Can density functional theory 'Cope' with highly fluxional shapeshifting molecules?

Shape-shifting molecules such as bullvalene undergo rapid structural reorganizations via degenerate Cope rearrangements. Here, we obtain accurate CCSD(T)/CBS barrier heights and reaction energies for a wide range of Cope rearrangements in substituted bullvalenes (C₁₀H₉R, R = NH₃, OH, CH₃, H, F, Cl, SH, and CN). We use this benchmark dataset to evaluate the performance of DFT and ab initio methods for the kinetics and thermodynamics of these reactions. The reaction barrier heights pose a significant challenge for DFT methods - the best methods attain root-mean-square deviations of 4.9 (BMK), 4.5 (PBE0), 4.2 (PW6B95), and 3.8 (B1B95) kJ mol⁻¹. Overall, only three DFT functionals (BMK, PW6B95, and MN12-SX) are able to surpass (or attain near) chemical accuracy for both barrier heights and reaction energies. In contrast, the double-hybrid DFT procedures ωB97X-2(LP), ωB97X-2(TQZ), PWPB95-D3, PBEQI-DH, and DSD-PBEB95-D3 give good-to-excellent performance.