W4 Theory Research Articles

A Metastable Ketenyl Radical-Water Complex from UV Photolysis of the Carboxymethyl Radical.

The unpaired electron impacts the binding between radicals and ordinary closed-shell molecules in noncovalent complexes. Conversely, the complexation partner can enhance, decrease, or even control the reactivity of the interacting radical. Previously, such radical-molecule (and especially radical-water) complexes were studied by controlled assembly of the interacting partners which mostly leads to formation of the thermodynamically most stable species. Here, we show that UV photolysis of the resonance-stabilized carboxymethyl radical isolated in a cryogenic argon matrix at 4 K leads to the intermediary formation of a metastable, noncovalent complex of the ketenyl radical with a water molecule. In this complex, the ketenyl radical binds water at its terminal carbon atom, although a more stable isomer exists in which water interacts with the C-H bond of the radical. Rigorous W1 theory computations confirm that the ketenyl radical is a stronger donor in C-H···O interactions than ketene itself, while it performs comparably well as an acceptor. We propose that complex formation proceeds via an initial excited-state C-O bond breaking reaction in carboxymethyl under release of an OH radical, which is supported by multireference QD-NEVPT2 computations.

Brueckner Doubles variation of W1 theory (W1BD) adapted to pseudopotential: W1BDCEP theory.

Composite methods are the combination of ab initio calculations used to achieve high precision in the face of a computational reduction. Weizmann-n theories (n = 1, 2, 3, and 4) stand out for presenting a high precision, and a version of the W1 theory is the W1BD theory that uses ab initio Brueckner Doubles (BD) methods. One way to reduce the computational cost of composite methods and maintain accuracy is to use pseudopotentials in the calculation steps; in this context, W1BDCEP composite method was developed from the respective W1BD all-electron version by considering the implementation of compact effective pseudopotential (CEP). The test set used to evaluate the theory were 8 proton affinities (PA0), 46 electron affinities (EA0), 54 ionization energies (IE0), 80 enthalpies of formation (ΔfH0), and 10 bond dissociation energies (BDE). The mean absolute deviation values (MADs) for W1BD and for the version adapted to the pseudopotential, W1BDCEP, were similar, with values of 0.97kcalmol-1 and 1.03kcalmol-1, respectively, when the properties PA0, EA0, IE0, and ΔfH0 were evaluated together. Comparing the versions of the theories that employ ab initio Brueckner Doubles calculations with the W1 and W1CEP theories, it is possible to observe that the W1BD and W1BDCEP theories are more accurate than the W1 theory (MADW1 = 1.25kcalmol-1) and W1CEP (MADW1CEP = 1.44kcalmol-1), proving the accuracy of using the BD method. Pseudopotential reduces computational time by up to 30% and thus enables more accurate calculations with less computational time.

W2SDD theory for computational thermochemistry: study of the addition of hydrogen halide to propene

The Weizmann-n theories are characterized by a rigorous and well-defined series of ab initio calculations avoiding any empirical correction. W1 and W2 are two compound methods that aim for high accuracy by combining the results of several calculations. To expand W2 applicability to large molecules, an effective core potential, including relativistic effects, was included in its computational procedure, referred to as W2SDD. The cost-effective (accuracy/computational cost) W2SDD approach has a good performance in predicting both proton affinity and enthalpy of formation for a selected group of molecules containing halide atoms. The values obtained by W2SDD are very close to the original W2 theory. The W2SDD approach has also been applied to the mechanism for the hydrohalogenation of propene, and only one transition state for the reaction mechanism in cyclohexane medium has been found. In addition, the TD-DFT electronic circular dichroism spectrum of 2-chlorobutane shows a signal inversion for the gas-phase versus in cyclohexane solvent.

Benchmark study of DFT and composite methods for bond dissociation energies in argon compounds

We introduce a database of 14 accurate bond dissociation energies (BDEs) of noble gas compounds. Reference CCSD(T)/CBS BDEs are obtained by means of W1 theory. We evaluate the performance of contemporary density functional theory (DFT), double-hybrid DFT (DHDFT), and composite ab initio procedures. A general improvement in performance is observed along the rungs of Jacob’s Ladder; however, only a handful of functionals give good performance for predicting the bond dissociation energies in the NGC14 database. Thus, this database represents a challenging test for DFT methods. Most of the conventional DFT functionals (71%) result in root-mean-square deviations (RMSDs) between 10.0 and 82.1 kJ mol−1. The rest of the DFT functionals attain RMSDs between 2.5 and 8.9 kJ mol−1. The best performing functionals from each rung of Jacob’s Ladder are (RMSD given in parenthesis): HCTH407 (30.9); M06-L (5.4); PBE0 (2.8); B1B95, M06, and PW6B95 (2.7–2.9); CAM-B3LYP-D3 (5.4); and B2T-PLYP (2.5 kJ mol−1).

