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In two recent papers [A. D. Becke, J. Chem. Phys. 156, 214101 (2022) and A. D. Becke, J. Chem. Phys. 157, 234102 (2022)], we compared two Kohn–Sham density functionals based on physical modeling 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 general main-group thermochemistry, kinetics, and noncovalent interactions (GMTKN55) chemical database of Goerigk et al. [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 density functional with the lowest GMTKN55 WTMAD2 "weighted total mean absolute deviation" error (1.76 kcal/mol) yet seen for any hybrid or double-hybrid density-functional approximation. We call it "DH23." [ABSTRACT FROM AUTHOR]

Partial charges are a central concept in general chemistry and chemical biology, yet dozens of different computational definitions exist. In prior work [Cho et al., ChemPhysChem21, 688‐696 (2020)], we showed that these can be reduced to at most three 'principal components of ionicity'. The present study addressed the dependence of 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 GAPT. 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 nonlocal correlation is important, especially when there is a substantial amount of nonlocal exchange. Employing range separation proves to be "mostly" not advantageous, while global hybrids perform optimally for 20%–30% Hartree‐Fock exchange across all charge types. Basis set convergence analysis shows that an augmented triple‐zeta heavy‐aug‐cc‐pV(T+d)Z basis set or a partially augmented jun‐cc‐pV(T+d)Z basis set is sufficient for Hirshfeld, Hirshfeld‐I, HLY, and GAPT charges. In contrast, QTAIM and NPA display slower basis set convergence. It is noteworthy that for both NPA and QTAIM, HF exhibits markedly slower basis set convergence than the correlation components of MP2 and CCSD. Triples corrections in CCSD(T), denoted as CCSD(T)‐CCSD, exhibit even faster basis set convergence. [ABSTRACT FROM AUTHOR]

Minimally empirical G4-like composite wavefunction theories [E. Semidalas and J. M. L. Martin, J. Chem. Theory Comput.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-n, cc-G4-n, and G4-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} $ 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} $ − 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-pVmZ and [CCSD(T)-MP2]/ano-pVTZ (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. [ABSTRACT FROM AUTHOR]

The importance of post-CCSD(T) corrections as high as CCSDTQ56 for ground-state spectroscopic constants ( $ D_e $ D e , $ \omega _e $ ω e , $ \omega _ex_e $ ω e x e , and $ \alpha _e $ α 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 } $ Λ 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 } $ Λ vs. CCSDTQ5, while CCSDTQ5(6) $ _{\Lambda } $ Λ is essentially indistinguishable from CCSDTQ56. A composite of CCSD(T)-X2C/ACV5Z-X2C with [CCSDT(Q) $ _{\Lambda } $ Λ – 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 } $ Λ handles them gracefully. [ABSTRACT FROM AUTHOR]

A detailed mechanistic density functional theory (DFT) and coupled cluster study of Csp²−H activation in benzene and methyl acrylate by the catalyst RuClm(CO)n (m=2,3; n=0–4) is presented. We trace the entire reaction pathways from the precursor to the active form of the catalysts followed by catalytic hydroarylation and oxidative coupling reactions. Our results reveal that both computational methods provide very similar qualitative pictures, but only the coupled cluster DLPNO‐CCSD(T1) results are quantitatively consistent with experiment. At the latter level of theory, the Ru(II) and Ru(III) catalyst precursors transform into the same active form of the catalyst, which explains the experimental results. Oxidative addition is extremely endergonic, especially in the presence of CO. Oxidative hydrogen migration (OHM) occurs in complexes with a low Ru coordination number and leads to olefine hydroarylation. Strongly bound carbonyl ligands suppress this interaction. Concerted metalation‐deprotonation (CMD) of the aromatic C−H bond and σ‐bond metathesis mechanisms of catalyst regeneration do not involve Ru−H bonding and form the energetically favorable catalytic cycle of the oxidative coupling reaction. The key interaction in CMD mechanisms consists of proton abstraction by an inner‐sphere Cl‐anion. Carbonyl ligands facilitate CMD by weakening the Ru−Cl bond. An excess of CO slows the interaction by leading to replacement of the reactants in the Ru coordination sphere. [ABSTRACT FROM AUTHOR]

