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?

Abstract

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 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.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core–Valence Correlation, and F12 Alternatives

“… 36 Hence, we were able to repurpose the CCSD(T) total energies from our previous study. 38 Similarly, we repurposed MP3/def2-TZVPP along with the def2 small-core energy-consistent relativistic pseudopotentials 73 for elements heavier than Kr. The augmented def2 basis sets are available for the elements H–La and Hf–Rn; the nonaugmented ones are additionally available for Ce–Lu.…”

“…The primary standard for training the presented cWFT methods was the GMTKN55 benchmark; 37 as in ref ( 44 ) for the minimally empirical double hybrids, and in our previous paper on G4-T-type methods, 38 the reference data, geometries, and charge/multiplicity information were extracted from the ACCDB database of Morgante and Peverati 93 and reused verbatim (without geometry optimization). See ref ( 37 ) for details of all of the reference data, which were either CCSD(T)/CBS (i.e., extrapolation to the complete basis set limit) or higher level, many taken from previous benchmark studies in our group.…”

“…The two-tier methods are based on the extrapolated Hartree–Fock energy, the post-HF second-order MP correction, and a CCSD(T)-MP2 component in a smaller basis set. For instance, the highly accurate G4-T method from ref ( 38 ) has the following energy expression where E corr,MP2 is the total second-order MP correlation energy, E C,CCSD is the coupled-cluster single and double valence correlation energy, and E C,(T) is the quasi-perturbative coupled-cluster triple excitation term. The extrapolated HF energy to the basis limit in the standard G4-type methods is given in exponential form as 101 …”

“…It is important to note that fitting the HF/CBS extrapolation coefficient has no perceptible effect (to two decimal places) on the WTMAD2 in cc-G4-type methods, as we found in the previous paper. 38 …”

“…As it turned out, by refitting to GMTKN55 and carefully monitoring statistical significance of empirical parameters, we were able to develop 38 a new family of cWFT methods using def2 basis sets: in particular, G4-T and G4-T-DLPNO methods reached WTMAD2 values of just 1.51 and 1.66 kcal/mol, respectively. Particularly, G4-T-DLPNO is an economical option.…”