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We have investigated the title question for both a subset of the W4-11 total atomization energies benchmark, and for the A24x8 noncovalent interactions benchmark. Overall, counterpoise corrections to post-CCSD(T) contributions are about two orders of magnitude less important than those to the CCSD(T) interaction energy. Counterpoise corrections for connected quadruple substitutions (Q) are negligible, and $(Q)_\Lambda - (Q)$ or $T_4 - (Q)$ especially so. In contrast, for atomization energies, the $T_3-(T)$ CP correction can reach about 0.05 \kcalmol~for small basis sets like cc-pVDZ, thought it rapidly tapers off with cc-pVTZ and especially aug-cc-pVTZ basis sets. It is reduced to insignificance by the extrapolation of $T_3-(T)$ applied in both W4 and HEAT thermochemistry protocols., Comment: 5 pages

This article presents a comprehensive computational investigation into chalcogen bonding interactions, focusing specifically on elucidating the role of subvalence (n$-$1)d and (n$-$1)sp correlation. The incorporation of inner-shell (n$-$1)d correlation leads to a decrease in interaction energies for chalcogen-bonded systems (at least those studied herein), contradicting the observations regarding halogen bonding documented by Kesharwani et al. in \textit{J. Phys. Chem. A}, \textbf{2018}, 122 (8), 2184-2197. The significance of (n$-$1)sp subvalence correlation appears to be lower by an order of magnitude. Notably, among the various components of interaction energies computed at the PNO-LCCSD(T) or DF-CCSD levels, we identify the PNO-LMP2 or DF-MP2 component of the (n$-$1)d correlation as predominant. Furthermore, we delve into the impact of second-order spin-orbit coupling (SOC2) on these interactions. Specifically, for the Te complexes, SOC2 effects rival (n$-$1)d correlation in importance; for the Se complexes, SOC2 is much less important. Generally, SOC2 stabilizes monomers more than dimers, resulting in reduced binding of the latter. Notably, at equilibrium and stretched geometries, SOC2 and (n$-$1)d destabilize the complex; however, at compressed geometries, they exhibit opposing effects, with (n$-$1)d becoming stabilizing., Comment: PCCP, EarlyView (2024). CC:BY open access. Special collection "Emerging Investigators" (Dr. Nisha Mehta is senior author)

Basis set extrapolations are typically rationalized either from analytical arguments involving the partial-wave or principal expansions of the correlation energy in helium-like systems, or from fitting extrapolation parameters to reference energetics for a small(ish) training set. Seeking to avoid both, we explore a third alternative: extracting extrapolation parameters from the requirement that the BSSE (basis set superposition error) should vanish at the complete basis set limit. We find this to be a viable approach provided that the underlying basis sets are not too small and reasonably well balanced. For basis sets not augmented by diffuse functions, BSSE minimization and energy fitting yield quite similar parameters., Comment: J. Phys. Chem. A, ASAP (Gustavo E. Scuseria festschrift); CC:BY 4.0 Open Access

High-accuracy composite wavefunction methods like Weizmann-4 (W4) theory, high-accuracy extrapolated \textit{ab initio} thermochemistry (HEAT), and Feller-Peterson-Dixon (FPD) enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the lambda coupled cluster expansion converges more rapidly and smoothly than the regular coupled cluster series. By means of CCSDT(Q)$_\Lambda$ and CCSDTQ(5)$_\Lambda$, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4$\Lambda$ and W4.3$\Lambda$ computational thermochemistry protocols., Comment: J. Phys. Chem. A 128, 1715-1724 (2024). PDF is CC:BY 4.0

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [M. Cho et al., \textit{ChemPhysChem} {\bf 21}, 688-696 (2020)], we showed that these can be reduced to at most three `principal components of ionicity'. The present study addressed the dependance on computed partial charges $q$ on 1-particle basis set and (for WFT methods) $n$-particle correlation treatment or (for DFT methods) exchange-correlation functional, for several representative partial charge definitions such as QTAIM, Hirshfeld, Hirshfeld-I, HLY (electrostatic), NPA, and APT. Our findings show that semi-empirical double hybrids can closely approach the CCSD(T) `gold standard' for this property. In fact, owing to an error compensation in MP2, CCSD partial charges are further away from CCSD(T) than is MP2. The non-local correlation is important, especially when there is a substantial amount of non-local exchange. Employing range separation provides no clear advantage, while global hybrids with 20-30\% Hartree-Fock exchange exhibit the best performance across all charge types. Basis set convergence analysis shows that an augmented triple-zeta haVTZ+d basis set is sufficient for Hirshfeld, Hirshfeld-I, HLY, and APT methods. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits the slowest basis set convergence when contrasted with the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)-CCSD, exhibit even faster basis set convergence., Comment: Final published manuscript (CC-BY Open Access); part of special correction in honor of Elfi Kraka

Benchmark calculations on noncovalent interactions typically exclude correlation effects beyond valence CCSD(T) owing to their steep computational cost scaling. In this work, we consider their importance for water clusters, specifically, eight isomers of (H$_2$O)$_6$ and four Wales-Hodges isomers of (H$_2$O)$_{20}$. Higher order connected triples, $T_3$--(T), reduce dissociation energies of the latter by about 0.4 kcal/mol, but this is more than compensated by an increase of up to 0.85 kcal/mol due to connected quadruple excitations. In general, higher-order correlation effects favor more compact isomers over more `spread-out' ones. We also consider additional small effects for balance: scalar relativistics reduce binding in (H$_2$O)$_{20}$ by ca. --0.4 kcal/mol, which fortuitously is compensated by the ca. 0.55 kcal/mol diagonal Born-Oppenheimer correction. Core-valence correlation has the greatest impact, at ca. 1.3 kcal/mol for the icosamer., Comment: version updated from ResearchGate, now including 3-body contributions for water20

