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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]

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]

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]

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]

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]

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]

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]

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]

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]

A new benchmark study has been performed for six isomers of C20 and four isomers of C24 using explicitly correlated methods, together with coupled cluster theory with large basis sets and DFT with advanced functionals. The relative energy trends obtained are extremely sensitive to the methods used. Combining our best CCSD(T)-MP2 difference with our best MP2 basis set limit, the dehydrocorannulene bowl is found to be the most stable for C20, followed by the cage at about 8 kcal/mol, and the ring at about 46 kcal/mol. For C24, the D3d cage is found to be the most stable isomer, followed at only a few kilocalories per mole by dehydrocoronene, and at larger separations by then octahedral cage and the ring, respectively. This makes C24 the smallest classical fullerene. The estimated residual basis set error of the estimated CCSD(T) basis set limit is conservatively expected to be ±1 kcal/mol. In general, DFT exhibits large errors for relative energies with RMSD values in the 8-34 kcal/mol range. However, among the DFT functionals, the DSD-PBEP86-D3BJ double hybrid comes close to our best ab initio results, while the ωB97X-V range-separated hybrid is in semiquantitative agreement. [ABSTRACT FROM AUTHOR]

Such fifth-rung functionals approach the performance of com-posite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives avail-able. In this article, we provide a critical analysis of the varia-bles and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density func-tional theory (DFT), exact exchange, and perturbative correla-tion in both the same spin and opposite spin terms], and the addition of an ad-hoc dispersion correction; we have termed these parametrizations "DSD-DFT" (Dispersion corrected, Spin-component scaled, Double-hybrid DFT). Somewhat surpris-ingly, the quality of DSD-DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD-LDA yielding respectable performance. Simple, non-empirical GGAs appear to work best, whereas meta-GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD-PBEhB95, DSD-PBEP86, DSD-PBEPW91, and DSD-PBEPBE. In addition, DSD-PBEP86 and DSD-PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information. [ABSTRACT FROM AUTHOR]

Using the large and chemically diverse GMTKN55 dataset, we have tested the performance of pure and hybrid KS-DFT and HF-DFT functionals constructed from three variants of the SCAN meta-GGA exchange-correlation functional: original SCAN, rSCAN, and r2SCAN. Without any dispersion correction involved, HF-SCANn outperforms the two other HF-DFT functionals. In contrast, among the self-consistent variants, SCANn and r2SCANn offer essentially the same performance at lower percentages of HF-exchange, while at higher percentages, SCANn marginally outperforms r2SCANn and rSCANn. However, with D4 dispersion correction included, all three HF-DFT-D4 variants perform similarly, and among the self-consistent counterparts, r2SCANn-D4 outperforms the other two variants across the board. In view of the much milder grid dependence of r2SCAN vs. SCAN, r2SCAN is to be preferred across the board, also in HF-DFT and hybrid KS-DFT contexts. [ABSTRACT FROM AUTHOR]

Inearlier work [Gruzman, D.; Karton, A.; Martin, J. M. L.J. Phys. Chem. A2009, 113, 11974], we showed that conformer energiesin alkanes (and other systems) are highly dispersion-driven and thatuncorrected DFT functionals fail badly at reproducing them, whilesimple empirical dispersion corrections tend to overcorrect. To gaingreater insight into the nature of the phenomenon, we have mappedthe torsional surface of n-pentane to 10-degree resolutionat the CCSD(T)-F12 level near the basis set limit. The data obtainedhave been decomposed by order of perturbation theory, excitation level,and same-spin vs opposite-spin character. A large number of approximateelectronic structure methods have been considered, as well as severalempirical dispersion corrections. Our chief conclusions are as follows:(a) the effect of dispersion is dominated by same-spin correlation(or triplet-pair correlation, from a different perspective); (b) singlet-paircorrelation is important for the surface, but qualitatively very dissimilarto the dispersion component; (c) single and double excitations beyondthird order are essentially unimportant for this surface; (d) connectedtriple excitations do play a role but are statistically very similarto the MP2 singlet-pair correlation; (e) the form of the damping functionis crucial for good performance of empirical dispersion corrections;(f) at least in the lower-energy regions, SCS-MP2 and especially MP2.5perform very well; (g) novel spin-component scaled double hybrid functionalssuch as DSD-PBEP86-D2 acquit themselves very well for this problem. [ABSTRACT FROM AUTHOR]

Ab initio and density functional theory (DFT) calculations were performed for obtaining fundamental vibrational frequencies of methylamine, CH3NH2, and its deuterated variants CH3ND2, CD3NH2, and CD3ND2. The calculations were carried out using the CCSD(T) coupled cluster approximation with cc-pVTZ and cc-pVQZ basis sets, and by the DFT method with the semiempirical hybrid functional B97-1 with polarization consistent pc-2 and pc-3 basis sets. Reasonable performance of the DFT harmonic and ab initio harmonic calculations was found, which improved considerably upon combination of the harmonic fundamental frequencies with anharmonic corrections from the smaller, pc-2, basis. The computed anharmonic fundamental frequencies of methylamine isotopologues agree very well with the experimental values and represent a useful tool for assignment and analysis of the dominant resonances. © 2007 Wiley Periodicals, Inc. J Comput Chem, 2008 [ABSTRACT FROM AUTHOR]

