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.

We present a family of minimally empirical double-hybrid DFT functionals parametrized against the very large and diverse GMTKN55 benchmark. The very recently proposed ωB97M(2) empirical double hybrid (with 16 empirical parameters) has the lowest WTMAD2 (weighted mean absolute deviation over GMTKN55) ever reported at 2.19 kcal/mol. However, refits of the DSD-BLYP and DSD-PBEP86 spin-component-scaled, dispersion-corrected double hybrids can achieve WTMAD2 values as low as 2.37 with the very recent D4 dispersion correction, (2.55 kcal/mol with the D3BJ dispersion term) using just a handful of adjustable parameters. If we use full DFT correlation in the initial orbital evaluation, the xrevDSD-PBEP86-D4 functional reaches WTMAD2=2.23 kcal/mol, statistically indistinguishable from ωB97M(2) but using just four non-arbitrary adjustable parameters (and three semi-arbitrary ones). The changes from the original DSD parametrizations are primarily due to reaction and isomerization energies for large systems, which were undersampled in the original parametrization set. With the new parametrization, same-spin correlation can be eliminated at minimal cost in performance, which permits revDOD-PBEP86-D4 and revDOD-PBE-D4 functionals that scale as N4 or even N3 with the size of the system. Dependence of WTMAD2 for DSD functionals on the percentage of HF exchange is roughly quadratic; it is sufficiently weak that any reasonable value in the 64% to 72% range can be chosen semi-arbitrarily. DSD-SCAN and DOD-SCAN double hybrids involving the SCAN non-empirical meta-GGA as the semi-local component have also been considered, and offer a good alternative if one wishes to eliminate either the empirical dispersion correction or the same-spin correlation component. noDispSD-SCAN66 achieves WTMAD2=3.00 kcal/mol, while DOD-SCAN66-D4 reaches 2.61 kcal/mol. Finally, in the context of double-hybrid functionals, the very recent D4 dispersion correction is clearly superior over D3BJ.

The S66x8 dataset for noncovalent interactions of biochemical relevance has been re-examined by means of MP2-F12 and CCSD(F12*)(T) methods. We deem our revised benchmark data to be reliable to about 0.05 kcal mol⁻¹ RMS. Most levels of DFT perform quite poorly in the absence of dispersion corrections: somewhat surprisingly, that is even the case for the double hybrids and for dRPA75. Analysis of optimized D3BJ parameters reveals that the main benefit of dRPA75 and DSD double hybrids alike is the treatment of midrange dispersion. dRPA75-D3BJ is the best performer overall at RMSD = 0.10 kcal mol⁻¹. The nonlocal VV10 dispersion functional is especially beneficial for the double hybrids, particularly in DSD-PBEP86-NL (RMSD = 0.12 kcal mol⁻¹). Other recommended dispersion-corrected functionals with favorable price/performance ratios are ωB97X-V, and, surprisingly, B3LYP-D3BJ and BLYP-D3BJ (RMSDs of 0.23, 0.20 and 0.23 kcal mol⁻¹, respectively). Without dispersion correction (but parametrized for midrange interactions) M06-2X has the lead (RMSD = 0.45 kcal mol⁻¹). A collection of three energy-based diagnostics yields similar information to an SAPT analysis about the nature of the noncovalent interaction. Two of those are the percentages of Hartree–Fock and of post-MP2 correlation effects in the interaction energy; the third, CSPI = [IE⁽²⁾ _ss − IE⁽²⁾ _ab]/[IE⁽²⁾ _ss + IE⁽²⁾ _ab] or its derived quantity DEBC = CSPI/(1 + CSPI²)^1/2, describes the character of the MP2 correlation contribution, ranging from 0 (purely dispersion) to 1 (purely other effects). In addition, we propose an improved, parameter-free scaling for the (T) contribution based on the E_corr[CCSD-F12b]/E_corr[CCSD] and E_corr[CCSD(F12*)]/E_corr[CCSD] ratios. For Hartree–Fock and conventional DFT calculations, full counterpoise generally yields the fastest basis set convergence, while for double hybrids, half-counterpoise yields faster convergence, as previously established for correlated ab initio methods.