Thermochemistry of phosphorus sulfide cages: an extreme challenge for high-level ab initio methods

The enthalpies of formation and isomerization energies of P4Sn molecular cages are not experimentally (or theoretically) well known. We obtain accurate enthalpies of formation and isomerization energies for P4Sn cages (n = 3, 4, 5, 6, and 10) by means of explicitly correlated high-level thermochemical procedures approximating the CCSD(T) and CCSDT(Q) energies at the complete basis set (CBS) limit. The atomization reactions have very significant contribution from post-CCSD(T) correlation effects and, due to the presence of many second-row atoms, the CCSD and (T) correlation energies converge exceedingly slowly with the size of the one-particle basis set. As a result, these cage structures are challenging targets for thermochemical procedures approximating the CCSD(T) energy (e.g., W1-F12 and G4). Our best enthalpies of formation at 298 K (∆fH°298) are obtained from thermochemical cycles in which the P4Sn cages are broken down into P2S2 and S2 fragments for which highly accurate ∆fH°298 values are available from W4 theory. For the smaller P4S3 and P4S4 cages, the reaction energies are calculated at the CCSDT(Q)/CBS level and for the larger P4S5, P4S6, and P4S10 cages, they are obtained at the CCSD(T)/CBS level. Our best ∆fH°298 values are − 94.5 (P4S3), − 108.4 (α-P4S4), − 98.7 (β-P4S4), − 126.2 (α-P4S5), − 126.1 (β-P4S5), − 112.7 (γ-P4S5), − 144.7 (α-P4S6), − 153.9 (β-P4S6), − 134.4 (γ-P4S6), − 136.3 (δ-P4S6), − 118.7 (e-P4S6), and − 215.4 (P4S10) kJ mol−1. Interestingly, we find a linear correlation (R2 = 0.992) between the enthalpies of formation of the most stable isomers of each molecular formula and the number of atoms in the P4Sn cages. We use our best ∆fH°298 values to assess the performance of a number of lower-cost composite ab initio methods. For absolute enthalpies of formation, G4(MP2) and G3(MP2)B3 result in the best overall performance with root-mean-square deviations (RMSDs) of 10.6 and 12.9 kJ mol−1, respectively, whereas G3, G3B3, and CBS-QB3 result in the worst performance with RMSDs of 27.0–38.8 kJ mol−1. In contrast to absolute enthalpies of formation, all of the considered composite procedures give a good-to-excellent performance for the isomerization energies with RMSDs below the 5 kJ mol−1 mark.

Toward a W4-F12 approach: Can explicitly correlated and orbital-based ab initio CCSD(T) limits be reconciled?

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.

Acidity of Strong Acids in Water and Dimethyl Sulfoxide.

Careful analysis and comparison of the available acidity data of HCl, HBr, HI, HClO4, and CF3SO3H in water, dimethyl sulfoxide (DMSO), and gas-phase has been carried out. The data include experimental and computational pKa and gas-phase acidity data from the literature, as well as high-level computations using different approaches (including the W1 theory) carried out in this work. As a result of the analysis, for every acid in every medium, a recommended acidity value is presented. In some cases, the currently accepted pKa values were revised by more than 10 orders of magnitude.

A dataset of highly accurate homolytic NBr bond dissociation energies obtained by Means of W2 theory

Homolytic NBr bond dissociation constitutes the initial step of numerous reactions involving N‐brominated species. However, little is known about the strength of NBr bonds toward homolytic cleavage. We herein report accurate bond dissociation energies (BDEs) for a set of 18 molecules using the high‐level W2 thermochemical protocol. The BDEs (at 298 K) of the species in this set range from 162.2 kJ mol−1 (N‐bromopyrrole) to 260.6 kJ mol−1 ((CHO)2NBr). In order to compute BDEs of larger systems, for which W2 theory is not applicable, we have benchmarked a wide range of more economical theoretical procedures. Of these, G3‐B3 offers the best performance (root‐mean‐square deviations = 2.9 kJ mol−1), and using this method, we have computed NBr BDEs for four widely used N‐brominated compounds. These include (BDEs are given in parentheses): N‐bromosuccinimide (281.6), N‐bromoglutarimide (263.2), N‐bromophthalimide (274.7), and 1,3‐dibromo‐5,5‐dimethylhydantoin (218.2 and 264.8 kJ mol−1). © 2015 Wiley Periodicals, Inc.