Minimally empirical G4-like composite wavefunction theories [E. Semidalas and J. M. L. Martin, \textit{J. Chem. Theory Comput.} {\bf 16}, 4238-4255 and 7507-7524 (2020)] trained against the large and chemically diverse GMTKN55 benchmark suite have demonstrated both accuracy and cost-effectiveness in predicting thermochemistry, barrier heights, and noncovalent interaction energies. Here, we assess the spectroscopic accuracy of top-performing methods: G4-\textit{n}, cc-G4-\textit{n}, and G4-\textit{n}-F12, and validate them against explicitly correlated coupled cluster CCSD(T*)(F12*) harmonic vibrational frequencies and experimental data from the HFREQ2014 dataset, of small first- and second-row polyatomics. G4-T is three times more accurate than plain CCSD(T)/def2-TZVP, while G4-T$_{\rm ano}$ is two times superior to CCSD(T)/ano-pVTZ. Combining CCSD(T)/ano-pVTZ with MP2-F12 in a parameter-free composite scheme results to a root-mean-square deviation of ~5 cm$^{-1}$ relative to experiment, comparable to CCSD(T) at the complete basis set limit. Application to the harmonic frequencies of benzene reveals a significant advantage of composites with ANO basis sets -- MP2/ano-pV\textit{m}Z and [CCSD(T)-MP2]/ano-pVTZ (\textit{m} = Q or 5) -- over similar protocols based on CCSD(T)/def2-TZVP. Overall, G4-type composite energy schemes, particularly when combined with ANO basis sets in CCSD(T), are accurate and comparatively inexpensive tools for computational vibrational spectroscopy., Comment: Molecular Physics, in press [Timothy J. Lee memorial issue]

The importance of post-CCSD(T) corrections as high as CCSDTQ56 for ground-state spectroscopic constants ($D_e$, $\omega_e$, $\omega_ex_e$, and $\alpha_e$) has been surveyed for a sample of two dozen mostly heavy-atom diatomics spanning a broad range of static correlation strength. While CCSD(T) is known to be an unusually felicitous `Pauling point' between accuracy and computational cost, performance leaves something to be desired for molecules with strong static correlation. We find CCSDT(Q)$_\Lambda$ to be the next `sweet spot' up, of comparable or superior quality to the much more expensive CCSDTQ. A similar comparison applies to CCSDTQ(5)$_\Lambda$ vs. CCSDTQ5, while CCSDTQ5(6)$_\Lambda$ is essentially indistinguishable from CCSDTQ56. A composite of CCSD(T)-X2C/ACV5Z-X2C with [CCSDT(Q)$_\Lambda$ -- CCSD(T)]/cc-pVTZ or even cc-pVDZ basis sets appears highly effective for computational vibrational spectroscopy. Unlike CCSDT(Q) which breaks down for the ozone vibrational frequencies, CCSDT(Q)$_\Lambda$ handles them gracefully., Comment: Mol. Phys., in press [Timothy J. Lee memorial issue]

It is well-known that both wavefunction ab initio and DFT calculations on second-row compounds exhibit anomalously slow basis set convergence unless the basis sets are augmented with additional `tight' (high-exponent) $d$ functions, as in the cc-pV($n+d$)Z and aug-cc-pV($n+d$)Z basis sets. This has been rationalized as being necessary for a better description of the low-lying $3d$ orbital, which as the oxidation state increases sinks low enough to act as a back-donation acceptor from chalcogen and halogen lone pairs. This prompts the question whether a similar phenomenon exists for the isovalent compounds of the heavy p-block. We show that for the fourth and fifth row, this is the case, but this time for tight $f$ functions enhancing the description of the low-lying $4f$ and $5f$ Rydberg orbitals, respectively. In the third-row heavy $p$ block, the $4f$ orbitals are too far up, while the $4d$ orbitals are adequately covered by the basis functions already present to describe the $3d$ subvalence orbitals., Comment: CC:BY 4.0 Open Access (Krishnan Raghavachari festschrift)

In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and 157, 234102 (2022)] we compared two Kohn-Sham density functionals based on physical modelling and theory with the best density-functional power-series fits in the literature. The best error statistics reported to date for a hybrid functional on the GMTKN55 chemical database of Goerigk, Grimme, and coworkers [Phys. Chem. Chem. Phys. 19, 32184 (2017)] were obtained. In the present work, additional second-order perturbation-theory terms are considered. The result is a 12-parameter double-hybrid (DH) density functional with the lowest GMTKN55 "WTMAD2" error yet seen for a DH functional. We call it "DH23"., Comment: 23 pages + supporting information, J. Chem. Phys., accepted

We have investigated the effect of F12 geminals on the basis set convergence of harmonic frequencies calculated using two representative double-hybrid density functionals, namely B2GP-PLYP and revDSD-PBEP86-D4. Like previously found for energetics [N. Mehta and J. M. L. Martin, \textit{J. Chem. Theor. Comput.} \textbf{18}, 5978--5991 (2022)] one sees an acceleration by two zeta steps, such that even the cc-pVDZ-F12 basis set is quite close to the complete basis set (CBS) limit. However, the basis set convergence problem is not as acute as for energetics, and compared to experimental harmonic frequencies, conventional orbital calculations with augmented triple zeta quality basis set are acceptably close to the CBS limit, and can be carried out using analytical second derivatives. An efficient implementation of double hybrid-F12 analytical derivatives would make the F12 approach attractive in the sense that even an $spd$ orbital basis set would be adequate. For the accurate revDSD-PBEP86-D4 functional, the role of differing local correlation terms (Perdew-Zunger 1981 vs. VWN5) in different electronic structure programs has been investigated: while optimal double hybrid parameters and performance statistics for energetics as well as frequencies differ slightly between the two implementations, these differences are insignificant for practical purposes., Comment: Can. J. Chem., minor revision (WATOC 2022 special issue)

