Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

Extrapolating DFT Towards the Complete Basis Set Limit: Lessons from the PBE Family of Functionals

<div>In this work, I derive a set of formulas for calculating extrapolation parameters based on the percentage of HF exchange and PT correlation within the functional recipe. I use a set of CBS energies from finite element calculations, calculated with PBE and related functionals, to do so.<br></div><div>The obtained extrapolation parameters perform better than previous, empirically-derived values. They are shown to be transferrable to non-PBE functionals, and the [2,3]-zeta extrapolations work well in cases with non-covalent character.<br></div>

SVECV-f12: benchmark of a composite scheme for accurate and cost effective evaluation of reaction barriers.

A simple composite scheme is presented, based on a combination of density functional geometry and frequencies evaluation, valence energies obtained using the CCSD(T)-f12 method extrapolated to the complete basis set limit, and core-valence correlation corrections employing the MP2 method. The procedure was applied to the 38 reactions in Truhlar’s HTBH38/08 and NHTBH38/08 databases and the errors in the barriers with respect to their best values are presented. Mean unsigned deviation (MUD) for the complete set of 68 independent barriers is 0.40 kcal mol-1 , compared to 1.31 kcal/mol for G4 and 1.62 kcal/mol for the dispersion-corrected M06- 2X method. The accuracy of the procedure is also better that that of other calculations using composite methods of similar cost. The MUD of the new scheme on the barriers in the DBH24/08 subset (12 out of the 38 reactions in the other two sets) is 0.27 kcal mol-1 , better than that obtained at the expensive CCSD(T,full)/aug-cc-pCV(T+d)Z level (0.46 kcal mol-1 ) and comparable to the 2 most exact (and costly) Wn calculations (MUD=0.14 kcal mol-1 ). The maximum unsigned deviation (MaxUD) for all the reactions studied is 0.99 kcal/mol. G4 and M06-2X, on the other side, exhibit MaxUDs of 6.7 and 8.0 kcal/mol respectively. The method was further tested against a subset of the reactions in the databases, for which the geometry and energies of all species were determined at the much more demanding CCSD(T)-F12//pVQZ-F12 level. These results showed that Truhlar’s calculations in this subset are off the best values by a considerable amount, with an rmse of 0.56 kcal/mol. As a consequence, a new dataset of barrier heights, SV20, is presented. The SVECV-F12 procedure on this SV20 database results in rmse and MUD values of only 0.21 and 0.16 kcal/mol. The possible residual errors introduced by the approximations used for each component of the method are tested against more sophisticated calculations and shown to be accurate enough to obtain barriers well under the chemical precision limit at a reasonable cost for molecules of interest in atmospheric chemistry.

A Guide to Benchmarking Enzymatically Catalysed Reactions: The Importance of Accurate Reference Energies and the Chemical Environment

We explore two significant factors on the outcomes of benchmark studies for enzymatically catalysed reactions, namely the level of theory of the benchmarks and the size of the model system used to represent the enzyme active site. For the benchmarks, we compare two potential alternatives to canonical coupled cluster results for situations where CCSD(T) is computationally too demanding: a strategy to estimate finite basis set coupled cluster values and the local-correlation DLPNO-CCSD(T) method at the complete basis set limit. We confirm the high accuracy of DLPNO-CCSD(T) used with tight thresholds. We also show that notable differences can be seen when using both sets of references for a benchmark study, with absolute deviations from the higher quality references generally smaller than those from lowerquality ones as well as changes in the ranking of the assessed methods. For geometries, we test three models for the active site of 4-oxalocrotonate tautomerase: one typical of the QM region that may be used in QM/MM studies, and two smaller variants that neglect the surrounding chemical environment. Benchmarking of 12 density functionals known to perform well on enzymatically catalysed reactions shows inconsistent performance of each method across the three models, contradicting the common idea that small representative systems can be used to accurately assess the applicability of low-level methods for larger biochemical applications. Our findings shall serve as a reminder on the standards that should be adhered to in benchmark studies, and as a guide for future studies, both on enzyme-related and other chemical problems.