W1CEP theory for computational thermochemistry

W1 theory is characterized by a rigorous well-defined series of ab initio calculations not explicitly including any empirical adjustment based on experimental results. To expand its applicability to large molecules, a compact effective pseudopotential was included in its computational procedure and the combination is referred to as W1CEP. The values obtained by W1CEP are very close to the original W1 theory, with a mean absolute deviation of 1.2kcalmol−1 for W1 and of 1.4kcalmol−1 for W1CEP. The range of the deviations with a 95% confidence interval are ±3.4kcalmol−1 for W1 and ±4.0kcalmol−1 for W1CEP. In addition to accuracy of the results, another important result is that the calculations using W1CEP decrease the CPU time by 13–30%.

Assessment of Coupled Cluster Theory and more Approximate Methods for Hydrogen Bonded Systems

To assess the accuracy of post-Hartree-Fock methods like CCSD(T), MP3, MP2.5, MP2, SCS-MP2, SOS-MP2, and DFT-SAPT, we evaluated several effects going beyond valence-correlated CCSD(T). For 16 small hydrogen bonded systems, CCSD(T) achieves an RMS error of 0.17 kJ/mol in the dissociation energy compared to our best estimate, which is a composite method akin to W4 theory. The error of CCSD(T) is thus much lower than for atomization energies. MP2 is surprisingly accurate for these systems with an RMS error of 1.3 kJ/mol. MP2.5 yields a clear improvement over MP2 (RMS of 0.5 kJ/mol) but still has an error about 3 times as large as CCSD(T) for the absolute RMS and almost 10 times as large for the relative RMS error. Neither SCS-MP2, SOS-MP2, nor DFT-SAPT yield lower errors than MP2. With a ΔCCSD(T) correction to MP2, the basis set limit is readily achieved when employing diffuse functions-without these, the convergence is rather slow.

Explicitly correlated Wn theory: W1-F12 and W2-F12

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: Δ(f)H(298)(∘) = 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 Δ(f)H(298)(∘)[naphthacene(g)] = 74.25 ± 1 kcal/mol is a more realistic estimate.

O(3P) + CO2 Collisions at Hyperthermal Energies: Dynamics of Nonreactive Scattering, Oxygen Isotope Exchange, and Oxygen-Atom Abstraction

The dynamics of O((3)P) + CO(2) collisions at hyperthermal energies were investigated experimentally and theoretically. Crossed-molecular-beams experiments at <E(coll)> = 98.8 kcal mol(-1) were performed with isotopically labeled (12)C(18)O(2) to distinguish products of nonreactive scattering from those of reactive scattering. The following product channels were observed: elastic and inelastic scattering ((16)O((3)P) + (12)C(18)O(2)), isotope exchange ((18)O + (16)O(12)C(18)O), and oxygen-atom abstraction ((18)O(16)O + (12)C(18)O). Stationary points on the two lowest triplet potential energy surfaces of the O((3)P) + CO(2) system were characterized at the CCSD(T)/aug-cc-pVTZ level of theory and by means of W4 theory, which represents an approximation to the relativistic basis set limit, full-configuration-interaction (FCI) energy. The calculations predict a planar CO(3)(C(2v), (3)A'') intermediate that lies 16.3 kcal mol(-1) (W4 FCI excluding zero point energy) above reactants and is approached by a C(2v) transition state with energy 24.08 kcal mol(-1). Quasi-classical trajectory (QCT) calculations with collision energies in the range 23-150 kcal mol(-1) were performed at the B3LYP/6-311G(d) and BMK/6-311G(d) levels. Both reactive channels observed in the experiment were predicted by these calculations. In the isotope exchange reaction, the experimental center-of-mass (c.m.) angular distribution, T(θ(c.m.)), of the (16)O(12)C(18)O products peaked along the initial CO(2) direction (backward relative to the direction of the reagent O atoms), with a smaller isotropic component. The product translational energy distribution, P(E(T)), had a relatively low average of <E(T)> = 35 kcal mol(-1), indicating that the (16)O(12)C(18)O products were formed with substantial internal energy. The QCT calculations give c.m. P(E(T)) and T(θ(c.m.)) distributions and a relative product yield that agree qualitatively with the experimental results, and the trajectories indicate that exchange occurs through a short-lived CO(3)* intermediate. A low yield for the abstraction reaction was seen in both the experiment and the theory. Experimentally, a fast and weak (16)O(18)O product signal from an abstraction reaction was observed, which could only be detected in the forward direction. A small number of QCT trajectories leading to abstraction were observed to occur primarily via a transient CO(3) intermediate, albeit only at high collision energies (149 kcal mol(-1)). The oxygen isotope exchange mechanism for CO(2) in collisions with ground state O atoms is a newly discovered pathway through which oxygen isotopes may be cycled in the upper atmosphere, where O((3)P) atoms with hyperthermal translational energies can be generated by photodissociation of O(3) and O(2).

