Computing enthalpy–entropy interplay for isomeric fullerenes

Abstract

ABSTRACT:Fullerenes represent unique species in many respects, one of them being one of the highest temperature regions ever used for preparation of chemical species. This very factor automatically substantially enhances the importance of the TS part of the Gibbs function. The essential feature of fullerenic systems has consistently been ignored in computational studies of fullerenes, almost always drawing their conclusions from potential energies or heats of formation. This report demonstrates that the simplified treatment cannot really describe all the features of complex mixtures of isomeric fullerenes. General formulas are surveyed and illustrated on C 96 -the biggest set of isomeric fullerenes characterized by 13 C NMR spectra to date. Computations are carried out for the complete set of 187 isolated-pentagon-rule (IPR) isomers of C 96 , using four semiempirical quantum chemical methods (MNDO, AM1, PM3, and SAM1). Entropy terms are also computed and the relative-stability problem is entirely treated in terms of the Gibbs function. In overall, the computed data match the observed data reasonably well, although no method can really reproduce the complete ten-membered observed set. There are however still several aspects to be checked and several possibilities how to improve quality of the computed terms. In principle, such developments are, however, only a question of available computing power. There are, nevertheless, some remaining questions, such as inclusion of anharmonicity effects, contribution from electronic partition function, or even interactions between individual, yet separated motions. This article also discusses a subsequent, more general task of relative stabilities of carbon cages of different dimensions, i.e., relative stabilities of nonisomeric fullerenes. The computational treatment of isomeric mixtures has several interesting features: the results depend on temperature, but not on pressure; only the relative, and not the absolute, values of the heats of formation are needed; and the form of the master equation allows for an ample cancellation of terms in the partition functions. In contrast, for the more general task-relative stabilities of fullerenes of different dimensions-the absolute values of the heats of formation are required, the mentioned cancellations do not operate there, and the scheme is essentially pressure dependent.

Computed Relative Populations of D2(22)‐C84 Endohedrals with Encapsulated Monomeric and Dimeric Water

“…He selected cage hydrocarbons (he called polyhedrans) based on Platonic or Archimedean polyhedra, including C 60 H 60 (fully hydrogenated fullerene C 60 ). His 50‐year‐old predictions, based only on very simple molecular mechanics, agree reasonably well with advanced present‐day calculations . They both point out the well‐known synthetic hydrocarbon dodecahedrane C 20 H 20 as the most stable cage hydrocarbon and C 60 H 60 as the third‐most stable (which comes before another synthetic polyhedrane, cubane C 8 H 8 ).…”

Isomers of C36 and free energy criteria for cluster growth

“…Using the same formula as that used by Slanina et al, 30 we calculated the relative concentration of the isomers without considering all the quantum effects to understand the classical results ͑Fig. 9͒, showing that the number of the D 6h cages should be about only 3% of the D 2d cages and formation of the other isomers would be ignored at all in the temperature range of about 2300 K ͑Fig.…”

Isolation of Four Isomers of C96 and Crystallographic Characterization of Nanotubular D3d(3)‐C96 and the Somewhat Flat‐Sided Sphere C2(181)‐C96

“…[16,17] Experimentally, Kikuchi, Achiba and co-workers briefly reported that they had isolated ten isomers of C 96 and identified their symmetries through 13 C NMR spectroscopy as C 1 (4 isomers), C 2 (3 isomers), C s (l isomer), D 2 (1 isomer), and D 3d (l isomer). [18] Kemnitz and Troyanov reacted C 2 F 5 I with a mixture of higher fullerenes and were able to obtain crystals of the adduct C 96 A C H T U N G T R E N N U N G (C 2 F 5 ) 12 , which were shown by singlecrystal X-ray diffraction to utilize the C 1 A C H T U N G T R E N N U N G (145)-C 96 cage.…”