Frequency and zero-point vibrational energy scale factors for double-hybrid density functionals (and other selected methods): Can anharmonic force fields be avoided?

We have obtained uniform frequency scaling factors λ_harm (for harmonic frequencies), λ_fund (for fundamentals), and λ_ZPVE (for zero-point vibrational energies (ZPVEs)) for the Weigend-Ahlrichs and other selected basis sets for MP2, SCS-MP2, and a variety of DFT functionals including double hybrids. For selected levels of theory, we have also obtained scaling factors for true anharmonic fundamentals and ZPVEs obtained from quartic force fields. For harmonic frequencies, the double hybrids B2PLYP, B2GP-PLYP, and DSD-PBEP86 clearly yield the best performance at RMSD = 10-12 cm^-1 for def2-TZVP and larger basis sets, compared to 5 cm^-1 at the CCSD(T) basis set limit. For ZPVEs, again, the double hybrids are the best performers, reaching root-mean-square deviations (RMSDs) as low as 0.05 kcal/mol, but even mainstream functionals like B3LYP can get down to 0.10 kcal/mol. Explicitly anharmonic ZPVEs only are marginally more accurate. For fundamentals, however, simple uniform scaling is clearly inadequate.