We report an update and enhancement of the ACONFL (conformer energies of large alkanes [Ehlert, S.; Grimme, S.; Hansen, A. J. Phys. Chem. A 2022, 126, 3521-3535]) dataset. For the ACONF12 (n-dodecane) subset, we report basis set limit canonical CCSD(T) reference data obtained from MP2-F12/cc-pV{T,Q}Z-F12 extrapolation, [CCSD(F12*)-MP2-F12]/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/aug-cc-pV{D,T}Z calculations. Then we explored the performance of a variety of single and composite localized-orbital CCSD(T) approximations, ultimately finding an affordable LNO-CCSD(T)-based post-MP2 correction that agrees to 0.008 kcal/mol MAD (mean absolute deviation) with the revised canonical reference data. In tandem with canonical MP2-F12/CBS extrapolation, this was then used to re-evaluate the ACONF16 and ACONF20 subsets for n-hexadecane and n-icosane, respectively. A revised ACONFL set was thus obtained. It was then used to assess the performance of different localized-orbital coupled cluster approaches, such as PNO-LCCSD(T) as implemented in MOLPRO, DLPNO-CCSD (T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, at their various accuracy settings. A three-tier LNO-CCSD(T)-based composite scheme disagrees by only 0.02 kcal/mol from the revised ACONFL reference data. When extrapolated to the complete PNO space limit, DLPNO-CCSD(T1, Tight) and a composite method are the best picks among all the localized coupled cluster methods tested for the dodecane conformers. Dispersion-corrected dRPA-based double hybrids perform remarkably well for the ACONFL set. While the revised reference data do not affect any conclusions on the less accurate methods, they may upend orderings for more accurate methods with error statistics on the same order as the difference between reference datasets., Comment: Revised MS submitted to JPC A: level of theory for reference calculations upgraded; many other changes

The S66x8 noncovalent interactions benchmark has been re-evaluated at the "sterling silver" level, using explicitly correlated MP2-F12 near the complete basis set limit, CCSD(F12*)/aug-cc-pVTZ-F12, and a (T) correction from conventional CCSD(T)/sano-V{D,T}Z+ calculations. The revised reference value disagrees by 0.1 kcal/mol RMS with the original Hobza benchmark and its revision by Brauer et al, but by only 0.04 kcal/mol variety from the "bronze" level data in Kesharwani et al., Aust. J. Chem. 71, 238-248 (2018). We then used these to assess the performance of localized-orbital coupled cluster approaches with and without counterpoise corrections, such as PNO-LCCSD(T) as implemented in MOLPRO, DLPNO-CCSD (T1) as implemented in ORCA, and LNO-CCSD(T) as implemented in MRCC, for their respective "Normal", "Tight", and "very Tight" settings. We also considered composite approaches combining different basis sets and cutoffs. Furthermore, in order to isolate basis set convergence from domain truncation error, for the aug-cc-pVTZ basis set we compared PNO, DLPNO, and LNO approaches with canonical CCSD(T). We conclude that LNO-CCSD(T) with veryTight criteria performs very well for "raw" (CP-uncorrected), but struggles to reproduce counterpoise-corrected numbers even for veryVeryTight criteria: this means that accurate results can be obtained using either extrapolation from basis sets large enough to quench basis set superposition error (BSSE) such as aug-cc-pV{Q,5}Z, or using a composite scheme such as Tight{T,Q}+1.11[vvTight(T) - Tight(T)]. In contrast, PNO-LCCSD(T) works best with counterpoise, while performance with and without counterpoise is comparable for DLPNO-CCSD(T1). Among more economical methods, the highest accuracies are seen for dRPA75-D3BJ, {\omega}B97M-V, {\omega}B97M(2), revDSD-PBEP86-D4, and DFT(SAPT) with a TDEXX or ATDEXX kernel., Comment: Final published version with CC license

Following earlier work [Mehta, N.; Martin, J. M. L.; J. Chem. Theory Comput. 2022, 18, acs.jctc.2c00426] that showed how the slow basis set convergence of double hybrid density functional theory can be obviated by the use of F12 explicit correlation in the GLPT2 step (second order G\"orling-Levy perturbation theory), we demonstrate here, for the very large and chemically diverse GMTKN55 benchmark suite, and using the B2GP-PLYP-D3BJ functional as a proof of principle, that the CPU time scaling of this step can be reduced (asymptotically linearized) using the PNO-L (pair natural orbitals, localized) approximation, at negligible cost in accuracy., Comment: Published version [Open Access CC:BY 4.0]

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energy are vital. Due to the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), DFT remains the workhorse for such calculations. In this paper, we have assessed the performance of 88 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse dataset (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybris for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, the exchange term's range separation helps improve the performance for barrier heights and reaction energies. The sixteen-parameter Berkeley double hybrid, {\omega}B97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than {\omega}B97M(2) for BH9 barrier heights and reaction energies., Comment: J. Phys. Chem. A, revised (Vincenzo Barone festschrift)

