Comments on The Co-emergence of Machine Techniques, Paper-and-Pencil Techniques, and Theoretical Reflection

We comment on the paper The co-emergence of machine techniques, paper-and-pencil techniques, and theoretical reflection: A study of CAS use in secondary school algebra by Carolyn Kieran and Paul Drijvers. We look at aspects of Kieran and Drijvers' analysis with regard to ‚task-technique-theory’ in the light of a model of abstraction in context and suggest that this re-viewing brings mutual analytic benefits.     

Redox induced reactions of transition metal π- and σ,π-complexes

In this review, redox-induced reactions of π- and σ,π-complexes leading to the selective formation (or cleavage) of C–H, C–C, and C–O bonds have been summarized. To illustrate the synthetic potential of such methodology, the following representative reactions studied in our group are discussed: (1) oxidatively induced hydrogen elimination from “open” cyclic diene and dienyl complexes resulting in formation of “closed” dienyl and arene complexes, respectively; (2) reductive activation of C–H bonds in diene, vinylidene, and carbyne complexes forming new multiple C–C bonds; (3) oxidative dehydrodimerization of vinylidene complexes into binuclear μ-divinylidene species; and (4) oxidatively induced addition of oxygen nucleophiles to μ-divinylidene complexes affording cyclic μ-dicarbene derivatives. Oleg V. Gusev, deceased on October 31.     

A framework to categorize students as learners based on their cognitive practices while learning differential equations and related concepts

There are numerous theories that offer cognitive processes of students of mathematics, all documenting various ways to describe knowledge acquisition leading to successful transitions from one stage to another, be it characterized by Dubinsky's encapsulation, Sfard's reification or Piaget's equilibration. We however are interested in the following question. Who succeeds at making the leap and can we describe the attributes that set them apart from the ones that do not? In this article, we offer a framework to categorize students as learners based on their individual approaches towards learning concepts in differential equations and related concepts – as demonstrated by their efforts to resolve a conflict, conserve and rebuild their cognitive structures.     

Hydridoorganostannylene Coordination: Group 4 Metallocene Dichloride Reduction in Reaction with Organodihydridostannate Anions

Organodihydridoelement anions of germanium and tin were reacted with metallocene dichlorides of Group 4 metals Ti, Zr and Hf. The germate anion [Ar*GeH₂]⁻ reacts with hafnocene dichloride under formation of the substitution product [Cp₂Hf(GeH₂Ar*)₂]. Reaction of the organodihydridostannate with metallocene dichlorides affords the reduction products [Cp₂M(SnHAr*)₂] (M=Ti, Zr, Hf). Abstraction of a hydride substituent from the titanium bis(hydridoorganostannylene) complex results in formation of cation [Cp₂M(SnAr*)(SnHAr*)]⁺ exhibiting a short Ti–Sn interaction. (Ar*=2,6-Trip₂C₆H₃, Trip=2,4,6-triisopropylphenyl).     

Gas-Phase Synthesis of Triphenylene (C18H12)

For the last decades, the hydrogen-abstraction−acetylene-addition (HACA) mechanism has been widely invoked to rationalize the high-temperature synthesis of PAHs as detected in carbonaceous meteorites (CM) and proposed to exist in the interstellar medium (ISM). By unravelling the chemistry of the 9-phenanthrenyl radical ([C₁₄H₉]^.) with vinylacetylene (C₄H₄), we present the first compelling evidence of a barrier-less pathway leading to a prototype tetracyclic PAH – triphenylene (C₁₈H₁₂) – via an unconventional hydrogen abstraction–vinylacetylene addition (HAVA) mechanism operational at temperatures as low as 10 K. The barrier-less, exoergic nature of the reaction reveals HAVA as a versatile reaction mechanism that may drive molecular mass growth processes to PAHs and even two-dimensional, graphene-type nanostructures in cold environments in deep space thus leading to a better understanding of the carbon chemistry in our universe through the untangling of elementary reactions on the most fundamental level.     