The benzene–ethene and parallel-displaced (PD) benzene–benzene dimers are the most fundamental systems involving π–π stacking interactions. Several high-level ab initio investigations calculated the binding energies of these dimers using the coupled-cluster with singles, doubles, and quasi-perturbative triple excitations [CCSD(T)] method at the complete basis set [CBS] limit 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 self-consistent field (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 ∆Ee,all,rel = 1.234 (benzene–ethene) and 2.550 (benzene–benzene PD), ∆H0 = 0.949 (benzene–ethene) and 2.310 (benzene–benzene PD), and ∆H298 = 0.130 (benzene–ethene) and 1.461 (benzene–benzene PD) kcal mol−1. 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−1, and thus, they cannot be neglected if sub-chemical accuracy is sought (i.e., errors below 0.1 kcal mol−1). CCSD(T)/aug-cc-pwCVTZ core–valence corrections increase the binding energies by 0.018 (benzene–ethene) and 0.027 (benzene–benzene PD) kcal mol−1. Scalar-relativistic and diagonal Born–Oppenheimer corrections are negligibly small. We use our best CCSDT(Q) binding energies to evaluate the performance of MP2-based, CCSD-based, and lower-cost composite ab initio procedures for obtaining these challenging π–π stacking binding energies. [ABSTRACT FROM AUTHOR]

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 values differ by 0.1 kcal mol−1 RMS from the original Hobza benchmark and its revision by Brauer et al., but by only 0.04 kcal mol−1 RMS from the "bronze" level data in Kesharwani et al., Aust. J. Chem., 2018, 71, 238–248. 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, ωB97M-V, ωB97M(2), revDSD-PBEP86-D4, and DFT(SAPT) with a TDEXX or ATDEXX kernel. [ABSTRACT FROM AUTHOR]

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 convergence to the basis set limit of CCSD (coupled cluster theory with all single and double excitations) and of different approximate implementations of CCSD-F12 (explicitly correlated CCSD) has been investigated in 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 ±0.04 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. [ABSTRACT FROM AUTHOR]

Explicitly correlated calculations, aside from the orbital basis set, typically require three auxiliary basis sets: Coulomb‐exchange fitting (JK), resolution of the identity MP2 (RI‐MP2), and complementary auxiliary basis set (CABS). 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), the W4‐08 thermochemical benchmark, and the HFREQ2014 set of harmonic frequencies, 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. [ABSTRACT FROM AUTHOR]

We have developed a new basis set family, denoted as 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 atoms), 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 Benchmark Energy and Geometry Data Base water cluster 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 CABSs (complementary auxiliary basis sets) were explored for the S66 noncovalent interaction benchmark: between similarsized basis sets, CABSs were found to be more transferable than generally assumed. [ABSTRACT FROM AUTHOR]

In the context of high-accuracy computational thermochemistry, the valence coupled cluster with all singles and doubles (CCSD) correlation component of molecular atomization energies presents 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 total atomization energies 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 (high-accuracy extrapolated ab-initio thermochemistry) lead to different CCSD(T) limits than "valence limit+CV correction" approaches like Feller-Peterson-Dixon and Weizmann-4 (W4) theory can be rationalized in terms of the greater radial flexibility of core-valence basis sets. For (T) corrections, conventional CCSD(T)/AV{Q,5}Z+d calculations are found to be superior to scaled or extrapolated CCSD(T)-F12b calculations of similar cost. For a W4-F12 protocol, we recommend obtaining the Hartree-Fock and valence CCSD components from CCSD-F12b/cc-pV{Q,5}Z-F12 calculations, but the (T) component from conventional CCSD(T)/aug'-cc-pV{Q,5}Z+d calculations using Schwenke's extrapolation; post-CCSD(T), core-valence, and relativistic corrections are to be obtained as in the original W4 theory. W4-F12 is found to agree slightly better than W4 with ATcT (active thermochemical tables) data, at a substantial saving in computation time and especially I/O overhead. A W4-F12 calculation on benzene is presented as a proof of concept. [ABSTRACT FROM AUTHOR]

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 "Jacob's 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. [ABSTRACT FROM AUTHOR]

