  The reliability of popular density functionals was studied for the
description of torsional profiles of 36 molecules: glyoxal, oxalyl halides and
their thiocarbonyl derivatives. HF and \textcolor{black}{eighteen} functionals
of varying complexity, from local density to range-separated hybrid
approximations and double-hybrid, have been considered and benchmarked against
CCSD(T)-level rotational profiles. For molecules containing heavy halogens, all
functionals except M05-2X and M06-2X fail to reproduce barrier heights
accurately and a number of functionals introduce spurious minima. Dispersion
corrections show no improvement. Calibrated torsion-corrected atom-centered
potentials rectify the shortcomings of PBE and also improve on $\sigma$-hole
based intermolecular binding in dimers and crystals.
