Performance of DFT for C₆₀ Isomerization Energies: A Noticeable Exception to Jacob's Ladder

The ability to accurately calculate relative energies of fullerenes is important in many areas of computational nanotechnology. Because of the large size of fullerenes, their relative energies cannot normally be calculated by means of high-level ab initio procedures, and therefore, density functional theory (DFT) represents a cost-effective alternative. In an extensive benchmark study, we calculate the electronic energies of eight C₆₀ isomers by means of the high-level G4(MP2) composite procedure. G4(MP2) isomerization energies span a wide range between 307.5 and 1074.0 kJ mol^-1. We use these benchmark data to assess the performance of DFT, double-hybrid DFT (DHDFT), and MP2-based ab initio methods. Surprisingly, functionals from the second and third rungs of Jacob's Ladder (i.e., GGA and meta-GGA functionals) significantly and systematically outperform hybrid and hybrid-meta-GGA functionals, which occupy higher rungs of Jacob's Ladder. In addition, DHDFT functionals do not offer a substantial improvement over meta-GGA functionals, with respect to isomerization energies. Overall, the best performing functionals with mean absolute deviations (MADs) below 15.0 kJ mol^-1 are (MADs given in parentheses) the GGA N12 (14.7); meta-GGAs M06-L (10.6), M11-L (10.8), MN15-L (11.9), and TPSS-D3BJ (12.8); and the DHDFT functionals B2T-PLYP (9.3), mPW2-PLYP (9.8), B2K-PLYP (12.1), and B2GP-PLYP (12.3 kJ mol^-1). In light of these results, we recommend the use of meta-GGA functionals for the calculation of fullerene isomerization energies. Finally, we show that inclusion of very small percentages of exact Hartree-Fock exchange (3-5%) slightly improves the performance of the GGA and meta-GGA functionals. However, their performance rapidly deteriorates with the inclusion of larger percentages of exact Hartree-Fock exchange.