Diborylated Magnesium Anthracene as Precursor for B2H5−‐Bridged 9,10‐Dihydroanthracene

9,10‐(Bpin)₂‐anthracene ( 3 , HBpin=pinacolborane) was synthesized from 9,10‐dibromoanthracene in a stepwise lithiation/borylation sequence. The reaction of 3 with highly activated magnesium furnished the diborylated magnesium anthracene 4 , which was quenched in situ with ethereal HCl to yield cis‐9,10‐(Bpin)₂‐DHA (cis‐ 5 , DHA=9,10‐dihydroanthracene). Compound cis‐ 5 , in turn, can be reduced with Li[AlH₄] in THF to give its diborate Li₂[cis‐9,10‐(BH₃)₂‐DHA] (Li₂[cis‐ 6 ]). In the crystal lattice, the THF solvate Li₂[cis‐ 6 ] ? 3 THF establishes a dimeric structure with Li‐(μ‐H)‐B coordination modes. Hydride abstraction from Li₂[cis‐ 6 ] with Me₃SiCl yields the B?H?B‐bridged DHA Li[ 7 ]. This product can also be viewed as a unique cyclic B₂H₇^? derivative with a hydrocarbon backbone. Treatment of Li₂[cis‐ 6 ] with the stronger hydride abstracting agent Me₃SiOTf (HOTf=trifluoromethanesulfonic acid) in THF affords the THF diadduct of cis‐9,10‐(BH(OTf))₂‐DHA.     

Magnetic field as a means to identify initiating reaction in oxidation of organic substances with molecular oxygen

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When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra‐atomic and inter‐atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra‐atomic and inter‐atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange‐correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange‐correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.     

Reaction of CO2 with a Vanadium(II) Aryl Oxide: Synergistic Activation of CO2/Oxo Groups towards H‐Atom Radical Abstraction

Treatment of divalent (ONNO)V(TMEDA) ( 1 ; ONNO=[2,4‐Me₂‐2‐(OH)C₆H₂CH₂]₂N(CH₂)₂NMe₂) with CO₂ afforded [(ONNO)V]₂(μ‐OH)(μ‐formate) ( 2 ). Whereas the bridging hydroxo and formate groups both originated from CO₂, the H atoms present on the two residues were obtained through H‐atom radical abstraction from the solvent. DFT calculations revealed an initially linear CO₂ bonding mode, followed by deoxygenation, and highlighted a synergistic effect between the so‐formed oxo group and an additional bridging CO₂ residue in promoting radical behavior.     

A DFT‐Based Investigation of Hydrogen Abstraction Reactions from Methylated Polycyclic Aromatic Hydrocarbons

The growth of polycyclic aromatic hydrocarbons (PAHs) is in many areas of combustion and pyrolysis of hydrocarbons an inconvenient side effect that warrants an extensive investigation of the underlying reaction mechanism, which is known to be a cascade of radical reactions. Herein, the focus lies on one of the key reaction classes within the coke formation process: hydrogen abstraction reactions induced by a methyl radical from methylated benzenoid species. It has been shown previously that hydrogen abstractions determine the global PAH formation rate. In particular, the influence of the polyaromatic environment on the thermodynamic and kinetic properties is the subject of a thorough exploration. Reaction enthalpies at 298 K, reaction barriers at 0 K, rate constants, and kinetic parameters (within the temperature interval 700–1100 K) are calculated by using B3LYP/6‐31+G(d,p) geometries and BMK/6‐311+G(3df,2p) single‐point energies. This level of theory has been validated with available experimental data for the abstraction at toluene. The enhanced stability of the product benzylic radicals and its influence on the reaction enthalpies is highlighted. Corrections for tunneling effects and hindered (or free) rotations of the methyl group are taken into account. The largest spreading in thermochemical and kinetic data is observed in the series of linear acenes, and a normal reactivity–enthalpy relationship is obtained. The abstraction of a methyl hydrogen atom at one of the center rings of large methylated acenes is largely preferred. Geometrical and electronic aspects lie at the basis of this striking feature. Comparison with hydrogen abstractions leading to arylic radicals is also made.