Internally solvated cyclopentadienyllithium compounds: structural integrity of the Cp-Li+ moiety. NMR, dynamics, X-ray crystallography, and calculations

[Structure: see text]. N(CH2CH2OCH3)2 are as follows: T = CHCH(CH3)2, 6; T = (CH2)2, 10; T = (CH2)3, 14. The results of NOE NMR experiments for 6, 10, and 14 together with X-ray crystallography of 14 support internally coordinated monomeric structures for all three compounds. Models have been constructed for 6, 10, and 14 from modifications of an internally solvated allylic lithium compound at the B3LYP level of theory using basis set 6-311G*. The resulting structural features are very similar to those obtained from the NMR and crystallographic data. In addition, 13C NMR shifts obtained with the GIAO procedure using the results of the B3LYP/6-311G* calculations are closely similar to the experimental shifts, which validate B3LYP as a suitable model for these compounds. The Li+ centroid distance of ca. 1.9 A to 2.0 A obtained for 6, 10, and 14 is common to most crystallographic data for externally solvated Cp-Li+ compounds as well as one which incorporates a (CpLiCp)- triple ion. It is concluded that the ligand tether and the stereochemistry around Li+ accommodate to maintain the structural integrity of Cp-Li+. NMR and crystallography show 14 to be chiral. Carbon-13 NMR line shape changes are attributed to inversion via a lateral wobble mechanism with DeltaH++ = 6 kcal x mol(-1) and DeltaS++ = -2 eu. It is also shown that a 6,6-dimethylfulvene is deprotonated at methyl by LiN(CH2CH2OCH3)3 as well as by butyllithium in the presence of PMDTA producing isopropenyl Cp-Li+ compounds 24 and 25, respectively. NMR line shape changes of the sample containing 24 have been qualitatively interpreted to result from a combination of fast transfer of coordinated ligand between faces of the carbanion plane as well as a lithium-exchange process.     

Diagnostics of dielectronic processes in laser produced samarium plasma

Spatially-resolved time-integrated X-ray spectra of laser produced samarium plasma were recorded, in the spectral range from 7 to 10 Å. The spectrum of samarium is characterized by the prominent pattern of transitions 3d – nf (n = 4–7) belonging to Co-like (Sm³⁵⁺), Ni-like (Sm³⁴⁺) and Cu-like (Sm³³⁺) ions. Spectral lines of Mn-like (Sm³⁷⁺) to Zn-like (Sm³²⁺) were identified. The appearance of these ionization stages as a function of distance from the target was measured. Transfer of the dominant ion stages to lower stages with increasing distance from the original target surface was demonstrated, probably indicating dielectronic recombination. The Hebrew University Lawrence Livermore Atomic Code was used to generate emission spectra for comparison with the experimental ones.A radiation-hydrodynamics code coupled to three non-Local Thermal Equilibrium ionization and equation of state models with different approaches for dielectronic processes was used to model the plasma. The simulated plasma ionization and electron densities and temperatures were found to be consistent with the experimental results.     

Simplified electrostatic model for the thermodynamic excess potentials of binary strong electrolyte solutions with size-dissimilar ions

Modern theories of electrolyte solutions are physically accurate but difficult to apply for real-life systems; a need therefore exists to theoretically derive simplified and practically useful mathematical expressions for thermodynamic excess functions. This can be done by incorporating ion-size dissimilarity into the classical Debye-Hückel model [Physik Z. 24, 185 (1923)], under conditions at which non-electrostatic contributions are negligible. If the contact distance between the central (β) ion and a cloud (α) ion is a for counter-ions and b for co-ions, two basic cases exist, b < a and b > a. In both, a ‘smaller-ion shell’ (SiS) at the edge of the ionic cloud, bordered by the spherical surfaces of radius b and a, admits only the smaller α ions [Thomlinson and Outhwaite, Mol. Phys. 47, 1113 (1982)]. In the b < a case, the SiS contributes an ionic repulsion effect and the overall extra-electrostatic potential energy, Ψ _{b < a} (κ) ? κ, reciprocal screening length–exhibits a minimum. For b > a, the SiS contributes an ‘extra ionic attraction’ and the overall extra-electrostatic energy, Ψ _{b > a} (κ) declines monotonically with increasing κ. The entire Ψ contribution, Ψ_±, is a linear combination of the Ψs of the two counter β ions. The effectiveness of Ψ_± is demonstrated for real-life electrolyte systems, based on experimental mean ionic activity coefficients and their concentration dependencies. Fitting theory with experiment generates ion-size parameters that represent realistic interionic collision distances in solution, unlike parallel parameters based on other simplified theories.     

All optical electron injector using an intense ultrashort pulse laser and a solid wire target

Energetic electron bunches were generated by irradiating a solid tungsten wire 13 μm wide with 50 femtosecond pulses at an intensity of ∼3×10¹⁸ W/cm². The electron yield, energy spectrum and angular distribution were measured. These energetic electron bunches are suitable for injection into a laser driven plasma accelerator. An all-optical electron injector based on this approach could simplify timing and alignment in future laser-plasma accelerator experiments. PACS 41.75.Ht; 41.75.Lx; 52.38.Kd; 52.38.Ph     

A linear algorithm for nonhomogeneous spectra of numbers

Given a sequence of integers [a_i]_i=1ⁿ, an O(n) iterative algorithm is presented which decides whether there exist real numbers α and β such that a_i = [iα + β] (1 ? i ? n). In fact, the linear algorithm computes the partial quotients of the continued fraction expansions of $\text{d}$ and $\text{d}$ such that $\text{d < α <}\text{d}$ if and only if a_i = [iα + β] (1 ? i ? n) for suitable β = β(α).