Double-hybrid density functional theory (DHDFT) offers a pathway to accuracies approaching composite wavefunction approaches like G4 theory. However, the GLPT2 (G{\"o}rling 2nd order perturbation theory) term causes them to partially inherit the slow $\propto L^{-3}$ (with $L$ the maximum angular momentum) basis set convergence of correlated wavefunction methods. This could potentially be remedied by introducing F12 explicit correlation: we investigate the basis set convergence of both DHDFT and DHDFT-F12 for the large and chemically diverse GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) benchmark suite. The B2GP-PLYP-D3(BJ) and revDSD-PBEP86-D4 double hybrid density functionals (DHDFs) are investigated as test cases, together with orbital basis sets as large as aug-cc-pV5Z and F12 basis sets as large as cc-pV(Q+d)Z-F12. We show that F12 greatly accelerates basis set convergence of DHDFs, to the point that even the modest cc-pVDZ-F12 basis set is closer to the basis set limit than cc-pV(Q+d)Z or def2-QZVPP in orbital-based approaches, and in fact comparable in quality to cc-pV(5+d)Z. Somewhat surprisingly, aug-cc-pVDZ-F12 is not required even for the anionic subsets. In conclusion, DHDF-F12/VDZ-F12 eliminates concerns about basis set convergence in both the development and application of double-hybrid functionals. Mass storage and I/O bottlenecks for larger systems can be circumvented by localized pair natural orbital approximations, which also exhibit much gentler system size scaling., Comment: published version in JCTC: Open Access with Creative Commons license

Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: JK (Coulomb-exchange fitting), RI-MP2 (resolution of the identity MP2), and CABS (complementary auxiliary basis set). If unavailable for the orbital basis set and chemical elements of interest, the first two can be auto-generated on the fly using existing algorithms, but not the third. In this paper, we present a quite simple algorithm named autoCABS; a Python implementation under a free software license is offered at Github. For the cc-pVnZ-F12 (n=D,T,Q,5) and the W4-08 thermochemical benchmark, we demonstrate that autoCABS-generated CABS basis sets are comparable in quality to purpose-optimized OptRI basis sets from the literature, and that the quality difference becomes entirely negligible as n increases., Comment: 18 pages; new section on harmonic frequencies added

We have investigated the title question for the W4-08 thermochemical benchmark using partial-wave truncations of a large reference (REF) basis set, as well as for standard F12-optimized basis sets. With the REF basis set, the root mean square (RMS) contribution of i functions to the total atomization energies (TAEs) is about 0.01 kcal/mol, the largest individual contributions being 0.04 kcal/mol for \ce{P2} and \ce{P4}. However, even for these cases, basis set extrapolation from \{g,h\} basis sets adequately addresses the problem. Using basis sets insufficiently saturated in the $spdfgh$ angular momenta may lead to exaggerated $i$ function contributions. For extrapolation from $spdfg$ and $spdfgh$ basis sets, basis set convergence appears to be quite close to the theoretical asymptotic $\propto L^{-7}$ behavior. We hence conclude that $h$ functions are sufficient even for highly demanding F12 applications. With one-parameter extrapolation, $spdf$ and $spdfg$ basis sets are adequate, with aug-cc-pV\{T,Q\}Z-F12 yielding RMSD=0.03 kcal/mol. A limited exploration of CCSD(F12*) and CCSD-F12b suggests our conclusions are applicable to higher-level F12 methods as well., Comment: Final version: Open Access ACS AuthorChoice CC:BY 4.0

It can be argued that electron correlation, as a concept, deserves the same prominence in general chemistry as molecular orbital theory. We show how it acts as Nature's "chemical glue" at both the molecular and supramolecular levels. Electron correlation can be presented in a general chemistry course in an at least somewhat intuitive manner. We also propose a simple classification of correlation effects based on their length scales and the size of the orbital gap (relative to the two-electron integrals). In the discussion, we also show how DFT can shed light on wavefunction theory, and conversely. We discuss two types of "honorary valence orbitals", one related to small core-valence gaps, the other to the ability of empty 3d orbitals in 2nd row elements to act as backbonding acceptors. Finally, we show why the pursuit of absolute total energies for their own sake becomes a sterile exercise, and why atomization energies are a more realistic "fix point"., Comment: Israel Journal of Chemistry, Early View (2022) [Perspective Article for special issue "Rosarium Philosophorum" dedicated to computational chemistry] (CC-BY Open Access)

We have revisited the MOBH35 (Metal-Organic Barrier Heights, 35 reactions) benchmark [Iron, M. A.; Janes, T. J. Phys. Chem. A 2019, 123 (17), 3761-3781; ibid. 2019, 123, 6379-6380] for realistic organometallic catalytic reactions, using both canonical CCSD(T) and localized orbital approximations to it. For low levels of static correlation, all of DLPNO-CCSD(T), PNO-LCCSD(T), and LNO-CCSD(T) perform well; for moderately strong levels of static correlation, DLPNO-CCSD(T) and (T1) may break down catastrophically, and PNO-LCCSD(T) is vulnerable as well. In contrast, LNO-CCSD(T) converges smoothly to the canonical CCSD(T) answer with increasingly tight convergence settings. The only two reactions for which our revised MOBH35 reference values differ substantially from the original ones are reaction 9 and to a lesser extent 8, both involving iron. For the purpose of evaluating DFT methods for MOBH35, it would be best to excise reaction 9 entirely as its severe level of static correlation is just too demanding a test. The magnitude of the difference between DLPNO-CCSD(T) and DLPNO-CCSD(T1) is a reasonably good predictor for errors in DLPNO-CCSD(T1) compared to canonical CCSD(T); [...], Comment: J. Chem. Theor. Comput. 18, ASAP (2022). CC:BY 4.0. Dedicated to the memory of Shimon Vega (1943-2021)

