Nuclear magnetic resonance studies of sulfur inversion in bis(cyclopentadienyl)-molybdenum and -tungsten complexes with dithioethers

The metallocene thioether derivatives [Cp₂M(MeSCH₂CH₂SMe)][PF₆]₂ (1, M = MO; 2, M = W), [Cp₂Mo(SCH₂CH₂SMe)][PF₆] (3) and [Cp₂M(SCH₂CH₂S)] (4, M = Mo; 5, M = W) exhibit temperature-dependent fluxional behavior in solution, owing to the pyramidal sulfur inversion process. The activation energies for this process were determined from proton band-shape analysis in the cases of 1 (54.9 ± 2 kJ mol⁻¹), 2 (51.2 ± 4.6 kJ mol⁻¹) and 3 (30.0 ± 3.1 kJ mol⁻¹). Extended Hückel calculations on related model complexes suggest that local inversion at the sulfur atoms, rather that an inversion of the complete S---C---C---S chain, is responsible for the observed fluxional behaviour.     

A review ofL=λW and extensions

A fundamental principle of queueing theory isL=W (Little's law), which states that the time-average or expected time-stationary number of customers in a system is equal to the product of the arrival rate and the customer-average or expected customer-stationary time each customer spends in the system. This principle is now well known and frequently applied. However, in recent years there have been extensions, such as H=G and the continuous, distributional, ordinal and central-limit-theorem versions, which show that theL=W relation, when viewed properly, has much more power than was previously realized. Moreover, connections have been established between H=G and other fundamental relations, such as the rate conservation law and PASTA (Poisson arrivals see time averages), which show that there is a much greater unity in the overall theory than was previously realized. This paper provides a review.This paper is dedicated to the memory of our colleague Professor Peter Franken (1937–1989), who contributed greatly to the subject of this paper and to queueing theory more generally.     

NMR Studies of Mixed-Ligand Lanthanide Complexes in Solution: Pseudorotation and Ring Inversion of 18-Crown-6 Molecule in Cerium Subgroup Chelates

¹H and ¹³C NMR measurements are reported for the CDCl₃ and CD₂Cl₂ solutions of [La(NO₃)₃(18-crown-6)] (I), [Pr(NO₃)₃(18-crown-6)] (II) and [Ce(NO₃)₃(18-crown-6)] (III) complexes. Temperature dependencies of the ¹H NMR spectra of II have been analyzed using the dynamic NMR methods for multi-site exchange. Two types of conformational dynamic processes in II were identified (the first one with activation enthalpy ΔH ^‡=26 ± 4 kJ/mol is conditioned by interconversion of complex enantiomeric form and pseudorotation of macrocycle molecule upon the C ₂ symmetry axis, the second one with ΔH ^‡=46 ± 5 kJ/mol is conditioned by macrocycle molecule inversion). Studies of the values of the lanthanide-induced shifts revealed that the structure of complexes in solution is similar to that reported for the complex I in the crystal state.This revised version was published online in July 2005 with a corrected issue number.     

The Structure of Bis[N‐6‐aminopyridyl‐N‐(1S)‐(+)‐10‐camphorsulfonylamino]palladium in the Solid State and in Solution

The complex, bis[N‐6‐aminopyridyl‐N‐(1S)‐(+)‐10‐camphorsulfonylamino]palladium, Pd[(S)‐APCS]₂, 1 , was prepared by reaction of 2‐[(1S)‐(+)‐10‐camphorsulfonamino]‐6‐aminopyridine with PdCl₂ in THF. Complex 1 has been characterized by spectroscopic methods and its structure has been determined by X‐ray crystallography. Crystal data: space group C2, a= 16.082 (2), b = 17.104 (2), c = 13.051 (2)Å, β = 99.95 (1)°, V = 3535.9 (8) ų, Z = 2 with final residuals R1 = 0.0491 and wR2 = 0.0944. Two independent molecules, (S,S)‐Pd[(S)‐APCS]2, 1a , and (R,R)‐Pd[(S)‐APCS]2, 1b , were found in each asymmetric unit, which exchange to each other via a series of nitrogen inversion and C‐C bond rotation. The inversion energy (ΔGc₁^≠) and the energy barrier (δGc₂^≠) were 11.5 ± 0.1 Kcal mol^?1 at 246 K and 9.8 ± 0.1 Kcal mol^?1 at 199 K, respectively, calculated by dynamic NMR data.     

Synthese und Konformation einiger Azaspirane mit Alkyl-bzw. Aryl-Sulfonamid-Gruppen

Preferred conformations of some azaspiran systems substituted with large groups at the nitrogen atoms were established by UV absorption spectroscopy. These groups prohibit the inversion at nitrogen, as was deduced from the¹H NMR spectra.

     

Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach

In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.     

A systematic methodology to design silica templates: Silica microemulsion formulation and nanodroplet type and size estimation

A systematic study of the design and characterization of silica-microemulsion templates is presented. The ternary phase diagrams in micro-heterogeneous systems, by using a non-ionic surfactant (Brij 30) and different silica precursors (MTEOS, TEOS, PTEOS), have been drawn. Based on Khalweit diagrams, the phase inversion temperature was estimated as close to 315 K, for both alchil (TEOS) and aril (PTEOS) types of alcoxides. By correlating the information obtained from phase diagrams at room temperature with that of size effects revealed by VIS absorption molecular probes (bromthymol blue dye), the phase inversion point, i.e. the transition point from water-in-oil to oil-in-water microemulsion, was also clearly established as corresponding to R ∼ 1. Besides technically attractive features such as a wide variety of inorganic and hybrid nanomaterials, high specific surface and highly efficient applicative properties of the final materials, the approach of silica-microemulsion-based templates can be seen as a route towards the Green Chemistry concept.     

Regularized inversion of the Laplace transform for series of experiments

Not only in low-field nuclear magnetic resonance, Laplace inversion is a relevant and challenging topic. Considerable conceptual and technical progress has been made, especially for the inversion of data encoding two decay dimensions. Distortion of spectra by overfitting of even moderate noise is counteracted requiring a priori smooth spectra. In this contribution, we treat the case of simple and fast one-dimensional decay experiments that are repeated many times in a series in order to study the evolution of a sample or process. Incorporating the a priori knowledge that also in the series dimension evolution should be smooth, peak position can be stabilized and resolution improved in the decay dimension. It is explained how the standard one-dimensional regularized Laplace inversion can be extended quite simply in order to include regularization in the series dimension. Obvious improvements compared with series of one-dimensional inversions are presented for simulated as well as experimental data. For the latter, comparison with multiexponential fitting is performed.