In an attempt to extend the applicability of the W1 and W2 ab initio computational thermochemistry methods, we propose explicitly correlated versions thereof, denoted W1-F12 and W2-F12. In W2-F12, we can 'save' one cardinal number (viz., angular momentum) in the basis set sequences without loss in accuracy; in W1-F12, we can do so for first-row compounds but not for second-row compounds. At a root mean square deviation (RMSD) = 0.19 kcal/mol for the first-row molecules in the W4-11 benchmark dataset, W1-F12 is in fact superior to ordinary W1 theory. For the entire W4-11 set, W2-F12 yields a RMSD = 0.20 kcal/mol, comparable to 0.19 kcal/mol from ordinary W2 theory. The extended applicability ranges of W1-F12 and W2-F12 are not just due to the lower computational cost but also to greatly reduced memory and especially storage requirements. They are illustrated through applications to nucleic acids and to polyacenes (with up to four rings), for which the following revised gas-phase heats of formation are found: ΔfH298° = 19.6 (benzene), 34.94 (naphthalene), 53.9, (anthracene), 73.9 (naphthacene/tetracene), 54.9 (adenine), -16.3 (cytosine), 5.1 (guanine), -80.6 (thymine), and -71.6 (uracil) kcal/mol. Our theoretical values for the DNA/RNA bases largely confirm recent predictions based on much lower-level calculations. The W1-F12 theoretical values for benzene, naphthalene, and anthracene are in very good to reasonable agreement with experiment. However, both W1-F12 and other computational estimates show that the accepted experimental value for naphthacene cannot be reconciled with those for the lower acenes: we suggest that ΔfH298°[naphthacene(g)] = 74.25 ± 1 kcal/mol is a more realistic estimate. [ABSTRACT FROM AUTHOR]

Accurate spectroscopic constants and electrical properties of small molecules are determined by means of W4 and post-W4 theories. For a set of 28 first- and second-row diatomic molecules for which very accurate experimental spectroscopic constants are available, W4 theory affords near-spectroscopic or better predictions. Specifically, the root-mean-square deviations (RMSDs) from experiment are 0.04 pm for the equilibrium bond distances (re), 1.03 cm-1 for the harmonic frequencies (ωe), 0.20 cm-1 for the first anharmonicity constants (ωexe), 0.10 cm-1 for the second anharmonicity constants (ωeye), and 0.001 cm-1 for the vibration-rotation coupling constants (αe). These RMSDs imply 95% confidence intervals of about 0.1 pm for re, 2.0 cm-1 for ωe, 0.4 cm-1 for ωexe, and 0.2 cm-1 for ωeye. We find that post-CCSD(T) contributions are essential to achieve such narrow confidence intervals for re and ωe, but have little effect on ωexe and αe, and virtually none on ωeye. Higher-order connected triples T⁁3-(T) improve the agreement with experiment for the hydride systems, but their inclusion (in the absence of T⁁4) tends to worsen the agreement with experiment for the nonhydride systems. Connected quadruple excitations T⁁4 have significant and systematic effects on re, ωe, and ωexe, in particular they universally increase re (by up to 0.5 pm), universally reduce ωe (by up to 32 cm-1), and universally increase ωexe (by up to 1 cm-1). Connected quintuple excitations T⁁5 are spectroscopically significant for ωe of the nonhydride systems, affecting ωe by up to 4 cm-1. Diagonal Born-Oppenheimer corrections have systematic and spectroscopically significant effects on re and ωe of the hydride systems, universally increasing re by 0.01-0.06 pm and decreasing ωe by 0.3-2.1 cm-1. Obtaining re and ωe of the pathologically multireference BN and BeO systems with near-spectroscopic accuracy requires large basis sets in the core-valence CCSD(T) step and augmented basis sets in the valence post-CCSD(T) steps in W4 theory. The triatomic molecules H2O, CO2, and O3 are also considered. The equilibrium geometries and harmonic frequencies (with the exception of the asymmetric stretch of O3) are obtained with near-spectroscopic accuracy at the W4 level. The asymmetric stretch of ozone represents a severe challenge to W4 theory, in particular the connected quadruple contribution converges very slowly with the basis set size. Finally, the importance of post-CCSD(T) correlation effects for electrical properties, namely, dipole moments (μ), polarizabilities (α), and first hyperpolarizabilities (β), is evaluated. [ABSTRACT FROM AUTHOR]

Basis set convergence of correlation effects on molecular atomization energies beyond the coupled cluster with singles and doubles (CCSD) approximation has been studied near the one-particle basis set limit. Quasiperturbative connected triple excitations, (T), converge more rapidly than L-3 (where L is the highest angular momentum represented in the basis set), while higher-order connected triples, T3-(T), converge more slowly—empirically, ∝L-5/2. Quasiperturbative connected quadruple excitations, (Q), converge smoothly as ∝L-3 starting with the cc-pVTZ basis set, while the cc-pVDZ basis set causes overshooting of the contribution in highly polar systems. Higher-order connected quadruples display only weak, but somewhat erratic, basis set dependence. Connected quintuple excitations converge very rapidly with the basis set, to the point where even an unpolarized double-zeta basis set yields useful numbers. In cases where fully iterative coupled cluster up to connected quintuples (CCSDTQ5) calculations are not an option, CCSDTQ(5) (i.e., coupled cluster up to connected quadruples plus a quasiperturbative connected quintuples correction) cannot be relied upon in the presence of significant nondynamical correlation, whereas CCSDTQ(5)Λ represents a viable alternative. Connected quadruples corrections to the core-valence contribution are thermochemically significant in some systems. We propose an additional variant of W4 theory [A. Karton et al., J. Chem. Phys. 125, 144108 (2006)], denoted W4.4 theory, which is shown to yield a rms deviation from experimental atomization energies (active thermochemical tables, ATcT) of only 0.05 kcal/mol for systems for which ATcT values are available. We conclude that “3σ≤=1 kJ/mol” thermochemistry is feasible with current technology, but that the more ambitious goal of ±10 cm-1 accuracy is illusory, at least for atomization energies. [ABSTRACT FROM AUTHOR]

