Reactivity of Endohedral Metallofullerene La₂@C₈₀ in Nucleophilic and Electrophilic Attacks: Vibronic Coupling Density Approach

The regioselectivities of La2@C80 in thermal nucleophilic and electrophilic attacks were theoretically investigated using vibronic coupling density (VCD) analysis. Nucleophilic and electrophilic cycloadditions to La2@C80 were experimentally reported to yield [6,6] and [6,5] adducts, respectively, as major products. VCD analysis provided a clear explanation for these experimental results. For nucleophilic reactions, it was found that the reactive [6,6] bonds did not have a large lowest unoccupied molecular orbital (LUMO) density and Fukui function but a large potential derivative with respect to a reaction mode. The VCD illustrates the origin of the interaction between the electronic and vibrational states. On the other hand, conventional reactivity indices such as frontier orbital density take only the electronic state into account. The result suggested that the stabilization due to vibronic couplings plays an important role in the regioselectivity of nucleophilic cycloadditions. The VCD with respect to the effective mode could provide a picture of the functional groups, which are the double bonds of ethylene moieties. VCD analysis with respect to hypothetical localized modes enabled the quantitative prediction of regioselectivities

Jahn–Teller Instability of Icosahedral [W@Au₁₂]⁻

The anionic state of the icosahedral W@Au₁₂ cluster offers a rare example of a Jahn–Teller (JT) instability in an icosahedral fourfold degenerate Γ₈ spinor level. The JT energy splittings of the ground Γ₈ and excited sixfold degenerate Γ₉ splittings in the vicinity of the degeneracy point are calculated with relativistic density functional theory. The results are very well explained by a first-order coupling model, based on the orbital instability of the spherical <i>d</i>-shell of the cluster. In addition the pentagonal JT minimum has been determined. It presents a remarkable example of an auro-sandwich type compound

Chemical Reactivity in Nucleophilic Cycloaddition to C₇₀: Vibronic Coupling Density and Vibronic Coupling Constants as Reactivity Indices

The chemical reactivity in nucleophilic cycloaddition to C₇₀ is investigated on the basis of vibronic (electron-vibration) coupling density and vibronic coupling constants. Because the <i>e</i>₁^″ LUMOs of C₇₀ are doubly degenerate and delocalized throughout the molecule, it is difficult to predict the regioselectivity by frontier orbital theory. It is found that vibronic coupling density analysis for the effective mode as a reaction mode illustrates the idea of a functional group embedded in the reactive sites. Furthermore, the vibronic coupling constants for localized stretching vibrational modes enable us to estimate the quantitative reactivity. These calculated results agree well with the experimental findings. The principle of chemical reactivity proposed by Parr and Yang is modified as follows: the preferred direction is the one for which the initial vibronic coupling density for a reaction mode of the isolated reactant is a minimum

Diseases excluded from the analysis.

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Data for primary and sensitivity analysis.

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Origin of Stereoselectivity in a Mechanochemical Reaction of Diphenylfulvene and Maleimide

Mechanochemical reactions sometimes yield unexpected products or product ratios in comparison to conventional reaction conditions. In the present study, we theoretically reveal the origin of the mechanochemical selectivity by considering the Diels–Alder reaction of diphenylfulvene and maleimide as an example. The application of an external force is equivalent to the production of a structural deformation. Here, we show that a mechanical force applied in a direction orthogonal to the reaction mode can lower the activation barrier by varying the potential energy curvature in the transition state. In the case of the Diels–Alder reaction, the endo-type pathway was found to be more mechanochemically favorable than the exo-type pathway, which is consistent with the experimental observations

Sensitivity analyses of breakthrough exacerbations.

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Study design.

ICS, inhaled corticosteroid; LABA, long-acting β2-agonist. * Medical history and complications, respiratory function-related tests, asthma treatment management fee, and history of asthma exacerbations. † Asthma treatments (ICS, leukotriene receptor antagonist, slow-release theophylline, disodium cromoglycate, long-acting muscarinic antagonist, LABA, oral corticosteroid, and biologic agents). ‡ Censoring by re-switching to another ICS/LABA, adding an ICS, or switching to an ICS.</p

Flow of eligible patients.

ICS, inhaled corticosteroid; LABA, long-acting β2-agonist.</p

ICS/LABA before and after switch.

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