MP2-F12 basis set convergence near the complete basis set limit: are $h$ functions sufficient?

We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean square (RMS) contribution of i functions to the total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol for \ce{P2} and \ce{P4}. However, even for these cases, basis set extrapolation from \{g,h\} basis sets adequately addresses the problem. Using basis sets insufficiently saturated in the $spdfgh$ angular momenta may lead to exaggerated $i$ function contributions. For extrapolation from $spdfg$ and $spdfgh$ basis sets, basis set convergence appears to be quite close to the theoretical asymptotic $\propto L^{-7}$ behavior. We hence conclude that $h$ functions are sufficient even for highly demanding F12 applications. With one-parameter extrapolation, $spdf$ and $spdfg$ basis sets are adequate, with aug-cc-pV\{T,Q\}Z-F12 yielding RMSD=0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b suggests our conclusions are applicable to higher-level F12 methods as well.
Comment: Final version: Open Access ACS AuthorChoice CC:BY 4.0