Attempted Reduction of Divalent Rare Earth Iodo Aminopyridinates

Rare examples of amido‐iodo complexes of selected divalent lanthanides can be synthesized by using deprotonated Ap*H {Ap*H = 2,6‐diisopropylphenyl)‐[6‐(2,4,6‐triisopropylphenyl)‐pyridin‐2‐yl]‐amine} as a stabilizing ligand. Reaction of [Ap*K]_n with [LnI₂(thf)_n] (Ln = Eu, Yb, n = 4,5) in THF leads to [Ln(Ap*)I(thf)₂]₂ (Ln = Eu, Yb). An attempted reduction of these divalent heteroleptic complexes with KC₈ to synthesize complexes containing an unsupported Ln–Ln bond resulted in the formation of [Ln(Ap*)₂(thf)₂]. These lanthanide complexes were characterized by X‐ray structure analysis.     

On transformations of graded matrices,with applications to stiff ODE's

Summary Estimates concerning the spectrum of a graded matrix and other information useful for a reliable and efficient handling of certain complications in the numerical treatment of some stiff ODE's, can be inexpensively obtained from the factorized Jacobian. The validity of the estimates is studied by considering them as the first step in a block LR algorithm, which may be of interest in its own right. Its convergence properties are examined.Dedicated to Professor Lothar Collatz on the occasion of his 75th birthday     

33 years of numerical instability,Part I

BIT has played and plays a great role in the development of concepts concerning numerical (in)stability in initial value problems forODE's and related questions. This development is here seen through the looking-glass of the author, who experienced much of its pains and pleasures. The article is based on a talk given in 1981 at the Zürich symposium to commemorate the tenth anniversary of the death of the eminent Swiss numerical analyst, Heinz Rutishauser. The presentation is mainly chronological with a few digressions. Part I ends at the beginning of the stiff epoch.     

G-stability is equivalent toA-stability

In 1975 the author showed that a norm (Liapunov function) can be constructed for the stability and error analysis of a linear multistep method (and the related one-leg method) for the solution of stiff non-linear systems, provided that the system satisfies a monotonicity condition and the method possesses a property calledG-stability.In this paper it is shown thatG-stability is equivalent toA-stability. More generally, a Liapunov function exists if the stability region of the method contains a circle (half-plane), provided that the system satisfies a monotonicity condition related to this circle (half-plane). In the general case this condition depends on the stepsize.     

On accuracy and unconditional stability of linear multistep methods for second order differential equations

Linear multistep methods for solution of the equationy=f(t, y) are studied by means of the test equationy=–² y, with real. It is shown that the order of accuracy cannot exceed 2 for an unconditionally stable method.This work was supported by the NASA-Ames Research Center, Moffett Field, California, under Interchange No. NCA2-OR745-712, while the author was a visitor at the Computer Science Department, Stanford University, Stanford, California.     

Cyclic Hydroboration – The Structure of Perhydro‐9b‐boraphenalenes

Complete hydroboration of cyclododecatrienes was reported to give two isomers, depending on conditions. The assignment of their structure had been attempted without unequivocal proofs. We have now used NMR spectroscopy (¹¹B, ¹³C, ¹⁵N and ²³Na NMR) to study the sodium amides of these two polycyclic boranes. In addition, one of the isomeric borates could be crystallized, and the X‐ray analysis revealed a cis‐,cis‐,trans configuration of the six‐membered rings reversing the original structural assignment.     

Synthesis and Structure of a Hexameric Silver and Tetrameric Gold Aminopyridinates

4‐Methyl‐2‐((trimethylsilyl)amino)pyridine (Ap^TMSH) was synthesized via a salt metathesis reaction. Lithiation of Ap^TMSH with n‐BuLi afforded the transmetallation agent [(Ap^TMS)₂Li₂(OEt₂)₂] ( 1 ) which was structurally characterized. Reaction of 1 with AgCl and [AuCl(tht)] (tht = tetrahydrothiophene) at low temperatures in THF yielded homoleptic aminopyridinates of the heavier group 11 metals, namely [(Ap^TMS)₆Ag₆] ( 2 ) and [(Ap^TMS)₄Au₄] ( 3a and b ) after work‐up in hexane. All compounds were characterized by X‐ray crystal structure analysis. The quality of the structure determination of 3a allows establishing the connectivity only. The lithium complex 1 shows the expected structure from analogous compounds. The hexameric silver compound shows a new structural motif for silver aminopyridinates. The six‐membered ring of silver atoms has a chair conformation. Compounds 3a and b are the first homoleptic gold aminopyridinates and exhibit a rhombic arrangement of the four gold atoms.     

Synthesis of 4‐silaspiro[3.4]octa‐1,5‐diene derivatives: hybrid spiro compounds

Trialkynyl(vinyl)silanes CH₂?CH? Si(C?C? R)₃ (R = Bu, Ph, p‐tolyl) were prepared and treated with 9‐borabicyclo[3.3.1]nonane (9‐BBN). Consecutive 1,2‐hydroboration and intramolecular 1,1‐carboboration reactions (each requires different reaction conditions) were studied. 1,2‐Hydroboration of the Si? vinyl group takes place at ambient temperature (23°C in tetrahydrofuran), followed by intramolecular 1,1‐vinylboration to give 1‐silacyclopent‐2‐ene derivatives, bearing still two alkynyl functions at the silicon atom. Further treatment with a second equivalent of 9‐BBN affords 1‐alkenyl‐1‐(alkynyl)‐1‐silacyclopent‐2‐ene derivatives. These undergo intramolecular 1,1‐vinylboration to give 4‐silaspiro[3.4]octa‐1,5‐dienes bearing the boryl groups at 2 and 6 positions. Protodeborylation of all new compounds (intermediates and final products) using acetic acid in slight excess afforded corresponding silanes including spirosilanes. All compounds were characterized using multinuclear NMR spectroscopy (¹H, ¹¹B, ¹³C, ²⁹Si) in solution state. Solid‐state structures for one of the trialkynyl(vinyl)silanes (R = p‐tolyl) and one of the 1‐silacyclopent‐2‐ene derivatives (R = Ph) were confirmed using X‐ray diffraction. Copyright © 2015 John Wiley & Sons, Ltd.     

Single and Double C?Cl‐Activation of Methylene Chloride by P,N‐ligand Coordinated Rhodium Complexes

Two in one : The simultaneous formation of bimetallic μ‐methylene bridged Rh^III complexes as well as dimeric Rh^III complexes with terminal chloromethyl groups is observed for P,N‐ligand stabilized Rh^I complexes by C? Cl bond activation of methylene chloride. A mechanistic proposal for the formation of both activation products is also discussed.