Essential factors for control of the equilibrium in the reversible rearrangement of M3N@Ih-C80 fulleropyrrolidines: Exohedral functional groups versus endohedral metal clusters

The effects of exohedral moieties and endohedral metal clusters on the isomerization of M3N@Ih-C80 products from the Prato reaction through [1,5]-sigmatropic rearrangement were systematically investigated by using three types of fulleropyrrolidine derivatives and four different endohedral metal clusters. As a result, all types of derivatives provided the same ratios of the isomers for a given trimetallic nitride template (TNT) as the thermodynamic products, thus indicating that the size of the endohedral metal clusters inside C80 was the single essential factor in determining the equilibrium between the [6,6]-isomer (kinetic product) and the [5,6]-isomer. In all the derivatives, the [6,6]- and [5,6]-Prato adducts with larger metal clusters, such as Y3N and Gd3N, were equally stable, which is in good agreement with DFT calculations. The reaction rate of the rearrangement was dependent on both the substituent of exohedral functional groups and the endohedral metal-cluster size. Further DFT calculations and 13C NMR spectroscopic studies were employed to rationalize the equilibrium in the rearrangement between the [6,6]- and [5,6]-fulleropyrrolidines

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant mass absorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analytically solved by a discrete ordinate method. The general solution is analyzed for a water vapor saturated atmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stable equilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing from previous radiative–convective models, we find that the amount of carbon dioxide strongly modifies the value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption of radiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect of carbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runaway greenhouse state than thin carbon dioxide ones