Fullerenes isomer relative stability

The quantum-chemical calculations play an important role in investigation of electronic structure and stability of fullerenes. The relative positioning of the pentagons which set the surface curvature of fullerene molecule, presence of condensed hexagons, electronic effects - all of these factors define a total energy of a fullerene molecule and its stability or instability. The analysis has shown that the most stable fullerenes have minimal total energies among their isomers. Nevertheless, the reasons of why some fullerenes can be obtained and others cannot are not clear yet. 

Clearly, if any such quantitative explanation is to be found, it must take account of the fact that there can be a large number of distinct fullerene isomers for each given C . There are, for example, at least 1812 distinct fullerene isomers for Cso alone (vide infra). Icosahedral C o, which was first discovered by intuition [2], does indeed happen to be the most stable of these. However, since the majority of carbon clusters do not admit such remarkably symmetric closed-shell structures, the most stable C fullerene isomer is generally more difficult to find. Section 2 describes a practical solution to this problem, which amounts to no more than a direct computer search of all possible fullmne structures for each given C . Section 3 then ofTeit a semi-quantitative explanation for fig. 1, based on the relative kinetic stabilities of the fullerenes C34 to C70. 

Although the inter-isomeric separation energies are important, they alone cannot predict the relative stabilities of the isomers. Owing to very high temperatures, entropy contributions can even over-compensate the enthalpy terms. Hence, the enthalpy-entropy interplay represents an essential feature of fullerenes and metallofullerenes. 

The most extensive test of this idea is a study using the QCFF/PI semiempirical method to estimate the relative stabilities of all 1812 distinct fullerene isomers of As... 

Examples of specialized semiempirical methods include two MNDO variants for small carbon clusters [138] and for fullerenes [139]. Small carbon clusters (C2-C10) show many peculiar features and are difficult to handle by semiempirical or low-level ab initio calculations (e.g., with regard to the relative stabilities of isomers). A reparametrization [138] of the standard MNDO approach [19] (using experimental and high-level ab initio reference data for C3 and C4) leads to a much improved MNDO-... 

Helium ( He) (/= 1/2). The endohedral NMR chemical shifts of various known H2-H2O- and NH3-encapsulated fullerene compounds were calculated at the GIAO-B3LYP/3-21G and GIAO-HF/3-21G levels of theory with AMI- and PM3-optimised structures. The shift tendency of endohedral NMR chemical shifts were discussed and compared with that of endohedral He NMR chemical shifts.The equilibrium geometries and relative stabilities of the 19 possible isomers of C84O were studied... 

Austin, S. J., Fowler, P. W., Orlandi, G., Manolopou-los, D. E., Zerbetto, F. (1994). Relative stabilities of Cjs isomers - a numerical test of the fullerene isolated-pentagon rule. Chemical Physics Letters, 226(1-2), 219-225. 

---