Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.     

Metal‐Free Synthesis of Functional 1‐Substituted‐1,2,3‐Triazoles from Ethenesulfonyl Fluoride and Organic Azides

The boom in growth of 1,4‐disubstituted triazole products, in particular, since the early 2000’s, can be largely attributed to the birth of click chemistry and the discovery of the Cu^I‐catalyzed azide–alkyne cycloaddition (CuAAC). Yet the synthesis of relatively simple, albeit important, 1‐substituted‐1,2,3‐triazoles has been surprisingly more challenging. Reported here is a straightforward and scalable click‐inspired protocol for the synthesis of 1‐substituted‐1,2,3‐triazoles from organic azides and the bench stable acetylene surrogate ethenesulfonyl fluoride (ESF). The new transformation tolerates a wide selection of substrates and proceeds smoothly under metal‐free conditions to give the products in excellent yield. Under controlled acidic conditions, the 1‐substituted‐1,2,3‐triazole products undergo a Michael addition reaction with a second equivalent of ESF to give the unprecedented 1‐substituted triazolium sulfonyl fluoride salts.     

Direct Transformation of Arenols Based on C—O Activation

In the view of substrate availability, atomic efficiency and cost, directly using arenols as coupling partners in cross‐coupling, would be one of the most attractive goals. Up to date, many efforts have been made to activate the C—O bond of phenols with different strategies, for example, through in‐situ formed intermediates, through a catalytic reductive dearomatization‐condensation‐rearomatization sequence or catalytic deoxygenation. In this review, we summarized recent advances in cross‐couplings of arenols as the electrophiles via C—O activation.     

Polar Isotactic and Syndiotactic Polypropylenes by Organozirconium-Catalyzed Masking-Reagent-Free Propylene and Amino–Olefin Copolymerization

Polar functionalized isotactic and syndiotactic polypropylenes (PPs) are synthesized by direct, masking-reagent-free propylene and amino–olefin (AO, CH₂=CH(CH₂)_xNⁿPr₂, x=2, 3, 6) copolymerizations using the activated precatalysts rac-[Me₂Si(indenyl)₂]ZrMe₂ and [Me₂C(Cp)(fluorenyl)]ZrMe₂, respectively. Polymerization activities at 25 °C are as high as 4208 and 535 kg/(mol h atm) with AO incorporation up to 4.0 mol % and 1.6 mol %, respectively. Remarkably, introducing the amino-olefin comonomers significantly enhances stereoselection for both isotactic (mmmm: 59.5 %→91.0 %) and syndiotactic (rrrr: 66.3 %→81.3 %) products.     

An Integrated Microfluidic Probe for Mass Spectrometry Imaging of Biological Samples**

Ambient ionization based on liquid extraction is widely used in mass spectrometry imaging (MSI) of molecules in biological samples. The development of nanospray desorption electrospray ionization (nano-DESI) has enabled the robust imaging of tissue sections with high spatial resolution. However, the fabrication of the nano-DESI probe is challenging, which limits its dissemination to the broader scientific community. Herein, we describe the design and performance of an integrated microfluidic probe (iMFP) for nano-DESI MSI. The glass iMFP, fabricated using photolithography, wet etching, and polishing, shows comparable performance to the capillary-based nano-DESI MSI in terms of stability and sensitivity; a spatial resolution of better than 25 μm was obtained in these first proof-of-principle experiments. The iMFP is easy to operate and align in front of a mass spectrometer, which will facilitate broader use of liquid-extraction-based MSI in biological research, drug discovery, and clinical studies.     

Ligand Control of Palladium-Catalyzed Site-Selective α- and γ-Arylation of α,β-Unsaturated Ketones with (Hetero)aryl Halides

This study describes the first palladium-catalyzed, site-selective α- and γ-arylation of α,β-unsaturated ketones with (hetero)aryl halides. A wide range of hetero(aryl)halides coupled with α,β-unsaturated ketones, and transformation into the arylated products proceeded with excellent to good yields. The site selectivity of the reaction is switchable by simply changing the phosphine ligand to access either α-arylated or γ-arylated products in good to excellent yields by using a low catalyst loading, and the method demonstrates good functional-group compatibility.     

SCR performance enhancement of NiMnTi mixed oxides catalysts by regulating assembling methods of LDHs-Based precursor

A series of NiMnTi mixed metal oxides (Ni/Mn-TiO₂, Mn/NiTi-LDO and TiO₂/NiMn-LDO, NiMnTi-LDO) were synthesized via different assembling methods and evaluated in the selective catalytic reduction of NO_x with NH₃(NH₃-SCR). As the results presented, catalysts via diverse assembling methods of LDHs templates afforded different catalytic denitrification (DeNO_x) performance, which might be related to the exposure degree of active constituents and the interaction intensity between metal components. Noticeably, compared with Ni/Mn-TiO₂, Mn/NiTi-LDO and TiO₂/NiMn-LDO catalysts, the NiMnTi-LDO catalyst deriving from one step in-situ method NiMnTi-LDH precursor template exhibited the most desirable performance at temperature window of 150–360 °C in NH₃-SCR (above 90% NO_x conversion with 95% N₂ selectivity). The specific structure and property of samples were correlated by means of a series of characterizations, where the results indicated that NiMnTi-LDO possessed the highest surface area, the strongest redox ability, the most abundant acid amount and the best dispersion.     

Bi2O3/FAp,a sustainable catalyst for synthesis of dihydro-[1,2,4]triazolo[1,5-a]pyrimidine derivatives through green strategy

The bismuth loaded on fluorapatite (Bi₂O₃/FAp) proved to be an excellent catalyst for the synthesis of novel dihydro-[1,2,4]triazolo[1,5-a]pyrimidine derivatives via a three-component reaction involving the mixture of 1H-1,2,4-triazol-5-amine, ethyl cyanoacetate or ethyl acetoacetate, and different benzaldehydes in ethanol at room temperature. The catalyst material was characterized by X-ray diffraction, Brunauer–Emmett–Teller surface area analysis, Fourier-transform infrared, scanning electron microscopy, energy-dispersive X-ray spectroscopy, and transmission electron microscopy techniques. The efficacy of Bi₂O₃/FAp as a heterogeneous catalyst was evaluated with the loading of different wt% of bismuth on FAp. The 2.5% bismuth on FAp performed extremely well as a catalyst with a high yield of products (92%–96%) in a short reaction time (25–35 min). The catalyst was recovered by simple filtration. It showed undiminished activity up to five runs. Simple work-up, room temperature reaction, short reaction time, high yields, no column chromatography, and good reusability of catalyst are the merits of the proposed protocol. In addition, this process offers 100% carbon efficiency and 98% atom economy with noteworthy fiscal and environmental benefits.