of the ligand. DFT calculations indicate a 3B1(dz2)1(dyz)1 ground state for 2 versus the 3A2(dxz)1(dyz)1 ground state in the porphyrin analogue. The intermediate-spin state (S = 1) of 2 changed drastically upon addition of one or two axial ligands, as hexacoordination is preferred by iron(II). The hexacoordinate complexes [(Et6N4)Fe(L)(L')] (L = L' = THF, 3; L = L' = Py, 4; L = PhNO, L' = Py, 14) have been isolated and structurally characterized. Strong-field ligands lead to a low-spin diamagnetic state for iron(II), namely for complexes 4-7, 9, and 14, whereas 3 is a typical d6 high-spin complex, as is the pentacoordinate [(Et6N4)Fe(CN)]Bu4N (8). The structural analysis showed common features for 6, 7, 9, and 14: i) a small displacement of the metal from the N4 plane, and ii) an N4 cavity, larger than that in the corresponding porphyrins, affecting the Fe-N bond lengths. The 1H NMR spectrum is quite diagnostic of the two-fold symmetry in the diamagnetic hexacoordinate complexes, revealing either a D2h or a C2v symmetry. The CO stretching frequency (1951 cm(-1)) in complex 6 probes the good electron density at the metal. The one-electron oxidation of 2 led to pentacoordinate iron(III) derivatives [(Et6N4)Fe(Cl)] (10), [(Et6N4)2Fe2(mu-O)] (11), and [(Et6N4)2Fe2(mu-p-OC6H4-O)] (12). Complex 10 is a typical high-spin iron(III) (5.85muB at 298 K), while 11 and 12 behave as antiferromagnetic coupled iron(III) (J = -9.4cm(-1), 12, and J = -115cm(-1), 11). In complexes 10, 11, and 12 iron is sitting in a quite distorted square pyramidal geometry, in which the ligand displays a very distorted roof conformation with different degrees of ruffling. Distinctive structural and magnetic features have been found for the nitrosyl derivative [(Et6N4)Fe-NO], which has a low-spin state (S = 1/2) and the following structural parameters: Fe-N-O, 147.3(2) degrees; Fe-N, 1.708(2) A; N-O, 1.172(3) A. A comparative structural, magnetic, and theoretical analysis of the compounds listed above has been made with the analogous porphyrin derivatives. The detailed structural investigation has been mapped through the X-ray analysis of 2, 7, 8, 9, 11, 13, and 14.     

Correlating axial and equatorial ligand field effects to the single-molecule magnet performances of a family of dysprosium bis-methanediide complexes

Treatment of the new methanediide–methanide complex [Dy(SCS)(SCSH)(THF)] (1Dy, SCS = {C(PPh₂S)₂}²⁻) with alkali metal alkyls and auxillary ethers produces the bis-methanediide complexes [Dy(SCS)₂][Dy(SCS)₂(K(DME)₂)₂] (2Dy), [Dy(SCS)₂][Na(DME)₃] (3Dy) and [Dy(SCS)₂][K(2,2,2-cryptand)] (4Dy). For further comparisons, the bis-methanediide complex [Dy(NCN)₂][K(DB18C6)(THF)(toluene)] (5Dy, NCN = {C(PPh₂NSiMe₃)₂}²⁻, DB18C6 = dibenzo-18-crown-6 ether) was prepared. Magnetic susceptibility experiments reveal slow relaxation of the magnetisation for 2Dy–5Dy, with open magnetic hysteresis up to 14, 12, 15, and 12 K, respectively (∼14 Oe s⁻¹). Fitting the alternating current magnetic susceptibility data for 2Dy–5Dy gives energy barriers to magnetic relaxation (U_eff) of 1069(129)/1160(21), 1015(32), 1109(70), and 757(39) K, respectively, thus 2Dy–4Dy join a privileged group of SMMs with U_eff values of ∼1000 K and greater with magnetic hysteresis at temperatures >10 K. These structurally similar Dy-components permit systematic correlation of the effects of axial and equatorial ligand fields on single-molecule magnet performance. For 2Dy–4Dy, the Dy-components can be grouped into 2Dy–cation/4Dy and 2Dy–anion/3Dy, where the former have almost linear C Dy C units with short average Dy C distances, and the latter have more bent C Dy C units with longer average Dy C bonds. Both U_eff and hysteresis temperature are superior for the former pair compared to the latter pair as predicted, supporting the hypothesis that a more linear axial ligand field with shorter M–L distances produces enhanced SMM properties. Comparison with 5Dy demonstrates unusually clear-cut examples of: (i) weakening the equatorial ligand field results in enhancement of the SMM performance of a monometallic system; (ii) a positive correlation between U_eff barrier and axial linearity in structurally comparable systems.