In an attempt to improve on our earlier W3 theory [A. D. Boese et al., J. Chem. Phys. 120, 4129 (2004)] we consider such refinements as more accurate estimates for the contribution of connected quadruple excitations (T⁁4), inclusion of connected quintuple excitations (T⁁5), diagonal Born-Oppenheimer corrections (DBOC), and improved basis set extrapolation procedures. Revised experimental data for validation purposes were obtained from the latest version of the Active Thermochemical Tables thermochemical network. The recent CCSDT(Q) method offers a cost-effective way of estimating T⁁4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T⁁4, and anomalous basis set convergence in highly polar systems makes two-point extrapolation procedures unusable. However, we found that the CCSDTQ-CCSDT(Q) difference converges quite rapidly with the basis set, and that the formula 1.10[CCSDT(Q)/cc-pVTZ+CCSDTQ/cc-pVDZ-CCSDT(Q)/cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit T⁁4 contribution. The T⁁5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T⁁5 contribution found in the present work is on the order of 0.5 kcal/mol (for ozone). DBOCs are significant at the 0.1 kcal/mol level in hydride systems. Post-CCSD(T) contributions to the core-valence correlation energy are only significant at that level in systems with severe nondynamical correlation effects. Based on the accumulated experience, a new computational thermochemistry protocol for first- and second-row main-group systems, to be known as W4 theory, is proposed. Its computational cost is not insurmountably higher than that of the earlier W3 theory, while performance is markedly superior. Our W4 atomization energies for a number of key species are in excellent agreement (better than 0.1 kcal/mol on average, 95% confidence intervals narrower than 1 kJ/mol) with the latest experimental data obtained from Active Thermochemical Tables. Lower-cost variants are proposed: the sequence W1→W2.2→W3.2→W4lite→W4 is proposed as a converging hierarchy of computational thermochemistry methods. A simple a priori estimate for the importance of post-CCSD(T) correlation contributions (and hence a pessimistic estimate for the error in a W2-type calculation) is proposed. [ABSTRACT FROM AUTHOR]

A density functional theory exchange-correlation functional for the exploration of reaction mechanisms is proposed. This functional, denoted BMK (Boese-Martin for Kinetics), has an accuracy in the 2 kcal/mol range for transition state barriers but, unlike previous attempts at such a functional, this improved accuracy does not come at the expense of equilibrium properties. This makes it a general-purpose functional whose domain of applicability has been extended to transition states, rather than a specialized functional for kinetics. The improvement in BMK rests on the inclusion of the kinetic energy density together with a large value of the exact exchange mixing coefficient. For this functional, the kinetic energy density appears to correct “back” the excess exact exchange mixing for ground-state properties, possibly simulating variable exchange. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We are proposing a new computational thermochemistry protocol denoted W3 theory, as a successor to W1 and W2 theory proposed earlier [Martin and De Oliveira, J. Chem. Phys. 111, 1843 (1999)]. The new method is both more accurate overall (error statistics for total atomization energies approximately cut in half) and more robust (particularly towards systems exhibiting significant nondynamical correlation) than W2 theory. The cardinal improvement rests in an approximate account for post-CCSD(T) correlation effects. Iterative T[sub 3] (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T[sub 3] contribution overall. They almost universally decrease molecular binding energies. Their inclusion in isolation yields less accurate results than CCSD(T) nearly across the board: It is only when T[sub 4] (connected quadruple excitations) effects are included that superior performance is achieved. T[sub 4] effects systematically increase molecular binding energies. Their basis set convergence is quite rapid, and even CCSDTQ/cc-pVDZ scaled by an empirical factor of 1.2532 will yield a quite passable quadruples contribution. The effect of still higher-order excitations was gauged for a subset of molecules (notably the eight-valence electron systems): T[sub 5] (connected quintuple excitations) contributions reach 0.3 kcal/mol for the pathologically multireference X [sup 1]Σ[sub g][sup +] state of C[sub 2] but are quite small for other systems. A variety of avenues for achieving accuracy beyond that of W3 theory were explored, to no significant avail. W3 thus appears to represent a good compromise between accuracy and computational cost for those seeking a robust method for computational thermochemistry in the kJ/mol accuracy range on small systems. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In addition, the dependency of the semiempirical fits to a given basis set for a generalized gradient approximation and a hybrid functional is investigated. The resulting functionals are then tested for other basis sets, evaluating their errors and transferability. [ABSTRACT FROM AUTHOR]

