Mg@C72 MNDO/d evaluation of the isomeric composition.

Temperature development of the relative stabilities of isomers of Mg@C72 (which has not yet been isolated) is computed using the recently introduced MNDO/d method. Four isomers originally considered for the Ca@C72 case are treated: one isolated-pentagon-rule (IPR) structure, two structures with a pair of adjacent pentagons, and one cage with a heptagon. The IPR structure comes as the lowest in MNDO/d potential energy, being rather closely followed by the two structures with a pentagon-pentagon pair. On the other hand, the structure with a heptagon is located too high in potential energy to be of any experimental significance. The entropy contributions are evaluated by the MNDO/d-based partition functions so that the relative concentrations can be treated accordingly. The computations suggest that if Mg@C72 is isolated, it should be a mixture of either two or three isomers. The prediction depends on temperature prehistory. If preparation takes place at temperatures of approximately 1000 K, two isomers should be produced. If temperatures are increased to approximately 2000 K, there will already be three isomers with significant relative concentrations. The study supplies a further interesting example of the profound role of enthalpy-entropy interplay in stabilities of isomeric fullerenic structures.

Computing the relative gas-phase populations of C60 and C70: beyond the traditional delta H(fo),298 scale.

Computations and experiments have shown that the relative heat of formation (i.e., the heat of formation per carbon atom) of C70 is lower than of C60. Moreover, various computations suggest that this is actually a general trend among fullerene cages. The relationship is particularly important for gas-phase fullerenes. Experiments have shown that C60 is typically more populated than C70 when produced in high-temperature gas-phase synthesis. It is not immediately obvious how to reconcile those two terms, or whether the relative heats of formation and the relative populations are in conflict or in agreement. This article deals with this problem, treating it as a general task of relative stabilities of gas-phase clusters of different dimensions (i.e., nonisomeric clusters) under different types of thermodynamic equilibria. The results are then applied to C60 and C70 and point out that the conventional standard pressure of 1 atm is considerably different from actual fullerene-synthesis conditions. Apparently, we should expect considerably lower cluster pressures in carbon-arc synthesis. At 1 atm, C70 is more populated than C60, but at the conditions of a saturated carbon vapor the stability order is reversed in favor of C60 so that an agreement with experiment is obtained already within the thermodynamic treatment. The pressure effects are modeled using the MNDO, AM1, PM3, and SAM1 quantum-chemical semi-empirical methods as well as the available experimental data. The computations consistently show that, if the pressure effects are considered, C60 becomes more populated than C70. Relationships of the thermodynamic treatment to more sophisticated but impractical kinetic analysis are also discussed.