Error estimators for stiff differential equations

When solving ordinary differential equations numerically, the local error is estimated at each step. In the classical situation of ‘small’ step sizes, it is clear what is required of the error estimators. Stiff problems are solved with ‘large’ step sizes. The quality of error estimators is studied in this situatuion, and it is shown how to modify unsatisfactory estimators so as to improve them greatly. Several formulas from the literature are treated as examples.     

Unmasking the constitution and bonding of the proposed lithium nickelate “Li3NiPh3(solv)3”: revealing the hidden C6H4 ligand

More than four decades ago, a complex identified as the planar homoleptic lithium nickelate “Li₃NiPh₃(solv)₃” was reported by Taube and co-workers. This and subsequent reports involving this complex have lain dormant since; however, the absence of an X-ray diffraction structure leaves questions as to the nature of the Ni–PhLi bonding and the coordination geometry at Ni. By systematically evaluating the reactivity of Ni(COD)₂ with PhLi under different conditions, we have found that this classical molecule is instead a unique octanuclear complex, [{Li₃(solv)₂Ph₃Ni}₂(μ-η²:η²-C₆H₄)] (5). This is supported by X-ray crystallography and solution-state NMR studies. A theoretical bonding analysis from NBO, QTAIM, and ELI perspectives reveals extreme back-bonding to the bridging C₆H₄ ligand resulting in dimetallabicyclobutane character, the lack of a Ni–Ni bond, and pronounced σ-bonding between the phenyl carbanions and nickel, including a weak σ_C–Li → s_Ni interaction with the C–Li bond acting as a σ-donor. Employing PhNa led to the isolation of [Na₂(solv)₃Ph₂NiCOD]₂ (7) and [Na₂(solv)₃Ph₂(NaC₈H₁₁)Ni(COD)]₂ (8), which lack the benzyne-derived ligand. These findings provide new insights into the synthesis, structure, bonding and reactivity of heterobimetallic nickelates, whose prevalence in organonickel chemistry and catalysis is likely greater than previously believed.

We disclose the actual octanuclear nature of the major compound from reacting Ni(COD)₂ and PhLi, assigned for more than four decades as ‘Li₃NiPh₃(solv)₃’. We provide a thorough bonding analysis and discuss its potential implications in catalysis.     

Conformational Analysis of Fluorinated Pyrrolidines Using 19F–1H Scalar Couplings and Heteronuclear NOEs

A series of 3‐fluoropyrrolidines have been studied to investigate the influence of the stereoelectronic fluorine gauche effect on ring conformations in the solid state by single‐crystal X‐ray analysis and in solution phase by NMR spectroscopy. As part of these studies 1D ¹⁹F–¹H heteronuclear NOE (HOESY) experiments have been optimised for applications to small molecules and are described in detail. These have been employed to estimate ¹⁹F–¹H internuclear distances and were combined with vicinal ³J(F,H) and ³J(H,H) scalar coupling constants to analyse the ring conformations. Where possible the derived solution‐phase structural data have been compared with those of the crystalline state. The results demonstrate the influence of the gauche effect in stabilising C^γ‐exo conformations of the fluorinated pyrrolidines. It was further shown that when steric interactions were also present, this conformational bias was diminished and the contribution of the alternative C^γ‐endo conformation was seen to increase in solution at lower sample temperatures.     

CryoSEM investigation of latex coatings dried in walled substrates

Nonuniformities, such as heavy edges or "coffee rings", frequently develop as particulate coatings dry. One idea for avoiding these nonuniformities is to engineer the substrate edges. In this work, monodisperse latex coatings were deposited on substrates with photoresist walls around their edges. Cryogenic scanning electron microscopy (cryoSEM) results show particle accumulation near the walls and at the free surface. The contact line, pinned at the wall, generates lateral transport of water and particles, leading to a nonuniform coating thickness. Still, coatings on substrates with walls were shown to have a higher degree of thickness uniformity after drying than those without walls.     

NMR Investigation of Ring Conformation in Substituted Dihydronaphthalenes

Vicinal J_HH couplings were investigated for a series of substituted dihydronaphthalenes allowing the conformation of the non-aromatic ring to be evaluated. It was found that the substitution of bromine for hydrogen increases the total puckering amplitude of the non-aromatic ring. Different formulations of the Karplus equation were investigated and the influence on the observed results are discussed.     

NMR Studies of Drugs. Application of Achiral and Chiral Lanthanide Shift Reagents to α-Ethyl-α-Phenylsuccinimide

The 60 MHz ¹H NMR spectra of 3-ethyl-3-phenylpyrrolidine-2,5-dione, 1, were studied in CDCl₃ at 28° using the achiral lanthanide shift reagent (LSR) tris(6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium(III), Eu(FOD)₃ 2, for spectral simplification, and the chiral LSR, tris[3-heptafluoropropylhydroxymethylene)-(+)-camphorato]-europium(III), Eu(HFC)₃ 3, to induce enantiomeric shift differences (δδδ) for several nuclei. A non-racemic sample of 1 was treated with 3 to determine the sense of magnetic nonequivalence of selected nuclei. Significant δδδ is seen for the signals of the methyl and aryl ortho protons. Modest δδδ can also be seen for the NH signal and for one of the H-4 protons, although LSR-induced broadening for the two latter signals is severe. The (-) enantiomer appeared to exhibit an upfield sense of magnetic nonequivalence (3:1 molar ratio ca. 0.15—0.35) for the methyl signal but a downfield sense for H_ortho (3:1 ratio ca. 0.6).     

Intramolecular Reaction of Transient Phosphenium and Arsenium Ions Giving Rise to Isolable 9‐Phospha‐ and 9‐Arsena‐Fluorenium Ions

Transient phosphenium and arsenium ions, generated by fluoride abstraction from bis(m‐terphenyl)fluoropnictogens, underwent intramolecular electrophilic attack prior to methyl group migration and gave rise to isolable 9‐phospha‐ and 9‐arsena‐fluorenium ions.     

Localized grafting through chemical lift-off

In this work we present two techniques that provide localized functionalization of the surface of materials. Both lead to localized grafted thin organic films (10-200 nm). The localization is brought by a chemical lift-off process, which relies on patterned weakly bonded films as sacrificial layers, combined with electrochemical (SEEP) or chemical (GraftFast©) processes which provides the final robust pattern on the surface. Both grafting processes, which were recently described, take advantage of the redox activation of diazonium salts associated with vinylic monomers in aqueous solution, and lead to similar grafted polymer films. Thanks to the high difference in adhesion between the grafted polymer and the patterned sacrificial layer (either an ink or weakly bound self-assembled monolayers), the latter may be easily removed, which unveils uncovered areas of the substrate.