The total atomization energy at absolute zero, (TAE[sub 0]) of benzene, C[sub 6]H[sub 6], was computed fully ab initio by means of W2h theory as 1306.6 kcal/mol, to be compared with the experimentally derived value 1305.7±0.7 kcal/mol. The computed result includes contributions from inner-shell correlation (7.1 kcal/mol), scalar relativistic effects (-1.0 kcal/mol), atomic spin–orbit splitting (-0.5 kcal/mol), and the anharmonic zero-point vibrational energy (62.1 kcal/mol). The largest-scale calculations involved are CCSD/cc-pV5Z and CCSD(T)/cc-pVQZ; basis set extrapolations account for 6.3 kcal/mol of the final result. Performance of more approximate methods has been analyzed. Our results suggest that, even for systems the size of benzene, chemically accurate molecular atomization energies can be obtained from fully first-principles calculations, without resorting to corrections or parameters derived from experiment. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised 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. [ABSTRACT FROM AUTHOR]

The inner-shell correlation contributions to the total atomisation energies 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 n: however, there are considerable differences in convergence behaviour 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, 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, we recommend a previously proposed combination of CCSD-F12b/cc-pCVTZ-F12 and CCSD(T)/pwCVTZ(no f). While in first-row molecules core-valence correlation on average accounts for over 90% of the inner-shell contribution, in second-row molecules core-core contributions may become important, particularly in systems like P4 and S4 with multiple adjacent second-row atoms. [ABSTRACT FROM AUTHOR]

The quartic force field of cyclic C4 has been computed using basis sets of spdf quality and augmented coupled cluster methods. The effect of core correlation and further basis set extension has been investigated. Vibrational energy levels have been obtained using perturbation theory and two different variational approaches. A severe Fermi resonance exists between the most intense vibration, ν6, and ν3+ν5 through an exceptionally large k356=-258.2 cm-1; a large k1356 =-54.8 cm-1 causes significant higher-order anharmonicity, including a shift in ν6 of +9 cm-1. C4 appears to be an excellent test case for methods for solving the vibrational Schrödinger equation, since perturbation theory breaks down even when the above resonances are accounted for. Our best estimate for ν6, 1320±10 cm-1, may suggest its assignment to a feature detected at 1284 cm-1 in argon and 1302 cm-1 in krypton matrix, but this would imply an unusually large matrix red shift in argon. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the 12C isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals are reproduced to better than 10 cm-1, except for three cases where the error is 11 cm-1. Our calculated harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: Both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch–bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the ν8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper via the World-Wide Web. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The total atomization energies of the carbon clusters Cn (n=2–10) have been calculated ab initio using augmented coupled-cluster methods and basis sets of spdf and spdfg quality. The values agree to within experimental uncertainty with recent Knudsen effusion measurements for Cn (n=2–7), but suggest actual values on the high side of their experimental range. For the odd-numbered clusters, an additivity approximation holds very well, and extrapolated ∑D0 values are proposed for C11, C13, C15, C17, and C19. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A very accurate ab initio quartic force field for CH4 and its isotopomers is presented. The quartic force field was determined with the singles and doubles coupled-cluster procedure that includes a quasiperturbative estimate of the effects of connected triple excitations, CCSD(T), using the correlation consistent polarized valence triple zeta, cc-pVTZ, basis set. Improved quadratic force constants were evaluated with the correlation consistent polarized valence quadruple zeta, cc-pVQZ, basis set. Fundamental vibrational frequencies are determined using second-order perturbation theory anharmonic analyses. All fundamentals of CH4 and isotopomers for which accurate experimental values exist and for which there is not a large Fermi resonance, are predicted to within ±6 cm-1. It is thus concluded that our predictions for the harmonic frequencies and the anharmonic constants are the most accurate estimates available. It is also shown that using cubic and quartic force constants determined with the correlation consistent polarized double zeta, cc-pVDZ, basis set in conjunction with the cc-pVQZ quadratic force constants and equilibrium geometry leads to accurate predictions for the fundamental vibrational frequencies of methane, suggesting that this approach may be a viable alternative for larger molecules. Using CCSD(T), core correlation is found to reduce the CH4 re by 0.0015 Å. Our best estimate for re is 1.0862±0.0005 Å. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The potential energy surface for the B2C molecule and the potential energy curve for the ground state of BC have been investigated using full-valence complete active space SCF (CASSCF), augmented coupled cluster [CCSD(T)] and multireference treatments. The ground state of B2C is an extraordinarily stable ring (∑ De=261.6±1 kcal/mol) with two 2-electron π systems. The first excited state is linear BCB (1Σ+g), which is essentially biconfigurational due to a (4σg)–(3σu) near degeneracy. Anharmonic spectroscopic constants were obtained from quartic force fields at the CCSD(T) level with a correlation-consistent basis set of [4s3p2d1f] quality. A severe Fermi resonance exists between the bending and symmetric stretching modes. All computed intensities are fairly weak. Spectroscopic constants for BC using elaborate multireference techniques were very well reproduced using the CCSD(T) method with a spin-restricted Hartree–Fock reference configuration, but not with an unrestricted Hartree–Fock reference. This suggests that even moderate levels of spin contamination that do not significantly affect relative energies may have a detrimental effect on computed spectroscopic constants. [ABSTRACT FROM AUTHOR]

