NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

Synthesis of μ2-Oxo-Bridged Iron(III) Tetraphenylporphyrin–Spacer–Nitroxide Dimers and their Structural and Dynamics Characterization by using EPR and MD Simulations

Iron(III) porphyrins have the propensity to form μ₂-oxo-dimers, the structures of which resemble two wheels on an axle. Whereas their crystal structure is known, their solution structure and internal dynamics is not. In the present work, the structure and dynamics of such dimers were studied by means of electron paramagnetic resonance (EPR) spectroscopy and quantum chemistry based molecular dynamics (MD) simulations by using the semiempirical tight-binding method (GFN-xTB). To enable EPR investigation of the dimers, a nitroxide was attached to each of the tetraphenylporphyrin cores through a linear and a bent linker. The inter-nitroxide distance distributions within the dimers were determined by continuous-wave (cw)-EPR and pulsed electron–electron double resonance (PELDOR or DEER) experiments and, with the help of MD, interpreted in terms of the rotation of the porphyrin planes with respect to each other around the Fe–O–Fe axis. It was found that such rotation is restricted to the four registers defined by the phenyl substituents. Within the registers, the rotation angle swings between 30° and 60° in the proximal and between 125° and 145° in the distal register. With EPR, all four angles were found to be equally populated, whereas the 30° and 145° angles are strongly favored to the expense of the 60° and 125° angles in the MD simulation. In either case, the internal dynamics of these dimers thus resemble the motion of a step motor.     

Synthesis of Highly Functionalized N,N-Diarylamides by an Anodic C,N-Coupling Reaction

We report an innovative, sustainable and straightforward protocol for the synthesis of N,N-diarylamides equipped with nonprotected hydroxyl groups by using electrosynthesis. The concept allows the application of various substrates furnishing diarylamides with yields up to 57 % within a single and direct electrolytic protocol. The method is thereby easy to conduct in an undivided cell with constant current conditions offering a versatile and short-cut alternative to conventional pathways.     

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

The Role of Ate Complexes in the Copper‐Mediated Trifluoromethylation of Alkynes

Trifluoromethylation reactions have recently received increased attention because of the beneficial effect of the trifluoromethyl group on the pharmacological properties of numerous substances. A common method to introduce the trifluoromethyl group employs the Ruppert–Prakash reagent, that is, Si(CH₃)₃CF₃, together with a copper(I) halide. We have applied this method to the trifluoromethylation of aromatic alkynes and used electrospray‐ionization mass spectrometry to investigate the mechanism of these reactions in tetrahydrofuran, dichloromethane, and acetonitrile as well as with and without added 1,10‐phenanthroline. In the absence of the alkyne component, the homoleptic ate complexes [Cu(CF₃)₂]^? and [Cu(CF₃)₄]^? were observed. In the presence of the alkynes RH, the heteroleptic complexes [Cu(CF₃)₃R]^? were detected as well. Upon gas‐phase fragmentation, these key intermediates released the cross‐coupling products R?CF₃ with perfect selectivity. Apparently, the [Cu(CF₃)₃R]^? complexes did not originate from homoleptic cuprate anions, but from unobservable neutral precursors. The present results moreover point to the involvement of oxygen as the oxidizing agent.     

Association and Dissociation of Grignard Reagents RMgCl and Their Turbo Variant RMgCl⋅LiCl

Grignard reagents RMgCl and their so‐called turbo variant, the highly reactive RMgCl?LiCl, are of exceptional synthetic utility. Nevertheless, it is still not fully understood which species these compounds form in solution and, in particular, in which way LiCl exerts its reactivity‐enhancing effect. A combination of electrospray‐ionization mass spectrometry, electrical conductivity measurements, NMR spectroscopy (including diffusion‐ordered spectroscopy), and quantum chemical calculations is used to analyze solutions of RMgCl (R=Me, Et, Bu, Hex, Oct, Dec, iPr, tBu, Ph) in tetrahydrofuran and other ethereal solvents in the absence and presence of stoichiometric amounts of LiCl. In tetrahydrofuran, RMgCl forms mononuclear species, which are converted into trinuclear anions as a result of the concentration increase experienced during the electrospray process. These trinuclear anions are theoretically predicted to adopt open cubic geometries, which remarkably resemble structural motifs previously found in the solid state. The molecular constituents of RMgCl and RMgCl?LiCl are interrelated via Schlenk equilibria and fast intermolecular exchange processes. A small portion of the Grignard reagent also forms anionic ate complexes in solution. The abundance of these more electron‐rich and hence supposedly more nucleophilic ate complexes strongly increases upon the addition of LiCl, thus rationalizing its beneficial effect on the reactivity of Grignard reagents.     

Thermally induced solid-state transformation of cimetidine. A multi-spectroscopic/chemometrics determination of the kinetics of the process and structural elucidation of one of the products as a stable N3-enamino tautomer

Exposure of cimetidine (CIM) to dry heat (160–180 °C) afforded, upon cooling, a glassy solid containing new and hitherto unknown products. The kinetics of this process was studied by a second order chemometrics-assisted multi-spectroscopic approach. Proton and carbon-13 nuclear magnetic resonance (NMR), as well as ultraviolet and infrared spectroscopic data were jointly used, whereas multivariate curve resolution with alternating least squares (MCR-ALS) was employed as the chemometrics method to extract process information. It was established that drug degradation follows a first order kinetics.