Characterization of the switch in the mechanism of an intramolecular Diels-Alder reaction

Changing the dienophile moiety of an intramolecular Diels-Alder (IMDA) cycloaddition from an allyl ether to an allenyl ether can dramatically change the regioselectivity. We hereby show by density functional theory computations that such unprecedented divergence is produced by an underlying change in the mechanism of the reaction. The allyl ether yields a fused tetrahydrofuran through a classical Diels-Alder reaction, whereas the allenyl ether yields a (methylidene)tetrahydropyran through a stepwise process. The latter reaction involves an extreme asynchronism in the bond-forming events with a diradicaloid intermediate that is stabilized by conjugation and synergistic (captodative) effects. Comparison with intermolecular model D-A reactions, which are concerted processes with various degrees of asynchrony, helps explain the change in regioselectivity for the IMDA reaction of allyl systems and the shift in mechanism for the IMDA reaction of the allenyl derivatives studied.     

Coexistence in exotic scenarios of a modified Abrams–Strogatz model

We work on a model that has succeeded in describing real cases of coexistence of two languages within a closed community of speakers, taking into account bilingualism and incorporating a parameter to measure the distance between languages. The dynamics of this model depend on a characteristic exponent, which weighs the power of the size of a group of speakers to attract new members. So far, this model had been solved only when this characteristic exponent is greater than 1. In this article, we have managed to solve the nature of the stability of all the possible situations for this characteristic exponent, that is, when it is less or equal than 1 and covering also the situations produced when it is 0 or negative. We interpret these new situations and find that, even in such exotic scenarios, there are configurations of the resulting societies where all the languages coexist. © 2014 Wiley Periodicals, Inc. Complexity 21: 86–93, 2016     

Pseudopericyclic design drives antara-antara [1,5] methylene sigmatropic shifts from a stepwise to a concerted mechanism

Antara-antara [1,5]-methylene sigmatropic shifts of propenylidene cyclopropane and its heteroanalogues are shown to proceed through concerted or stepwise mechanisms depending on a delicate balance that is directly related to the presence or absence of heteroatoms at the termini atoms of the rearrangement. Lowering of activation energies upon heteroatom replacement are more significant for the oxacyclopropane analogues 1D, 1E, and 1F but double heterosubstitution is still needed to achieve a pseudopericyclic reaction. In fact only after reaching a pseudopericyclic process the energy balance favors the concerted pathway. Negligible NICS values and a clear disconnection in the ACID plot as well as some structural and energetical parameters reveal the pseudopericyclic nature of this concerted antara-antara [1,5](CH(2) ) sigmatropic shift. Although the product of the pseudopericyclic process is unprecedented, similar cycloisomerizations after allene activation should be considered within this hitherto undescribed reactions.     

Cyclization cascade of allenyl azides: a dual mechanism

A density functional theory based computational approach to describing the mechanistic course of the allene azide cycloaddition cascade sequence has been developed. The results of these calculations permit characterization of key reactive intermediates (diradicals and/or indolidenes) and explain the different behaviors observed in the experimental studies between conjugated and nonconjugated species. Furthermore, computational analysis of certain intermediates offer insight into issues of regioselectivity and stereoselectivity in cases where different reaction channels are in competition, suggesting suitable substitutions to achieve a single regioisomer in the indole synthesis via azide-allene cyclization.     

Biimidazole and bis(amide)bipyridine molybdenum carbonyl complexes as anions receptors

Compounds [Mo(CO)4(N-N)] (N-N = 4,4'-bis((4-methylphenyl)carbamoyl)-2,2'-bipyridine, bipy', 1; or 2,2'-biimidazole, H2biim, 2), [MoCl(eta3-methallyl)(CO)2(N-N)] (N-N = bipy', 3; H2biim, 4), and [Mo(eta3-methallyl)(CNtBu)(CO2)(N-N)]BAr'4 (Ar' = 3,5-bis(trifluoromethyl)phenyl; N-N= bipy', 5; H2biim, 6) were synthesized and characterized, and their behavior toward anions was investigated in solution (IR and 1H NMR) and in solid state (X-ray diffraction).     

Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

We introduce the optimality question to the relaxation in multiple control problems described by Sobolev-type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of systems with respect to the trajectory, multicontrols, and the functional in suitable topologies.     

Fixed point theorems in ordered abstract spaces

We extend some fixed point theorems in -spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

     

Normal‐to‐Abnormal NHC Rearrangement of AlIII,GaIII, and InIII Trialkyl Complexes: Scope,Mechanism, Reactivity Studies,and H2 Activation

The present contribution reports experimental and theoretical mechanistic investigations on a normal‐to‐abnormal (C2‐to‐C4‐bonded) NHC rearrangement processes occurring with bulky group 13 metal NHC adducts, including the scope of such a reactivity for Al compounds. The sterically congested adducts (nItBu)MMe₃ (nItBu=1,3‐di‐tert‐butylimidazol‐2‐ylidene; M=Al, Ga, In; 1 a – c ) readily rearrange to quantitatively afford the corresponding C4‐bonded complexes (aItBu)MMe₃ ( 4 a – c ), a reaction that may be promoted by THF. Thorough experimental data and DFT calculations were performed on the nNHC‐to‐aNHC process converting the Al‐nNHC ( 1 a ) to its aNHC analogue 4 a . A nItBu/aItBu isomerization is proposed to account for the formation of the thermodynamic product 4 a through reaction of transient aItBu with THF–AlMe₃. The reaction of benzophenone with (nItBu)AlMe₃ afforded the zwitterionic species (aItBu)(CPh₂‐O‐AlMe₃) ( 6 ), reflecting the unusual reactivity that such bulky adducts may display. Interestingly, the nItBu/Al(iBu)₃ Lewis pair behaves like a frustrated Lewis pair (FLP) since it readily reacts with H₂ under mild conditions. This may open the way to future reactivity developments involving commonly used trialkylaluminum precursors.     

A new and reliable calibration method for vibrating tube densimeters over wide ranges of temperature and pressure

A new method for accurately converting vibrating tube periods of oscillation in density values is presented. This method is based on the fundamental requirement of the non-dependence on pressure of the vibration period of the cell under vacuum. An analytical method permits to correctly evaluate the evacuated vibrating tube periods of the Anton Paar cells namely the high pressure cells, 512 and 512P, as a function of temperature. It is further shown that the previously experimental method for the determination of this parameter is not suitable for obtaining reliable density values. A new simple calibration procedure is described and tested over wide ranges of temperature, T = (283.15 to 323.15) K and pressure, P = (0.1 to 60) MPa. New recommended density values for n-alkanes (C₆, C₇, C₈, and C₁₀) and tetrachloromethane, calculated by the proposed method, are given and compared with literature values in terms of mutual uncertainties.     

On the memory of chirality in gold(I)-catalyzed intramolecular carboalkoxylation of alkynes

A computational study of the mechanism of the intramolecular carboalkoxylation of alkynes reported by Toste et al. allows the characterization of the chirality transfer process that makes this reaction enantioselective. Memory of chirality is preserved up until the stereocenter-generating iso-Nazarov cyclization through the synergy between the helicity of a pentadienyl cation intermediate and the control in the conformation of the allyl group, both elements defined upon alkoxy migration. The high barriers to conformational scrambling relative to those corresponding to chemical steps ensure the robustness of the chirality transfer mechanism and result in an unusual importance of conformational changes in reactivity that seems to be common in gold-catalyzed transformations.