Diethyl Fluoronitromethylphosphonate: Synthesis and Application in Nucleophilic Fluoroalkyl Additions

Diethyl fluoronitromethylphosphonate ( 3 ), a previously unknown compound, was synthesized by electrophilic fluorination of diethyl nitromethylphosphonate with Selectfluor. Base‐induced decomposition of 3 was studied by NMR spectroscopy, which identified diethyl fluorophosphate and fluoronitromethane as the main decomposition products. C?H acidities [pK_a values in dimethyl sulfoxide (DMSO)] of 3 , 1‐fluoro‐1‐phenylsulfonylmethanephosphonate ( 1 ; McCarthy’s reagent), tetraethyl fluoromethylenebisphosphonate ( 2 ), and some nonfluorinated phosphonates were computed, and a good correlation between calculated and experimental pK_a values was found. The calculated C?H acidities increased in the sequence 2 < 1 < 3 . Diethyl fluoronitromethylphosphonate ( 3 ) was applied in the Horner–Wadsworth–Emmons reaction with aldehydes and trifluoromethyl ketones to provide new 1‐fluoro‐1‐nitroalkenes with good to high stereoselectivities. Alkylation of 3 was successful only with iodomethane, however, conjugate additions of 3 to Michael acceptors such as α,β‐unsaturated carbonyl compounds, sulfones, and nitro compounds allowed access to variously modified diethyl 1‐fluoro‐1‐nitrophosphonates.     

Backscattering of stationary radiation in time-dependent random media: average intensity and intensity fluctuations

We consider backscattering of stationary radiation in a random medium whose wavespeed fluctuations depend on time and on space. We modify a previous derivation of the equations that govern the range-evolution of the spectra of the ensemble-averaged forward-and back-propagating components of the field and their second-order statistics, and extend the approach to treat the fourth-order statistics. The latter are governed by integro-difference equations that account for the broadening of the signal spectra due to the time-dependence of the random fluctuations. In the quasi-monochromatic regime, where spectra owing to a monochromatic excitation remain confined to a narrow band over extensive ranges, the integro-difference equations transform into ordinary differential equations that govern the time-dependence of the quantities of interest. We use this simplification to track the power fluxes and their fluctuations (scintillation) in a one-dimensionally stratified slab, where the wave-speed fluctuations depend on the range-coordinate normal to the planes of stratification, and also to treat modal propagation in a duct, where the wave-speed fluctuations depend on all three spatial dimensions. The results suggest that a Gaussian equilibrium is approached at large ranges, on a suitably defined backscattering scale that depends on the medium parameters and the geometry.     

Thermodynamic study of lanthanide(III) complexes with bifunctional monophosphinic acid analogues of H4dota and comparative kinetic study of yttrium(III) complexes

New bifunctional H(4)dota-like ligands with three acetic acid and one phosphinic acid pendant arms and propionate (H(5)do3ap(PrA)) or 4-aminobenzyl (H(4)do3ap(ABn)) reactive groups bound to the phosphorus atom were investigated. Potentiometric studies showed that the ligands have a similar basicity to the parent H(4)dota and the stability constants of their complexes with sodium(i) and selected lanthanide(III) ions are also similar. Formation and acid-assisted decomplexation kinetics of yttrium(III) complexes with a series of H(4)dota-like ligands (H(4)dota and its phosphinic/phosphonic acid analogues) were studied and the reactions are sensitive to a slight modification of the ligand structure. The (2-carboxyethyl)phosphinic acid derivative H(5)do3ap(PrA) and the phosphonic acid ligand H(5)do3ap form complexes faster than H(4)dota. The most kinetically inert complex is that with H(4)do3ap(ABn). Rates of complexation and decomplexation can depend on the ability to transfer proton(s) outside/inside the complex cavity and, therefore, on the hydrophobicity of the ligands. The results demonstrate that the new bifunctional ligands are suitable for labelling biomolecules with yttrium(iii) radioisotopes for utilization in nuclear medicine.     

