Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The
large and chemically diverse GMTKN55 benchmark was used as
a training set for parametrizing composite wave function thermochemistry
protocols akin to G4­(MP2)­XK theory (Chan, B.; Karton, A.; Raghavachari,
K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability
for elements H through Rn, Karlsruhe def2 basis sets were employed.
Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute
deviation, type 2) for G4­(MP2)-XK is actually inferior to that of
the best rung-4 DFT functional, ωB97M-V. By increasing the basis
set for the MP2 part to def2-QZVPPD, we were able to substantially
improve performance at modest cost (if an RI-MP2 approximation is
made), with WTMAD2 for this G4­(MP2)-XK-D method now comparable to
the better rung-5 functionals (albeit at greater cost). A three-tier
approach with a scaled MP3/def2-TZVPP intermediate step, however,
leads to a G4­(MP3)-D method that is markedly superior to even the
best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating
the CCSD­(T) component with a triple-ζ, rather than split-valence,
basis set yields only a modest further improvement that is incommensurate
with the drastic increase in computational cost. G4­(MP3)-D and G4­(MP2)-XK-D
have about 40% better WTMAD2, at similar or lower computational cost,
than their counterparts G4 and G4­(MP2), respectively: detailed comparison
reveals that the difference lies in larger molecules due to basis
set incompleteness error. An E2/{T,Q} extrapolation and a CCSD­(T)/def2-TZVP
step provided the G4-T method of high accuracy and with just three
fitted parameters. Using KS orbitals in MP2 leads to the G4­(MP3|KS)-D
method, which entirely eliminates the CCSD­(T) step and has no steps
costlier than scaled MP3; this shows a path forward to further improvements
in double-hybrid density functional methods. None of our final selections
require an empirical HLC correction; this cuts the number of empirical
parameters in half and avoids discontinuities on potential energy
surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are
evaluated at the DLPNO-CCSD­(T) level, achieves nearly the accuracy
of G4-T but is applicable to much larger systems.