The high-accuracy W4 computational thermochemistry protocol, and several post-W4 methods, have been applied to the P2 and P4 molecules. Contrary to previous studies, we find the experimental thermochemistry to be fundamentally sound. The reaction enthalpy for P4→2P2 has a very significant contribution from post-CCSD(T) correlation effects. We derive a gas-phase heat of formation for the phosphorus atom of [image omitted] kcal mol-1 and [image omitted] kcal mol-1, in the upper half of the CODATA uncertainty interval. [ABSTRACT FROM AUTHOR]

We demonstrate that a minor modification of the extrapolation proposed by Jensen [(2005): Theor Chem Acc 113: 267] yields very reliable estimates of the Hartree–Fock limit in conjunction with correlation consistent basis sets. Specifically, a two-point extrapolation of the form $$E_{{\rm HF},L} = E_{{\rm HF},\infty} + A(L + 1)\exp (- 9{\sqrt {L}})$$ yields HF limits E HF,∞ with an RMS error of 0.1 millihartree using aug-cc-pVQZ and aug-cc-pV5Z basis sets, and of 0.01 millihartree using aug-cc-pV5Z and aug-cc-pV6Z basis sets. [ABSTRACT FROM AUTHOR]

The heats of formation of haloacetylenes are evaluated using the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects, and (where relevant) first-order spin-orbit coupling. The heats of formation determined using W2 theory are: ΔH[sup 298][sub f](HCCH) = 54.48 kcal mol[sup -1], ΔH [sup 298](HCCF) = 25.15 kcal mol[sup -1], ΔH [sup 298][sub f](FCCF) = 1.38 kcal mol[sup -1], ΔH [sup 298][sub f](HCCCl) = 54.83 kcal mol[sup -1], ΔH [sup 298](ClCCCl) = 56.21 kcal mol[sup -1], and ΔH [sup 298][sub f](FCCCl) = 28.47 kcal mol[sup -1]. Enthalpies of hydrogenation and destabilization energies relative to acetylene were obtained at the W1 level of theory. So doing we find the following destabilization order for acetylenes: FCCF > ClCCF > HCCF > ClCCCl > HCCCl > HCCH. By a combination of W1 theory and isodesmic reactions, we show that the generally accepted heat of formation of 1,2-dichloroethane should be revised to -31.8 ± 0.6 kcal mol[sup -1], in excellent agreement with a very recent critically evaluated review. The performance of compound thermochemistry schemes, such as G2, G3, G3X and CBSQB3 theories, has been analysed. [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]

From large basis set coupled cluster calculations and a minor empirical adjustment, an anharmonic force field for silane has been derived that is consistently of spectroscopic quality (1 cm-1 on vibrational fundamentals) for all isotopomers of silane studied. Inner-shell polarization functions have an appreciable effect on computed properties and even on anharmonic corrections. From large basis set coupled cluster calculations and extrapolations to the infinite-basis set limit, we obtain TAE0 = 303:80 0:18 kcal mol- 1, which includes an anharmonic zero-point energy (19.59 kcal mol- 1), inner-shell correlation (-0.36 kcal mol-1), scalar relativistic corrections (-0.70 kcal mol- 1) and atomic spin-orbit corrections (- 0.43 kcal mol- 1). In combination with the recently revised H f [sub 0][Si(g)], we obtain H f ;0[SiH4(g)] = 9:9 0:4 kcal mol- 1 in between the two established experimental values. [ABSTRACT FROM AUTHOR]

A benchmark ab initio study on the thermochemistry of the trans -HNNH, cis -HNNH, and H2NN isomers of diazene has been carried out using the CCSD(T) coupled cluster method, basis sets as large as [7s6p5d4f3g2h/5s4p3d2f1g], and extrapolations towards the 1-particle basis set limit. The effects on inner shell correlation and of anharmonicity in the zero-point energy were taken into account: thus accurate geometries and anharmonic force fields were obtained as by-products. The best computed DeltaHof0 for trans-HNNH, 49.2-0.3kcal mol-1, is in very good agreement with a recent experimental lower limit of 48.8 0.5kcal mol-1. CCSD(T) basis set limit values for the isomerization energies at 0K are 5.2 0.2kcal mol-1 (cis-trans) and 24.1 0.2kcal mol-1 (iso-trans). Our best computed geometry for trans-HNNH, reNN = 1.2468A, (NH) = 1.0283A, and thetae = 106.17o, reproduces the precisely known ground state rotational constants of trans-HNNH to within better than 0.1%. The rotation-vibration spectra of both cis-HNNH and H2NN are dominated by very strong Coriolis and Fermi resonances. In addition, the NH stretches in H2NN are so strongly anharmonic that vibrational perturbation theory breaks down, and the molecule appears to be an excellent test case for variational treatments of the vibrational Schrodinger equation. [ABSTRACT FROM AUTHOR]

