  Double-hybrid density functional theory (DHDFT) offers a pathway to
accuracies approaching composite wavefunction approaches like G4 theory.
However, the GLPT2 (G{\"o}rling 2nd order perturbation theory) term causes them
to partially inherit the slow $\propto L^{-3}$ (with $L$ the maximum angular
momentum) basis set convergence of correlated wavefunction methods. This could
potentially be remedied by introducing F12 explicit correlation: we investigate
the basis set convergence of both DHDFT and DHDFT-F12 for the large and
chemically diverse GMTKN55 (general main-group thermochemistry, kinetics, and
noncovalent interactions) benchmark suite. The B2GP-PLYP-D3(BJ) and
revDSD-PBEP86-D4 double hybrid density functionals (DHDFs) are investigated as
test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12
basis sets as large as cc-pV(Q+d)Z-F12. We show that F12 greatly accelerates
basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12
basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPP in
orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z.
Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic
subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set
convergence in both the development and application of double-hybrid
functionals. Mass storage and I/O bottlenecks for larger systems can be
circumvented by localized pair natural orbital approximations, which also
exhibit much gentler system size scaling.
