Constrained‐Geometry Bisphosphazides Derived from 1,8‐Diazidonaphthalene: Synthesis,Spectroscopic Characteristics,Structural Features,and Theoretical Investigations

Investigations on the Staudinger reaction between 1,8‐diazidonaphthalene and phosphorous(III) building blocks, a key step in the synthesis of superbasic bisphosphazene proton sponges, yielded a set of bisphosphazides with a constrained geometry 1,8‐disubstituted naphthalene backbone. This compound class has attracted our interest not only due to their surprisingly high stability, but in particular because of their theoretically predicted basicity in the range of their bisphosphazene analogues that can be referred to the constrained geometry interaction of two highly basic nitrogen atoms. Eleven new bisphosphazides bearing simple P‐amino groups as well as P‐guanidino substituents, azaphosphatrane moieties, P₂ building blocks, or chiral P‐amino substituents derived from L ‐proline are presented. They were studied concerning their spectroscopic properties and partly also their chromophoric and structural features. In the case of the pyrrolidino‐substituted TPPN(2N₂) (TPPN=1,8‐bis(trispyrrolidinophosphazenyl)naphthalene), the stepwise nitrogen elimination is investigated theoretically and experimentally, which led to the isolation and structural characterization of TPPN(1N₂) bearing a phosphazide and a phosphazene functionality in one molecule. Attempts to protonate the obtained bisphosphazides and to prove the computationally predicted pK_BH⁺ values through NMR titration reactions resulted in their decay, which again was rationalized by theoretical calculations. Altogether we present the so far most extensive spectroscopic, structural and theoretical investigation of constrained geometry bisphosphazides and their Brønsted and Lewis basic properties.     

Mono-Phosphazenyl Phosphines (R2N)3P=N–P(NR2)2 – Strong P-Bases,P-Donors,and P-Nucleophiles for the Construction of Chelates

We present a convenient three-step synthesis of amino substituted phosphazenyl phosphines of the general formula (R₂N)₃P=N–P(NR₂)₂ [NR₂ = N(CH₂)₄, N(CH₂)₅, N(CH₂)₆]. These easily accessible mixed valent compounds display a surprisingly high proton affinity and basicity in the same range as the corresponding Schwesinger diphosphazene (Me₂N)₃P=N–P=NEt(NMe₂)₂ (Et-P₂) and Verkade's proazaphosphatrane superbases. Within the central [P^III–N=P^V] scaffold, the phosphine P^III and not the phosphazene N^III atom is the center of highest proton affinity, basicity and donor strength. As P-bases, the title compounds display calculated proton affinities between 265.8 (NR₂ = NMe₂) and 274.7 kcal · mol^–1 [NR₂ = N(CH₂)₄] and pK_BH⁺ values between 26.4 (NR₂ = NMe₂) and 31.5 [NR₂ = N(CH₂)₄] on the acetonitrile scale. As P-nucleophiles, they are key intermediates in the synthesis of hyperbasic bis(diphosphazene) proton sponges, chiral bis(diphosphazene) proton pincers, bisphosphazides, and superbasic P₂-bisylides. Their Staudinger reactions as nucleophile towards 1,8-diazidonaphthalene leading to 1,8-naphthalene-bisphosphazides is described in detail. The donor strength of the title compounds towards fragments [Se] and [Ni(CO)₃] is in the same range as that of N-heterocyclic carbenes.     

High-speed energy efficient selective removal of large area copper layer by laser induced delamination

An indirect laser-induced method for selective removal of large copper areas from a printed circuit board is theoretically and experimentally investigated. The results show that the threshold condition for the process involves phase transition of the epoxy-based substrate resin. Optimal parameters for maximizing process speed are found and discussed.     

Eigenvalue estimates for Schrödinger operators on metric trees

We consider Schrödinger operators on radial metric trees and prove Lieb–Thirring and Cwikel–Lieb–Rozenblum inequalities for their negative eigenvalues. The validity of these inequalities depends on the volume growth of the tree. We show that the bounds are valid in the endpoint case and reflect the correct order in the weak or strong coupling limit.     

An extension of the Landau-Kolmogorov inequality. Solution of a problem of Erdös

For any fixed finite interval [a, b] on the real line, an arbitrary natural numberr and σ>0, we describe the extremal function to the problem $\left\| {f^{(k)} } \right\|L_p \left[ {a,b} \right]^{ \to \sup } \left( {1 \leqslant k \leqslant r - 1, 1 \leqslant p< \infty } \right)$ over all functionsf ∈W _∞ ^r such that |f ^(r)(x)| ≤σ, |f(x)|≤1 on (?∞, ∞). Similarly, we solve the problem, raised by Paul Erdös, of characterizing the trigonometric polynomial of fixed uniform norm whose graph has maximal arc length over [a, b].     

Semiempirical versusab initio calculations of molecular properties

A comparative study of the structural parameters in some strained spirohydrocarbons is presented. The theoretical values provided by the STO-3G, MINDO/3 and IMOA methods are in reasonable agreement with each other and with available experimental data offering thus a posteriori justification of the employed approximate schemes.     

Algorithms for nonlinear piecewise polynomial approximation: Theoretical aspects

In this article algorithms are developed for nonlinear -term Courant element approximation of functions in ( ) on bounded polygonal domains in . Redundant collections of Courant elements, which are generated by multilevel nested triangulations allowing arbitrarily sharp angles, are investigated. Scalable algorithms are derived for nonlinear approximation which both capture the rate of the best approximation and provide the basis for numerical implementation. Simple thresholding criteria enable approximation of a target function to optimally high asymptotic rates which are determined and automatically achieved by the inherent smoothness of . The algorithms provide direct approximation estimates and permit utilization of the general Jackson-Bernstein machinery to characterize -term Courant element approximation in terms of a scale of smoothness spaces (-spaces) which govern the approximation rates.