Comprehensive theoretical study of all 1812 C60 isomersElectronic supplementary information (ESI) available: Cartesian coordinates in Ångström at the PBE-D3/def2-TZVP level and relative energies at the PW6B95-D3ATM/def2-QZVP level are provided for all 1812 C60 isomers. Contributions to the DLPNO-CCSD(T)/CBS energies for the C60ISO benchmark set are given. Further, details of the statistical analysis for all stability criteria are tabulated and correlation plots are shown. See DOI: 10.1039/c7cp00

We investigate all 1812 isomers of the fullerene C 60 consistently with high-accuracy quantum chemistry methods. The isomers are optimized at the PBE-D3/def2-TZVP level of theory and their relative energies are obtained at the affordable and accurate hybrid-DFT level PW6B95-D3 ATM /def2-QZVP. For the first time reliable values for the relative energy distribution among the 1812 isomers (maximum value of 549.1 kcal mol −1 , average value of 189.8 ± 46.8 kcal mol −1 , 1267 isomers in an energy window of 150-250 kcal mol −1 ) are given. The quality of the DFT energies is verified by comparison with highly accurate DLPNO-CCSD(T)/CBS* results for ten selected C 60 isomers, and the DFT results are further used to benchmark several semiempirical methods. Our findings yield methodological insight into future multi-level modelling of larger carbon nano-structures. We correlate the best relative energies of the isomers to a number of topological indices, electronic properties, and geometrical measures in order to rationalize the isomeric stability aside from the common isolated pentagon rule minimizing the number of pentagon fusions. The information from the best qualitative measures can be condensed to the statement, that a small pentagon signature P 1 , a large volume, and a more spherical cage lead to a relatively stable isomer. In addition, the best semiempirical method was applied to all 31 924 isomers of C 80 . All 1812 C 60 isomers are investigated with high-level quantum chemical methods to benchmark semiempirical approaches and find appropriate stability criteria.