Exploring Avenues beyond Revised DSD Functionals: II. Random-Phase Approximation and Scaled MP3 Corrections

Abstract

For revDSD double hybrids, the Görling–Levy second-order perturbation theory component is an Achilles’ heel when applied to systems with significant near-degeneracy (“static”) correlation. We have explored its replacement by the direct random phase approximation (dRPA), inspired by the SCS-dRPA75 functional of Kállay and co-workers. The addition to the final energy of both a D4 empirical dispersion correction and of a semilocal correlation component lead to significant improvements, with DSD-PBEdRPA 75 -D4 approaching the performance of revDSD-PBEP86-D4 and the Berkeley ωB97M(2). This form appears to be fairly insensitive to the choice of the semilocal functional but does exhibit stronger basis set sensitivity than the PT2-based double hybrids (due to much larger prefactors for the nonlocal correlation). As an alternative, we explored adding an MP3-like correction term (in a medium-sized basis set) to a range-separated ωDSD-PBEP86-D4 double hybrid and found it to have significantly lower WTMAD2 (weighted mean absolute deviation) for the large and chemically diverse GMTKN55 benchmark suite; the added computational cost can be mitigated through density fitting techniques.

Do Double Hybrid Functionals Benefit from Regularization in the PT2 term? Observations from an Extensive Benchmark

“…52 Generally, inner-shell orbitals were frozen, but in subsets where such orbitals come close enough to the valence shell to qualify as 'honorary valence orbitals', 53 the same frozen-core settings were used as in Refs. 46,54,55 Similar to the unregularized (x)DSD functionals, one fully optimized κ-DSD also has six adjustable linear parameters: cX,HF, cC,DFT, c2ab, c2ss(=c2aa+c2bb), and for the D3(BJ) dispersion correction, one prefactor s6 and one parameter a2 for the damping function (like in refs 56,57 we constrain a1=s8=0). On top of that, our new κ(x)DSD functionals also contain the PT2 regularization parameter κ.…”

Do Double-Hybrid Functionals Benefit from Regularization in the PT2 Term? Observations from an Extensive Benchmark

“…The large pruned integration grid SG-3 was used across the board. 54 Generally, inner-shell orbitals were frozen, but in subsets where such orbitals come close enough to the valence shell to qualify as “honorary valence orbitals”, 55 the same frozen-core settings were used as in refs ( 48 ), ( 56 ), and ( 57 ).…”

Surprisingly Good Performance of XYG3 Family Functionals Using a Scaled KS-MP3 Correlation

“…Xu and co-workers ,, used B3LYP − orbitals while calculating the final energy for the original XYG3 functional and its later variants lrc-XYG3 and XYGJ-OS . Along this line, xDSD, − ωDSD, and ωDSD3 functionals from the Martin group and the combinatorially optimized range-separated double-hybrid ωB97M(2) by Mardirossian and Head-Gordon have shown remarkable performance for extensive and chemically diverse main-group benchmarks such as MGCDB84 (Main-Group Chemistry Database with about 5000 test cases divided into 84 subsets) and GMTKN55 (General Main-group Thermochemistry, Kinetics, and Noncovalent interactions, 55 problem subsets). In a recent study, Zhang and Xu explored the limits of the XYG3-type double hybrids utilizing B3LYP reference orbitals to be consistent with the original XYG3 functional.…”

“…The LD0110-LD0590 angular integration grid was used throughout, being a pruned Lebedev-type integration grid similar to Grid = UltraFine in Gaussian or SG-3 in Q-Chem . The same frozen core settings were used as in refs and . MP3 calculations in both HF and KS orbitals were performed using Q-Chem 5.4, def2-TZVPP being used throughoutwe previously found that this basis set is adequate for post-MP2 corrections, both in composite WFT and in double-hybrid DFT contexts. , All calculations were performed on the ChemFarm HPC cluster in the Faculty of Chemistry at the Weizmann Institute of Science.…”

“…Motivated by the above two findings, here we combine the scaled E 3 correlation energies with the XYG8@BnLYP functionals to check whether it is possible to improve their performance further. Similar to ref , we have omitted the 50 largest systems, i.e., the UPU23 and C60 subsets, 10 largest ISOL24, 3 INV24, and a single IDISP, and we refer to this reduced version of GMTKN55 as mod-GMTKN55 in this paper.…”