  The enigmatic mechanism underlying unconventional high-temperature
superconductivity, especially the role of lattice dynamics, has remained a
subject of debate. Theoretical insights have long been hindered due to the lack
of an accurate first-principles description of the lattice dynamics of
cuprates. Recently, using the r2SCAN meta-GGA functional, we were able to
achieve accurate phonon spectra of an insulating cuprate YBa$_2$Cu$_3$O$_6$,
and discover significant magnetoelastic coupling in experimentally interesting
Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126
(2023)]. We extend this work by comparing PBE and r2SCAN performances with
corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods,
aiming at further understanding on both the materials science side and the
density functional side. We demonstrate the importance of vdW and
self-interaction corrections for accurate first-principles YBa2 Cu3 O6 lattice
dynamics. Since r2SCAN by itself partially accounts for these effects, the good
performance of r2SCAN is now more fully explained. In addition, the
performances of the Tao-Mo series of meta-GGAs, which are constructed in a
different way from SCAN/r2SCAN, are also compared and discussed.
