Solution of large-scale plasmonic problems with the multilevel fast multipole algorithm

A surface integral equation together with the multilevel fast multipole algorithm is successfully applied to fast and accurate resolution of plasmonic problems involving a large number of unknowns. The absorption, scattering, and extinction efficiencies of several plasmonic gold spheres of increasing size are efficiently obtained solving the electric and magnetic current combined-field integral equation. The numerical predictions are compared with reference analytic results to demonstrate the accuracy, suitability, and capabilities of this approach when dealing with large-scale plasmonic problems.     

Do Carbon Nano-onions Behave as Nanoscopic Faraday Cages? A Comparison of the Reactivity of C60, C240, C60@C240, Li+@C60, Li+@C240, and Li+@C60@C240

From the analysis of the polarizability of carbon nano-onions (CNOs), it was concluded that CNOs behave as near perfect nanoscopic Faraday cages. If CNOs behave as ideal Faraday cages, the reactivity of the C₂₄₀ cage should be the same in Li⁺@C₂₄₀ and Li⁺@C₆₀@C₂₄₀. In this work, the Diels–Alder reaction of cyclopentadiene to the free C₂₄₀ cage and the C₆₀@C₂₄₀ CNO together with their Li⁺-doped counterparts were analyzed using DFT. It was found that in all cases the preferred cycloaddition is on bond [6,6] of type B of C₂₄₀. Encapsulation of Li⁺ results in lower enthalpy barriers due to the decrease of the energy of the LUMO orbital of the C₂₄₀ cage. When the Li⁺ is placed inside the CNO C₆₀@C₂₄₀, the decrease in enthalpy barrier is similar to that of Li⁺@C₂₄₀. However, the location of Li⁺ in Li⁺@C₂₄₀ (off-centered) and Li⁺@C₆₀@C₂₄₀ (centered) is quite different. When Li⁺ was placed in the center of the C₂₄₀ cage in Li⁺@C₂₄₀, the barriers increased significantly. Taking into account this effect, the barriers in Li⁺@C₂₄₀ and Li⁺@C₆₀@C₂₄₀ differ by about 4 kcal mol⁻¹. This result can be attributed to the shielding effect of C₆₀ in Li⁺@C₆₀@C₂₄₀. As a result, we conclude that this CNO does not act as a perfect Faraday cage.     

Chemical Reactions of Cationic Metallofullerenes: An Alternative Route for Exohedral Functionalization

The chemistry of cationic forms of clusterfullerenes remain less explored than that of the corresponding neutral or anionic species. In the present work, M₃N@I_h-C₈₀ (M=Sc or Lu) cations were generated by both electrochemical and chemical oxidation methods. The as-obtained cations successfully underwent the typical Bingel–Hirsch reaction that fails with neutral Sc₃N@I_h-C₈₀. Two isomeric Sc₃N@I_h-C₈₀ cation derivatives, [5,6]-open and [6,6]-open adducts, were synthesized, and the former has never been prepared by means of a Bingel–Hirsch reaction with neutral clusterfullerenes. In the case of the Lu₃N@I_h-C₈₀ cation, however, only a [6,6]-open adduct was obtained. Density functional theory (DFT) calculations indicated that the oxidized M₃N@I_h-C₈₀ was much more reactive than the neutral compound upon addition of the diethyl bromomalonate anion. The Bingel–Hirsch reaction of M₃N@I_h-C₈₀ cations occurred by means of an unusual outer-sphere single-electron transfer (SET) process from the diethyl bromomalonate anion to the stable intermediate [M₃N@C₈₀(C₂H₅COO)₂CBr]^.. Remarkably, the diethyl bromomalonate anion was found to act as both a nucleophile and an electron donor.     

Palladium- and Ruthenium-Catalyzed Intramolecular Carbene CAr−H Functionalization of γ-Amino-α-diazoesters for the Synthesis of Tetrahydroquinolines

A synthetic method to prepare tetrahydroquinoline-4-carboxylic acid esters has been developed through the transition-metal-catalyzed intramolecular aromatic C−H functionalization of α-diazoesters. Both [{Pd(IMes)(NQ)}₂] (IMes=1,3-dimesitylimidazol-2-ylidene, NQ=1,4-naphthoquinone) and the first-generation Grubbs catalyst proved effective for this purpose. The ruthenium catalyst was found to be the most versatile, although in a few cases the palladium complex afforded better yields or selectivities. According to DFT calculations, Pd⁰- and Ru^II-catalyzed sp²-C_Ar−H functionalization proceeds through different reaction mechanisms. Thus, the Pd⁰-catalyzed reaction involves a Pd-mediated 1,6-H migration from the sp²-C_Ar−H bond to the carbene carbon atom, followed by a reductive elimination process. In contrast, electrophilic addition of the ruthenacarbene intermediate to the aromatic ring and subsequent 1,2-proton migration are operative in the Grubbs catalyst promoted reaction.