The Suzuki–Miyaura cross-coupling reaction with the SPhos ligand was studied with DFT and analyzed within the energetic span model. With this information, we designed a modification to the SPhos (the “InPhos”), which theoretically corrects the deficiencies of the prior ligand. [ABSTRACT FROM AUTHOR]

The adiabatic electron affinity (AEA) of SF6 has been calculated near the relativistic CCSDT(Q) basis set limit. Our best theoretical value (1.0340 ± 0.03 eV) is in excellent agreement with the recently revised experimental value of 1.03 ± 0.05 eV reported by Troe et al. [J. Chem. Phys. 136, 121102 (2012)]. While our best nonrelativistic, clamped-nuclei, valence CCSD(T) basis set limit value of 0.9058 eV is in good accord with the previously reported CCSD(T)/CBS values, to obtain an accurate AEA, several additional contributions need to be taken into account. The most important one is scalar-relativistic effects (0.0839 eV), followed by inner-shell correlation (0.0216 eV) and post-CCSD(T) correlation effects (0.0248 eV), the latter almost entirely due to connected quadruple excitations. The diagonal Born-Oppenheimer correction is an order of magnitude less important at -0.0022 eV. [ABSTRACT FROM AUTHOR]

The performance of two recent ab initio computational thermochemistry schemes, W1 and W2 theory [J. M. L. Martin and G. de Oliveira, J. Chem. Phys. 111, 1843 (1999)], is assessed for an enlarged sample of thermochemical data consisting of the ionization potentials and electron affinities in the G2-1 and G2-2 sets, as well as the heats of formation in the G2-1 and a subset of the G2-2 set. We find W1 theory to be several times more accurate for ionization potentials and electron affinities than commonly used (and less expensive) computational thermochemistry schemes such as G2, G3, and CBS-QB3: W2 theory represents a slight improvement for electron affinities but no significant one for ionization potentials. The use of a two-point A+B/L[sup 5] rather than a three-point A+B/C[sup L] extrapolation for the self-consistent field (SCF) component greatly enhances the numerical stability of the W1 method for systems with slow basis set convergence. Inclusion of first-order spin-orbit coupling is essential for accurate ionization potentials and electron affinities involving degenerate electronic states: Inner-shell correlation is somewhat more important for ionization potentials than for electron affinities, while scalar relativistic effects are required for the highest accuracy. The mean deviation from experiment for the G2-1 heats of formation is within the average experimental uncertainty. W1 theory appears to be a valuable tool for obtaining benchmark quality proton affinities. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We propose large-core correlation-consistent (cc) pseudopotential basis sets for the heavy p-block elements Ga-Kr and In-Xe. The basis sets are of cc-pVTZ and cc-pVQZ quality, and have been optimized for use with the large-core (valence-electrons only) Stuttgart-Dresden-Bonn (SDB) relativistic pseudopotentials. Validation calculations on a variety of third-row and fourth-row diatomics suggest them to be comparable in quality to the all-electron cc-pVTZ and cc-pVQZ basis sets for lighter elements. Especially the SDB-cc-pVQZ basis set in conjunction with a core polarization potential (CPP) yields excellent agreement with experiment for compounds of the later heavy p-block elements. For accurate calculations on Ga (and, to a lesser extent, Ge) compounds, explicit treatment of 13 valence electrons appears to be desirable, while it seems inevitable for In compounds. For Ga and Ge, we propose correlation consistent basis sets extended for (3d) correlation. For accurate calculations on organometallic complexes of interest to homogenous catalysis, we recommend a combination of the standard cc-pVTZ basis set for first- and second-row elements, the presently derived SDB-cc-pVTZ basis set for heavier p-block elements, and for transition metals, the small-core [6s5p3d] Stuttgart-Dresden basis set-relativistic effective core potential combination supplemented by (2f1g) functions with exponents given in the Appendix to the present paper. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Core correlation and scalar relativistic contributions to the atomization energy of 120 first- and second-row molecules have been determined using coupled cluster and averaged coupled-pair functional methods and the MTsmall core correlation basis set. These results are used to parametrize an improved version of a previously proposed bond order scheme for estimating contributions to atomization energies. The resulting model, which requires negligible computational effort, reproduces the computed core correlation contributions with 88%-94% average accuracy (depending on the type of molecule), and the scalar relativistic contribution with 82%-89% accuracy. This permits high-accuracy thermochemical calculations at greatly reduced computational cost. © 2000 American Institute of Physics. [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]

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]