The total atomization energies (∑De values), geometries, and harmonic frequencies for a number of experimentally well-described molecules have been calculated at the CCSD(T) (coupled cluster) level using Dunning’s correlation-consistent cc-pVDZ([3s2p1d]), cc-pVTZ([4s3p2d1f]), and cc-pVQZ([5s4p3d2f1g]) basis sets. Additivity correction are proposed for binding energies and geometries. Using a three-term additive correction of the form proposed by Martin [J. Chem. Phys. 97, 5012 (1992)] mean absolute errors in ∑De are 0.46 kcal/mol for the cc-pVQZ, 0.93 for the cc-pVTZ, and 2.59 for the c-pVDZ basis sets. The latter figure implies that, although unsuitable for quantitatively accurate work, three-term corrected CCSD(T)/cc-pVDZ binding energies can still be used for a rough estimate when the cost of larger basis set calculations would be prohibitive. CCSD(T)/cc-pVQZ calculations reproduce bond lengths to 0.001 Å for single bonds, and 0.003 Å for multiple bonds; remaining error is probably partly due to core–core and core–valence correlation. CCSD(T)/cc-pVTZ calculations result in additional overestimates of 0.001 Å for single, 0.003 Å for double, and 0.004 Å for triple bonds. CCSD(T)/cc-pVDZ calculations result in further overestimates of 0.01 Å for single bonds, and 0.02 Å for multiple bonds.CCSD(T)/cc-pVDZ harmonic frequencies are in surprisingly good agreement with experiment, except for pathological cases like the umbrella mode in NH3. Both CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ harmonic frequencies generally agree with experiment to 10 cm-1 or better; performance of cc-pVQZ is somewhat superior on multiple bonds or the umbrella mode in NH3. Again, a source of remaining error appears to be core correlation. The use of MP2/6-31G* reference geometries in the ∑De calculation can result in fairly substantial errors in the uncorrected ∑De values for systems with cumulated multiple bonds.... [ABSTRACT FROM AUTHOR]

Pulsed laser evaporation of pellets pressed from boron and graphite powder gave a new 1:4 doublet at 1232.5 and 1194.6 cm-1 in addition to the carbon cluster absorptions reported previously. The 1232.5 cm-1 band dominated boron-10 experiments. The new bands increased as carbon cluster bands decreased with increasing B/C ratio in the pellet and with increasing laser power. Augmented coupled cluster and full-valence complete active space SCF (CASSCF) calculations predict the global minimum BC2 structure to be an asymmetric triangle: however, the vibrationally averaged structure will be an isosceles triangle with a strong symmetric B–C2 stretching frequency near 1200 cm-1. The calculated boron-10/boron-11 frequency ratio (1.0323) is in excellent agreement with the observed ratio (1.0317), and confirms assignment of the 1194.6 cm-1 band to the BC2 ring. Calculations predict linear BCC to be less stable by 6.2±2 kcal/mol and to absorb in the 2000–2050 cm-1 range: the barrier towards rearrangement to the cyclic structure is very low (1.1 kcal/mol). Linear BCC was not detected in these experiments. Computed energetics explain why BC2 is abundant in B/C experiments, but absent in B+C2H2 experiments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The S66 benchmark for non-covalent 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 non-covalent 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, whereas half-counterpoise CCSD (F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost. [ABSTRACT FROM AUTHOR]