The S66 non-covalent interactions are studied through localized coupled-cluster methods and general LNO-CCSD(T)-based composite schemes. Very small RMS deviations (\leq 0.05 kcal/mol) for the low-cost composite approaches from the SILVER reference interaction energies of S66 indicate that we can safely avoid carrying out the largest basis set calculations with veryVeryTight thresholds, and apply instead additivity corrections in smaller basis sets. Interestingly, the counterpoise corrections do not have an appreciable effect on the composite schemes. These findings may prove useful for intermolecular and intramolecular NCIs of larger systems., Comment: 6 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

While the inclusion of the nonlocal correlation in fifth rung "double hybrid" functionals is definitely beneficial, one might rightfully ask whether its evaluation in the basis of Kohn-Sham (KS) orbitals has additional value compared to the use of Hartree-Fock reference orbitals (in a type of multilevel scheme). We have investigated this question for a very large and chemically diverse dataset, GMTKN55. We conclude that KS reference orbitals are undoubtedly beneficial, but the benefit is not as large as one might intuitively expect., Comment: 4 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

We propose here a DFT-based diagnostic for static correlation %TAEX[TPSS@HF - HF] which effectively measures how different the DFT and HF exchange energies for a given HF density are. This and %TAEcorr[TPSS] are two cost-effective a priori estimates for the adequacy of the importance of static correlation. %TAEX[TPSS@HF - HF] contains nearly the same information as the earlier A diagnostic, but may be more intuitive to understand. Principal component and variable clustering analysis of a large number of static correlation diagnostics reveals much of the variation is explained by just two components, and almost all of it by four; these are blocked by four variable clusters (single excitations; correlation entropy; double excitations; pragmatic energetics)., Comment: 5 pages, AIP Conference Proceedings, in press (ICCMSE-2021)

By adding a GLPT3 (third-order G\"orling-Levy perturbation theory, or KS-MP3) term E3 to the XYG7 form for a double hybrid, we are able to bring down WTMAD2 (weighted total mean absolute deviation) for the very large and chemically diverse GMTKN55 benchmark to an unprecedented 1.17 kcal/mol, competitive with much costlier composite wavefunction ab initio approaches. Intriguingly: (a) the introduction of E3 makes an empirical dispersion correction redundant; (b) GGA or mGGA semilocal correlation functionals offer no advantage over LDA in this framework; (c) if a dispersion correction is retained, then simple Slater exchange leads to no significant loss in accuracy. It is possible to create a 6-parameter functional with WTMAD2=1.42 that has no post-LDA DFT components and no dispersion correction in the final energy.

The total atomization energy of a molecule is the thermochemical cognate of the heat of formation in the gas phase, its most fundamental thermochemical property. We decompose it into different components and provide a survey of them. It emerges that the connected triple excitations contribution is the third most important one, about an order of magnitude less important than the "big two" contributions (mean-field Hartree-Fock and valence CCSD correlation), but 1-2 orders of magnitude more important than the remainder. For the 200 total atomization energies of small molecules in the W4-17 benchmark, we have investigated the basis set convergence of the connected triple excitations contribution (T). Achieving basis set convergence for the valence triple excitations energy is much easier than for the valence singles and doubles correlation energy. Using reference data obtained from spdfghi and spdfghik basis sets, we show that extrapolation from quintuple-zeta and sextuple-zeta yields values within about 0.004 kcal/mol RMS. Convergence to within about 0.01 kcal/mol is achievable with quadruple- and quintuple-zeta basis sets, and to within about 0.05 kcal/mol with triple- and quadruple-zeta basis sets. It appears that radial flexibility in the basis set is more important here than adding angular momenta L: apparently, replacing nZaPa basis sets with truncations of 7ZaPa at L=n gains about one angular momentum for small values of n. We end the article with a brief outlook for the future of accurate electronic structure calculations., Comment: chapter for upcoming Springer book "Quantum Science-Frontier of Chemistry and Physics", edited by Taku Onishi. Revised version with additional background sections requested by editor

The benzene...ethene and parallel-displaced (PD) benzene...benzene dimers are the most fundamental systems involving p-p stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers at the CCSD(T)/CBS level of theory using various approaches such as reduced virtual orbital spaces and/or MP2-based basis set corrections. Here we obtain CCSDT(Q) binding energies using a Weizmann-3-type approach. In particular, we extrapolate the SCF, CCSD, and (T) components using large heavy-atom augmented Gaussian basis sets (namely, SCF/jul-cc-pV{5,6}Z, CCSD/jul-cc-pV{Q,5}Z, and (T)/jul-cc-pV{T,Q}Z). We consider post-CCSD(T) contributions up to CCSDT(Q), inner-shell, scalar-relativistic, and Born-Oppenheimer corrections. Overall, our best relativistic, all-electron CCSDT(Q) binding energies are Delta Ee,all,rel = 1.234 (benzene...ethene) and 2.550 (benzene...benzene PD), Delta H0 = 0.949 (benzene...ethene) and 2.310 (benzene...benzene PD), and Delta H298 = 0.130 (benzene...ethene) and 1.461 (benzene...benzene PD) kcal/mol. Important conclusions are reached regarding the basis set convergence of the SCF, CCSD, (T), and post-CCSD(T) components. Explicitly correlated calculations are used as a sanity check on the conventional binding energies. Overall, post-CCSD(T) contributions are destabilizing by 0.028 (benzene...ethene) and 0.058(benzene...benzene) kcal/mol, thus they cannot be neglected if 0.1 kcal/mol accuracy is sought., Comment: J. Chem. Phys., accepted with minor revision