Studies on equatorial donor and C Dy C angle variation effects on energy barriers to the slow relaxation of magnetisation are reported.     

Nitrile-functionalized pyridinium ionic liquids: synthesis, characterization, and their application in carbon-carbon coupling reactions

A series of relatively low-cost ionic liquids, based on the N-butyronitrile pyridinium cation [C(3)CNpy](+), designed to improve catalyst retention, have been prepared and evaluated in Suzuki and Stille coupling reactions. Depending on the nature of the anion, these salts react with palladium chloride to form [C(3)CNpy](2)[PdCl(4)] when the anion is Cl(-) and complexes of the formula [PdCl(2)(C(3)CNpy)(2)][anion](2) when the anion is PF(6)(-), BF(4)(-), or N(SO(2)CF(3))(2)(-). The solid-state structures of [C(3)CNpy]Cl and [C(3)CNpy](2)[PdCl(4)] have been established by single-crystal X-ray diffraction. The catalytic activity of these palladium complexes following immobilization in both N-butylpyridinium and nitrile-functionalized ionic liquids has been evaluated in Suzuki and Stille coupling reactions. All of the palladium complexes show good catalytic activity, but recycling and reuse is considerably superior in the nitrile-functionalized ionic liquid. Inductive coupled plasma spectroscopy reveals that the presence of the coordinating nitrile moiety in the ionic liquid leads to a significant decrease in palladium leaching relative to simple N-alkylpyridinium ionic liquids. Palladium nanoparticles have been identified as the active catalyst in the Stille reaction and were characterized using transmission electron microscopy.     

Selective chemical treatment of cellular microdomains using multiple laminar streams

There are many experiments in which it would be useful to treat a part of the surface or interior of a cell with a biochemical reagent. It is difficult, however, to achieve subcellular specificity, because small molecules diffuse distances equal to the extent of the cell in seconds. This paper demonstrates experimentally, and analyzes theoretically, the use of multiple laminar fluid streams in microfluidic channels to deliver reagents to, and remove them from, cells with subcellular spatial selectivity. The technique made it possible to label different subpopulations of mitochondria fluorescently, to disrupt selected regions of the cytoskeleton chemically, to dislodge limited areas of cell-substrate adhesions enzymatically, and to observe microcompartmental endocytosis within individual cells. This technique does not require microinjection or immobilization of reagents onto nondiffusive objects; it opens a new window into cell biology.     

Single metal four-electron reduction by U(ii) and masked “U(ii)” compounds

The redox chemistry of uranium is dominated by single electron transfer reactions while single metal four-electron transfers remain unknown in f-element chemistry. Here we show that the oxo bridged diuranium(iii) complex [K(2.2.2-cryptand)]₂[{((Me₃Si)₂N)₃U}₂(μ-O)], 1, effects the two-electron reduction of diphenylacetylene and the four-electron reduction of azobenzene through a masked U(ii) intermediate affording a stable metallacyclopropene complex of uranium(iv), [K(2.2.2-cryptand)][U(η²-C₂Ph₂){N(SiMe₃)₂}₃], 3, and a bis(imido)uranium(vi) complex [K(2.2.2-cryptand)][U(NPh)₂{N(SiMe₃)₂}₃], 4, respectively. The same reactivity is observed for the previously reported U(ii) complex [K(2.2.2-cryptand)][U{N(SiMe₃)₂}₃], 2. Computational studies indicate that the four-electron reduction of azobenzene occurs at a single U(ii) centre via two consecutive two-electron transfers and involves the formation of a U(iv) hydrazide intermediate. The isolation of the cis-hydrazide intermediate [K(2.2.2-cryptand)][U(N₂Ph₂){N(SiMe₃)₂}₃], 5, corroborated the mechanism proposed for the formation of the U(vi) bis(imido) complex. The reduction of azobenzene by U(ii) provided the first example of a “clear-cut” single metal four-electron transfer in f-element chemistry.

Both a masked and the actual complex [U(ii){N(SiMe₃)₂}₃]⁺ effect the reduction of azobenzene to yield a U(vi) bis-imido species providing the first example of a “clear-cut” metal centred four-electron reduction in f-element chemistry.