The reactivity of the H5PV2Mo10O40 polyoxometalate and its analogues as an electron transfer and electron transfer–oxygen transfer oxidant has been extensively studied in the past and has been shown to be useful in many transformations. One of the hallmarks of this oxidant is the possibility of its re-oxidation with molecular oxygen, thus enabling aerobic catalytic cycles. Although the re-oxidation reaction was known, the kinetics and mechanism of this reaction have not been studied in any detail. Experimentally, we show that both the one- and two-electron reduced polyoxometalate are reactive with O2, the two-electron one more so. The reactions are first-order in the polyoxometalate and O2. Solvents also have a considerable effect, protic solvents being preferred over aprotic ones. H5PV2Mo10O40 was reduced either by an electron transfer reaction (H2) or an electron transfer–oxygen transfer reaction (Ph3P). Similar rate constants and activation parameters were observed for both. DFT calculations carried out on the re-oxidation reactions strongly suggest an inner-sphere process. The process involves first the formation of a coordinatively unsaturated site (CUS) and subsequently the binding of O2 to form superoxo and then peroxo η2-O2 adducts. Most interestingly, although vanadium is the reactive redox centre as well as a necessary component for the oxidative activity of H5PV2Mo10O40, and a CUS can be formed at both Mo and V sites, O2 coordination occurs mostly at the Mo CUSs, preferably those where the vanadium centers are distal to each other. [ABSTRACT FROM AUTHOR]

The notoriously small X 3Π-a 1Σ+ excitation energy of the BN diatomic has been calculated using high-order coupled cluster methods. Convergence has been established in both the one-particle basis set and the coupled cluster expansion. Explicit inclusion of connected quadruple excitations T⁁4 is required for even semiquantitative agreement with the limit value, while connected quintuple excitations T⁁5 still have an effect of about 60 cm-1. Still higher excitations only account for about 10 cm-1. Inclusion of inner-shell correlation further reduces Te by about 60 cm-1 at the CCSDT, and 85 cm-1 at the CCSDTQ level. Our best estimate, Te=183±40 cm-1, is in excellent agreement with earlier calculations and experiment, albeit with a smaller (and conservative) uncertainty. The dissociation energy of BN(X 3Π) is De=105.74±0.16 kcal/mol and D0=103.57±0.16 kcal/mol. [ABSTRACT FROM AUTHOR]

Atomization reactions are among the most challenging tests for electronic structure methods. We use the first-principles Weizmann-4 (W4) computational thermochemistry protocol to generate the W4-17 dataset of 200 total atomization energies (TAEs) with 3σ confidence intervals of 1 kJ mol−1. W4-17 is an extension of the earlier W4-11 dataset; it includes first- and second-row molecules and radicals with up to eight non-hydrogen atoms. These cover a broad spectrum of bonding situations and multireference character, and as such are an excellent benchmark for the parameterization and validation of highly accurate ab initio methods (e.g., CCSD(T) composite procedures) and double-hybrid density functional theory (DHDFT) methods. The W4-17 dataset contains two subsets (i) a non-multireference subset of 183 systems characterized by dynamical or moderate nondynamical correlation effects (denoted W4-17-nonMR) and (ii) a highly multireference subset of 17 systems (W4-17-MR). We use these databases to evaluate the performance of a wide range of CCSD(T) composite procedures (e.g., G4, G4(MP2), G4(MP2)-6X, ROG4(MP2)-6X, CBS-QB3, ROCBS-QB3, CBS-APNO, ccCA-PS3, W1, W2, W1-F12, W2-F12, W1X-1, and W2X) and DHDFT methods (e.g., B2-PLYP, B2GP-PLYP, B2K-PLYP, DSD-BLYP, DSD-PBEP86, PWPB95, ωB97X-2(LP), and ωB97X-2(TQZ)). © 2017 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