For revDSD double hybrids, the G\"orling-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 K\'allay and coworkers. 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-PBEdRPA75-D4 approaching the performance of revDSD-PBEP86-D4 and the Berkeley $\omega$B97M(2). This form appears to be fairly insensitive to the choice of 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 sets) to a range-separated $\omega$DSD-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., Comment: J. Phys. Chem. A 125, ASAP (2021) Creative Commons License

We have explored the use of range separation as a possible avenue for further improvement on our revDSD minimally empirical double hybrid functionals. Such $\omega$DSD functionals encompass the XYG3 type of double hybrid (i.e., xDSD) as a special case for $\omega$->0. As in our previous studies, the large and chemically diverse GMTKN55 benchmark suite was used for evaluation. Especially when using the D4 rather than D3BJ dispersion model, xDSD has a slight performance advantage in WTMAD2. As found previously, PBEP86 is the winning combination for the semilocal parts. xDSDn-PBEP86-D4 marginally outperforms the previous 'best in class' $\omega$B97M(2) Berkeley double hybrid, but without range separation and using fewer than half the number of empirical parameters. Range separation turns out to offer only marginal further improvements on GMTKN55 itself. While $\omega$B97M(2) still yields better performance for small-molecule thermochemistry, this is outweighed in WTMAD2 by superior performance of the new functionals for conformer equilibria. Results for two external test sets with pronounced static correlation effects may indicate that range-separated double hybrids are more resilient to such effects., Comment: J. Phys. Chem. A 125, ASAP (2021) Creative Commons License (1st of two papers back-to-back)

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA exchange-correlation (XC) functionals (PBE, BLYP, TPSS, SCAN) as a function of the percentage of HF exchange in the hybrid. The D4 empirical dispersion correction has been added throughout. For subsets dominated by dynamical correlation -- particularly noncovalent interaction subsets -- HF-DFT is highly beneficial, particularly at low HF exchange percentages. For subsets with significant static correlation (i.e., where a Hartree-Fock determinant is not a good zero-order wavefunction), HF-DFT may do more harm than good. While the self-consistent series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals -- consistent with Grimme's proposal of the PBE38 functional -- HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4). Intriguingly, for HF-SCANn-D4, the minimum is near 10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is only barely lower than that of HF-SCAN-D4 (i.e., where the post-HF step is a pure meta-GGA). The latter becomes an attractive option, only slightly more costly than pure Hartree-Fock, and devoid of adjustable parameters other than the three in the dispersion correction. Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X and by the combinatorically optimized empirical range-separated hybrids wB97X-V and wB97M-V., Comment: Journal of Chemical Theory and Computation (2021)

A hierarchy of wavefunction composite methods (cWFT), based on G4- type cWFT methods available for elements H through Rn, was recently reported by Semidalas and Martin [J. Chem. Theor. Comput. 2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Moller-Plesset correction and replacing the Weigend-Ahlrichs def2-mZVPP(D) basis sets used in the aforementioned paper with complete basis set extrapolation from augmented correlation consistent core-valence triple-zeta, aug-cc-pwCVTZ(-PP), and quadruple-zeta, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4- type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion's share of the improvement comes from better capture of valence correlation; the inclusion of core-valence correlation is almost an order of magnitude less important. These robust correlation consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component., Comment: J. Chem. Theor. Comput., ASAP (Open Access under CC)

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 et al, JCTC 2019, 15, 4478-4484). 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, wB97M-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 wB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-zeta, 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. 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., Comment: J. Chem. Theor. Comp., ASAP (2020). CC:BY 4.0 Open Access article

We consider the performance of combined PNO-F12 approaches for the dissociation energy of water clusters as large as (H2O)20 by comparison to canonical CCSD(T)/CBS reference values obtained through n-body decomposition of post-MP2 corrections. We find that PNO-LCCSD(T)-F12b approaches with "Tight" cutoffs are generally capable of reproducing canonical CCSD(T) interaction energies to within ~0.25% and isomerization energies to ~1.5%, while requiring only a fraction of the canonical computational cost. However, basis set convergence patterns and effect of counterpoise corrections are more erratic than for canonical calculations, highlighting the need for canonical benchmarks on closely related systems., Comment: AIP Conference Proceedings, in press [ICCMSE-2020 issue]

Localized orbital coupled cluster theory has recently emerged as an nonempirical alternative to DFT for large systems. Intuitively, one might expect such methods to perform less well for highly delocalized systems. In the present work, we apply both canonical CCSD(T) and a variety of localized approximations thereto to a set of expanded porphyrins -- systems that can switch between H\"uckel, figure-eight, and M\"obius topologies under external stimuli. Both minima and isomerization transition states are considered. We find that M\"obius(-like) structures have much stronger static correlation character than the remaining structures, and that this causes significant errors in DLPNO-CCSD(T) and even DLPNO-CCSD(T1) approaches, unless TightPNO cutoffs are employed. If sub-kcal/mol reproduction of canonical relative energies is required even for M\"obius-type systems (or other systems plagued by strong static correlation), then Nagy and Kallay's LNO-CCSD(T) method with "tight" settings can provide that, at much greater computational expense than either the PNO-LCCSD(T) or DLPNO-LCCSD(T) approaches but with still a much gentler CPU time scaling than canonical approaches. We would propose the present POLYPYR21 dataset as a benchmark for localized orbital methods, or more broadly, for the ability of lower-level methods to handle energetics with strongly varying degrees of static correlation., Comment: 27 pages; revised version. J. Chem. Theory. Comput., ASAP (2020)

