  Most torsional barriers are predicted to high accuracy (about 1kJ/mol) by
standard semilocal functionals, but a small subset has been found to have much
larger errors. We create a database of almost 300 carbon-carbon torsional
barriers, including 12 poorly behaved barriers, all stemming from Y=C-X group,
where X is O or S, and Y is a halide. Functionals with enhanced exchange mixing
(about 50%) work well for all barriers. We find that poor actors have
delocalization errors caused by hyperconjugation. These problematic
calculations are density sensitive (i.e., DFT predictions change noticeably
with the density), and using HF densities (HF-DFT) fixes these issues. For
example, conventional B3LYP performs as accurately as exchange-enhanced
functionals if the HF density is used. For long-chain conjugated molecules,
HF-DFT can be much better than exchange-enhanced functionals. We suggest that
HF-PBE0 has the best overall performance.