Noncovalent interactions between molecules are key for many biological processes. Necessarily, when molecules interact, the electronic charge in each of them is redistributed. Here, we show experimentally that, in chiral molecules, charge redistribution is accompanied by spin polarization. We describe how this spin polarization adds an enantioselective term to the forces, so that homochiral interaction energies differ from heterochiral ones. The spin polarization was measured by using a modified Hall effect device. An electric field that is applied along the molecules causes charge redistribution, and for chiral molecules, a Hall voltage is measured that indicates the spin polarization. Based on this observation, we conjecture that the spin polarization enforces symmetry constraints on the biorecognition process between two chiral molecules, and we describe how these constraints can lead to selectivity in the interaction between enantiomers based on their handedness. Model quantum chemistry calculations that rigorously enforce these constraints show that the interaction energy for methyl groups on homochiral molecules differs significantly from that found for heterochiral molecules at van der Waals contact and shorter (i.e., -0.5 kcal/mol at 0.26 nm). [ABSTRACT FROM AUTHOR]

The S66x8 dataset for noncovalent interactions of biochemical relevance has been re-examined by means of MP2-F12 and CCSD(F12*)(T) methods. We deem our revised benchmark data to be reliable to about 0.05 kcal mol−1 RMS. Most levels of DFT perform quite poorly in the absence of dispersion corrections: somewhat surprisingly, that is even the case for the double hybrids and for dRPA75. Analysis of optimized D3BJ parameters reveals that the main benefit of dRPA75 and DSD double hybrids alike is the treatment of midrange dispersion. dRPA75-D3BJ is the best performer overall at RMSD = 0.10 kcal mol−1. The nonlocal VV10 dispersion functional is especially beneficial for the double hybrids, particularly in DSD-PBEP86-NL (RMSD = 0.12 kcal mol−1). Other recommended dispersion-corrected functionals with favorable price/performance ratios are ̉B97X-V, and, surprisingly, B3LYP-D3BJ and BLYP-D3BJ (RMSDs of 0.23, 0.20 and 0.23 kcal mol−1, respectively). Without dispersion correction (but parametrized for midrange interactions) M06-2X has the lead (RMSD = 0.45 kcal mol−1). A collection of three energy-based diagnostics yields similar information to an SAPT analysis about the nature of the noncovalent interaction. Two of those are the percentages of Hartree–Fock and of post-MP2 correlation effects in the interaction energy; the third, CSPI = [IE(2)ss− IE(2)ab]/[IE(2)ss + IE(2)ab] or its derived quantity DEBC = CSPI/(1 + CSPI2)1/2, describes the character of the MP2 correlation contribution, ranging from 0 (purely dispersion) to 1 (purely other effects). In addition, we propose an improved, parameter-free scaling for the (T) contribution based on the Ecorr[CCSD-F12b]/Ecorr[CCSD] and Ecorr[CCSD(F12*)]/Ecorr[CCSD] ratios. For Hartree–Fock and conventional DFT calculations, full counterpoise generally yields the fastest basis set convergence, while for double hybrids, half-counterpoise yields faster convergence, as previously established for correlated ab initio methods. [ABSTRACT FROM AUTHOR]

Hydrocarbon cages are key reference materials for the validation and parameterization of computationally cost-effective procedures such as density functional theory (DFT), semiempirical molecular orbital theory, and molecular mechanics. We obtain accurate total atomization energies (TAEs) and heats of formation (Δ fH°298) for platonic and prismatic hydrocarbon cages by means of the W n-F12 explicitly correlated thermochemical protocols. We consider the following kinetically stable (CH) n polycyclic hydrocarbon cages: (i) platonic hydrocarbons (tetrahedrane, cubane, and dodecahedrane), (ii) prismatic hydrocarbons (triprismane, cubane, and pentaprismane), and (iii) one truncated tetrahedrane (octahedrane). Our best theoretical heat of formation for cubane (144.8 kcal mol−1) suggests that the experimental value adopted by the NIST thermochemical database (142.7 ± 1.2 kcal mol−1) should be revised upwards by ∼2 kcal mol−1. Our best heat of formation for dodecahedrane (20.2 kcal mol−1) suggests that the semiexperimental value (22.4 ± 1 kcal mol−1) should be revised downward by ∼2 kcal mol−1. We use our benchmark W n-F12 TAEs to evaluate the performance of a variety of computationally less demanding composite thermochemical procedures. These include the Gaussian- n (G n) and the complete basis set (CBS) methods. The CBS-QB3 and CBS-APNO procedures show relatively poor performance with root-mean-squared deviations (RMSDs) of 4.2 and 2.5 kcal mol−1, respectively. The best performers of the G n procedures are G4 and G3(MP2)B3 (RMSD = 0.5 and 0.6 kcal mol−1, respectively), while the worst performers are G3 and G4(MP2)-6X (RMSD = 2.1 and 2.9 kcal mol−1, respectively). Isodesmic and even homodesmotic reactions involving these species are surprisingly challenging targets for DFT computations. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]