Double hybrid density functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacobs Ladder" of John P. Perdew. For large and chemically diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI-MP2 and/or another MP2 acceleration techniques are available in the electronic structure code. Only a half-dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range-separated and RPA-based approaches., Comment: Israel Journal of Chemistry, EarlyView (2020); 19 pages, Open Access

Benchmarks that span a broad swath of chemical space, such as GMTKN55, are very useful for assessing progress in the quest for more universal DFT functionals. We find that the WTMAD2 metrics for a great number of functionals show a clear "Jacob's Ladder hierarchy"; that the "combinatorial" development strategy of Head-Gordon and coworkers generates "best on rung" performers; that the quality of the nonlocal dispersion correction becomes more important as functionals become more accurate for nondispersion properties; that fitting against small, unrepresentative benchmark sets leads to underperforming functionals; and that {\omega}B97M(2) is currently the best DFT functional of any kind, but that revDSD-D4 functionals are able to reach similar performance using fewer parameters, and that revDOD-D4 in addition permits reduced-scaling algorithms. If one seeks a range-separated hybrid (RSH) GGA that also performs well for optical excitation energies, CAM-QTP-01 may be a viable option. The D4 dispersion model, with its partial charge dependence, appears to be clearly superior to D3BJ and even possibly NL. Should one require a double hybrid without dispersion model, noDispSD-SCAN is a viable option. Performance for the MOBH35 transition metal benchmark is different: the best double hybrids are competitive but not superior to {\omega}B97M-V, which offers the best performance compromise for mixed main group-transition metal problems., Comment: 5 pages (ICCMSE-2019 conference proceedings), AIP Conference Proceedings, in press

In the present work, we tested the performance of several new functionals for studying the mechanisms of concurrent reaction of hydroarylation and oxidative coupling catalyzed by Ru(II) chloride carbonyls. We find that DLPNO-CCSD(T) is an acceptable substitute for full canonical CCSD(T) calculations; that the recent {\omega}B97X-V and {\omega}B97M-V functionals exhibit superior performance to commonly used DFT functionals; and that the revised DSD-PBEP86 double hybrid represents an improvement over the original, even though transition metals were not involved in its parametrization., Comment: 5 pages (ICCMSE-2019 conference proceedings)

Scalar relativistic corrections to atomization energies of 1st-and 2nd-row molecules can be rationalized in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas-Kroll-Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies., Comment: Molecular Physics, submitted (SANIBEL special issue)

While the title question is a clear 'yes' from purely theoretical arguments, the case is less clear for practical calculations with finite (one-particle) basis sets. To shed further light on this issue, the basis set limits of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) have been investigated on detail for the W4-17 thermochemical benchmark. Near the CBS ([1-particle] complete basis set) limit, CCSD and CCSD(F12*) agree to within their respective uncertainties (about \pm0.04 kcal/mol) due to residual basis set incompleteness error, but a nontrivial difference remains between CCSD-F12b and CCSD(F12*), which is roughly proportional to the degree of static correlation. The observed basis set convergence behavior results from the superposition of a rapidly converging, attractive, CCSD[F12]--CCSD-F12b difference (consisting mostly of third-order terms), and a more slowly converging, repulsive, fourth-order difference between CCSD(F12*) and CCSD[F12]. For accurate thermochemistry, we recommend CCSD(F12*) over CCSD-F12b if at all possible. There are some indications that the nZaPa family of basis sets exhibits somewhat smoother convergence than the correlation consistent family., Comment: (J. Chem. Phys., revised)

Electronic coupling matrix elements are important to the theoretical description of electron transfer processes. However, they are notoriously difficult to obtain accurately from time- dependent density functional theory (TDDFT). Here, we use the HAB11 benchmark dataset of coupling matrix elements to assess whether TDDFT using optimally-tuned range-separated hybrid functionals, already known to be successful for the description of charge transfer excitation energies, also allows for an improved accuracy in the prediction of coupling matrix elements. We find that this approach outperforms all previous TDDFT calculations, based on semi-local, hybrid, or non-tuned range-separated hybrid functionals, with a remaining average deviation as low as ~12%. We discuss potential sources for the remaining error., Comment: Mol. Phys., in press (Michael Baer festschrift)

The inner-shell correlation contributions to the total atomization energies (TAEs) of the W4-17 computational thermochemistry benchmark have been determined at the CCSD(T) level near the basis set limit using several families of core correlation basis sets, such as aug-cc-pCVnZ (n=3-6), aug-cc-pwCVnZ (n=3-5), and nZaPa-CV (n=3-5). The three families of basis sets agree very well with each other (0.01 kcal/mol RMS) when extrapolating from the two largest available basis sets: however, there are considerable differences in convergence behavior for the smaller basis sets. nZaPa-CV is superior for the core-core term and awCVnZ for the core-valence term. While the aug-cc-pwCV(T+d)Z basis set of Yockel and Wilson is superior to aug-cc-pwCVTZ, further extension of this family proved unproductive. The best compromise between accuracy and computational cost, in the context of high-accuracy computational thermochemistry methods such as W4 theory, is CCSD(T)/awCV{T,Q}Z, where the {T,Q} notation stands for extrapolation from the awCVTZ and awCVQZ basis set pair. For lower-cost calculations, a previously proposed combination of CCSD-F12b/cc-pCVTZ-F12 and CCSD(T)/pwCVTZ(no f) appears to 'give the best bang for the buck'. While core-valence correlation accounts for the lion's share of the inner shell contribution in first-row molecules, for second-row molecules core-core contributions may become important, particularly in systems like P4 and S4 with multiple adjacent second-row atoms. The average absolute core-core/core-valence ratio is 0.08 for the first-row species in W4-17, but 0.47 for the second-row subset., Comment: Mol. Phys., in press (Dieter Cremer memorial issue)

