All calculations are stable broken-symmetry
solutions close to the complete basis set limit, and have been performed
using quadruple‑ζ quality basis sets using Q-Chem 5.1 \cite{shao_advances_2015}. Results for the three statistical criteria, AIC,
VCC, and CVC, are reported in Table \ref{182001}, as well as the ranking of each
functional according to each specific criterion (in parenthesis). The
average ranking of each functional across the three criteria is also
reported in the last column of Table \ref{182001}, and is used as the final
indicator for performance of a functional. It is clear that the rankings
obtained using the statistical criteria align well with the Jacob’s
ladder picture of functional approximations. According to all three
criteria, for example, the three best functionals are double-hybrid
“fifth rung” approximations. “Fourth rung” hybrid meta-GGA/NGA are
the second-best class, followed by “fourth rung” hybrid GGA/NGA and
“third rung” local meta-GGA, with similar average performance. “First
and second rung” Local GGA/NGA are on average at the bottom of the
rankings. Interestingly enough, modern non-fitted functionals such as
PBE and SCAN-D3(BJ) sits in the middle of the ranking, together with
most of the parametrized Minnesota functionals. Even more interesting than the general trends are some of the outliers.
For example, the B3LYP‑D3(BJ) ranks near the top according to all three
criteria, while its parent functional B3LYP is consistently ranked at
the bottom, more than 23 positions below B3LYP-D3(BJ), confirming the
trends observed in the literature. However, PBE-D3(BJ) is slightly more
transferable (despite a slightly higher wMUE) than B3LYP-D3(BJ),
confirming recent finding of transferability issues in the popular
B3LYP-D3(BJ) functional.