Symmetry breaking in benzene and larger aromatic molecules within generalized valence bond coupled cluster methods

The origin of symmetry breaking (SB) in benzene in generalized valence bond methods is investigated within a coupled cluster formalism that correlates all valence electrons. Retention of a limited number of pair correlation amplitudes (as in the perfect- and imperfect-pairing models) that incompletely describes interpair correlations leads to symmetry breaking as the orbitals and amplitudes are optimized. Local correlation models that are exact for one, two, and three interacting pairs at the doubles excitation level are compared against the exact pair correlation treatment, which correlates four interacting pairs at once in the connected double substitution operator. For simplicity, this comparison is performed with a second-order model of electron correlation, which is reasonably faithful to the infinite-order result. The significant SB known for the one-pair model (perfect pairing) is not eliminated at the two-pair level, but is virtually eliminated at the three-pair level. Therefore, a tractable hybrid model is proposed, which combines three-pair correlations at the second-order level and infinite-order treatment for the strong imperfect-pairing correlations involving one and two-pair correlations. This model greatly reduces SB in benzene and larger delocalized pi systems such as naphthalene and the phenalenyl cation and anion. The resulting optimized orbitals are localized in the sigma space but exhibit significant delocalization in the pi space. This means that correlation effects associated with different resonance structures are treated in a more balanced way than if the pi orbitals localize, leading to reduced SB.     

Visualizing the Relationship between Two Time Series by Hierarchical Smoothing Models

Abstract

Let x(t_i), y(t_i) be two time series such that y(t_i) = μ(t_i, x) + ε_i, where μ is a smooth function and ε_i is a zero mean stationary process. Which model may be assumed for μ depends on the subject specific context. This article was motivated by questions raised in the context of musical performance theory. The general problem is to understand the relationship between the symbolic structure of a music score and its performance. Musical structure typically consists of a hierarchy of global and local structures. This motivates the definition of hierarchical smoothing models (or HISMOOTH models) that are characterized by a hierarchy of bandwidths b ₁ > b ₂ > … > b_M and a vector of coefficients β ∈ R^M. The expected value μ(t_i x) = E[y(t_i)‖x] is equal to a weighted sum of smoothed versions of x. The “errors” ε_i are modeled by a Gaussian process that may exhibit long memory. More generally, we may observe a collection of time series y_r (r = 1, …, N) that are related to a common time series x by y_r(t_i) = μ _r(t_i, x) + ε_{r, i} where ε _r are independent error processes. For repeated time series, HISMOOTH models lead to a visual and formal classification into clusters that can be interpreted in terms of the relationship to x. An analysis of tempo curves from 28 performances of Schumann's “Träumerei” op. 15/7 illustrates the method. In particular, similarities and differences of “melodic styles” can be identified.     

Scattering of flexural waves by random density fluctuations in a plate

The scattering of flexural waves by random density fluctuations in a plate strip is studied by using a statistical modal analysis. Equations are derived governing the two-point coherence functions of the propagating modes using a parabolic approximation. The governing equations reduce to a coupled set of ordinary differential equations for the self-modes and an uncoupled set for the cross-modes. A sample solution is presented to show the order of magnitude of the rate of decay of the cross-modes and the distance at which mode coupling begins for the self-modes. It is further shown that fluid loading may also be considered in the same framework by using the parabolic approximation to simplify the integral term that is introduced by the fluid loading. Finally, the application of this work to cylindrical shells is discussed.     

Quantum chemical study of the stabilization process of faujasites

The CNDO/2 method is employed in the study of the energetics of the zeolite stabilization process in which skeletal Al atoms are replaced by amorphous Si. It is shown that such a process results in the stabilization of the zeolitic skeleton and that the stabilizing effect increases with decreasing Si: Al ratio as well as with the degree of hydration of the Al-cation formed.

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/2 , Al Si. , Si:Al, Al.

     

Propagation of acoustic waves scattered in a lossy three-dimensional channel

Abstract

In previous papers we discussed the scattering of acoustic waves by random sound-speed fluctuations in lossless two- and three-dimensional channels. Here we include the effect of bottom loss in a three-dimensional channel. The bottom loss is included by replacing the rigid bottom condition by one allowing for loss. We find an asymptotic solution for the angular distribution of the scattered acoustic energy and the characteristic propagation distance at which the asymptotic solution is valid. Beyond this characteristic distance the angular distribution saturates and is no longer dependent on the propagation distance. Before the mathematical development is given a simple physical argument is presented which shows why a saturation region is expected.     

Use of ultrathin zirconium phosphate layers for the preparation of alpha-spectrometric samples

Ultrathin zirconium phosphate layers about 300–600 nm in thickness have been prepared on stainless steel supports. The adherence and homogeneity of the layers are sufficient. The adsorption properies in respect to alpha-emitters (²³⁹Pu and²⁴¹Am) have been studied. The adsorption equilibrium is reached in half an hour and a total capacity of about 3–4 μg Pu has been estimated. Alpha-spectrometric properties of the samples have been evaluated by measuring the half-width of the²³⁹Pu main peak, which is close to the resolution ability of the detector.