We discuss the interrelations between various basis set extrapolation formulas and show that for the nZaPa and aug-cc-pVnZ basis set formulas, for n=4--6 their behavior closely resembles the Petersson (L+a)^{-3} formula with a shift a specific to the basis set family and level of theory. This is functionally equivalent to the Pansini-Varandas extrapolation for large L. This naturally leads to a simple way to extend these extrapolations to n=7 and higher. The formula is validated by comparison with newly optimized extrapolation factors for the AV{6,7}Z basis set pairs and literature values for {6,7}ZaPa. For L\geq5, the CCSD extrapolations of both the Schwenke and Varandas type are functionally equivalent to E(L)=E_\infty+A.(L-0.30)^{-3}, i.e., E(\infty)=E(L)+[E(L)-E(L-1)]/([(L-0.30)/(L-1.30)]^3-1), Comment: AIP Conference Proceedings, in press (ICCMSE-2018 issue); 4 pages, PDF

The S66 benchmark for noncovalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 "high-level corrections" are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66x8 problem set in particular, and for accurate calculations on noncovalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, while half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost., Comment: Australian Journal of Chemistry, in press [Graham S. Chandler special issue]

We have developed a new basis set family, denoted aug-cc-pVnZ-F12 (or aVnZ-F12 for short), for explicitly correlated calculations. The sets included in this family were constructed by supplementing the corresponding cc-pVnZ-F12 sets with additional diffuse functions on the higher angular momenta (i.e., additional d-h functions on non-hydrogen atoms, and p-g on hydrogen), optimized for the MP2-F12 energy of the relevant atomic anions. The new basis sets have been benchmarked against electron affinities of the first- and second-row atoms, the W4-17 dataset of total atomization energies, the S66 dataset of noncovalent interactions, the BEGDB water clusters subset, and the WATER23 subset of the GMTKN24 and GMTKN30 benchmark suites. The aVnZ-F12 basis sets displayed excellent performance, not just for electron affinities but also for noncovalent interaction energies of neutral and anionic species. Appropriate CABS (complementary auxiliary basis sets) were explored for the S66 noncovalent interactions benchmark: between similar-sized basis sets, CABS were found to be more transferable than generally assumed., Comment: J. Chem. Phys., in press

We show that the DCSD (distinguishable clusters with all singles and doubles) correlation method permits the calculation of vibrational spectra at near-CCSD(T) quality but at no more than CCSD cost, and with comparatively inexpensive analytical gradients. For systems dominated by a single reference configuration, even MP2.5 is a viable alternative, at MP3 cost. MP2.5 performance for vibrational frequencies is comparable to double hybrids such as DSD-PBEP86-D3BJ, but without resorting to empirical parameters. DCSD is also quite suitable for computing zero-point vibrational energies in computational thermochemistry., Comment: AIP Conference Proceedings, in press (ICCMSE-2017 proceedings), 4 pages

Complementary auxiliary basis sets for F12 explicitly correlated calculations appear to be more transferable between orbital basis sets than has been generally assumed. We also find that aVnZ-F12 basis sets, originally developed with anionic systems in mind, appear to be superior for noncovalent interactions as well, and propose a suitable CABS sequence for them., Comment: AIP Conference Proceedings, in press (ICCMSE-2017 proceedings), 4 pages

In the context of high-accuracy computational thermochemistry, the valence CCSD correlation component of molecular atomization energies present the most severe basis set convergence problem, followed by the (T) component. In the present paper, we make a detailed comparison, for an expanded version of the W4-11 thermochemistry benchmark, between on the one hand orbital-based CCSD/AV{5,6}Z+d and CCSD/ACV{5,6}Z extrapolation, and on the other hand CCSD-F12b calculations with cc-pVQZ-F12 and cc-pV5Z-F12 basis sets. This latter basis set, now available for H--He, B--Ne, and Al--Ar, is shown to be very close to the basis set limit. Apparent differences (which can reach 0.35 kcal/mol for systems like CCl4) between orbital-based and CCSD-F12b basis set limits disappear if basis sets with additional radial flexibility, such as ACV{5,6}Z, are used for the orbital calculation. Counterpoise calculations reveal that, while TAEs with V5Z-F12 basis sets are nearly free of BSSE, orbital calculations have significant BSSE even with AV(6+d)Z basis sets, leading to non-negligible differences between raw and counterpoise-corrected extrapolated limits. This latter problem is greatly reduced by switching to ACV{5,6}Z core-valence basis sets, or simply adding an additional zeta to just the valence orbitals. Previous reports that all-electron approaches like HEAT lead to different CCSD(T) limits than valence limit+CV correction approaches like FPD and W4 theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in CPU time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept., Comment: Journal of Chemical Physics, in press

We have compared the performance of Grimme style DH/DSD and Zhang-Xu-Goddard type xDH/xDSD forms for double hybrids. In the DH and DSD forms, KS orbitals with elevated HF exchange and damped DFT correlation are used, while in the xDH and xDSD forms, the KS orbitals are obtained from a conventional hybrid functional with undamped DFT correlation. Generally, the difference in performance between DSD and xDSD functionals is small, slightly favoring xDSD. Augmentation of the xDH form with either same-spin MP2 correlation or a dispersion correction markedly improves performance. Best xDSD results appear to be obtained for orbitals obtained with `exact exchange' fractions in the 50-70% range. The orbitals for xDSD appear to be fairly transferable between different correlation functionals., Comment: Journal of Chemical Physics, in press