Performance of W4 theory for spectroscopic constants and electrical properties of small molecules

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 (r(e)), 1.03 cm(-1) for the harmonic frequencies (ω(e)), 0.20 cm(-1) for the first anharmonicity constants (ω(e)x(e)), 0.10 cm(-1) for the second anharmonicity constants (ω(e)y(e)), and 0.001 cm(-1) for the vibration-rotation coupling constants (α(e)). These RMSDs imply 95% confidence intervals of about 0.1 pm for r(e), 2.0 cm(-1) for ω(e), 0.4 cm(-1) for ω(e)x(e), and 0.2 cm(-1) for ω(e)y(e). We find that post-CCSD(T) contributions are essential to achieve such narrow confidence intervals for r(e) and ω(e), but have little effect on ω(e)x(e) and α(e), and virtually none on ω(e)y(e). 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 r(e), ω(e), and ω(e)x(e), in particular they universally increase r(e) (by up to 0.5 pm), universally reduce ω(e) (by up to 32 cm(-1)), and universally increase ω(e)x(e) (by up to 1 cm(-1)). Connected quintuple excitations T(5) are spectroscopically significant for ω(e) of the nonhydride systems, affecting ω(e) by up to 4 cm(-1). Diagonal Born-Oppenheimer corrections have systematic and spectroscopically significant effects on r(e) and ω(e) of the hydride systems, universally increasing r(e) by 0.01-0.06 pm and decreasing ω(e) by 0.3-2.1 cm(-1). Obtaining r(e) and ω(e) 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 H(2)O, CO(2), and O(3) are also considered. The equilibrium geometries and harmonic frequencies (with the exception of the asymmetric stretch of O(3)) 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.

Performance of Ab Initio and Density Functional Methods for Conformational Equilibria of CnH2n+2 Alkane Isomers (n = 4−8)

Conformational energies of n-butane, n-pentane, and n-hexane have been calculated at the CCSD(T) level and at or near the basis set limit. Post-CCSD(T) contributions were considered and found to be unimportant. The data thus obtained were used to assess the performance of a variety of density functional methods. Double-hybrid functionals like B2GP-PLYP and B2K-PLYP, especially with a small Grimme-type empirical dispersion correction, are capable of rendering conformational energies of CCSD(T) quality. These were used as a “secondary standard” for a larger sample of alkanes, including isopentane and the branched hexanes as well as key isomers of heptane and octane. Popular DFT functionals like B3LYP, B3PW91, BLYP, PBE, and PBE0 tend to overestimate conformer energies without dispersion correction, while the M06 family severely underestimates GG interaction energies. Grimme-type dispersion corrections for these overcorrect and lead to qualitatively wrong conformer orderings. All of these functionals also exhibit deficiencies in the conformer geometries, particularly the backbone torsion angles. The PW6B95 and, to a lesser extent, BMK functionals are relatively free of these deficiencies. Performance of these methods is further investigated to derive conformer ensemble corrections to the enthalpy function, H298 − H0, and the Gibbs energy function, gef(T) ≡ −[G(T) − H0]/T, of these alkanes. These are essential for accurate computed heats of formation of especially the larger species as the corrections for these are several times the expected uncertainty in modern computational thermochemistry methods such as W4 theory. While H298 − H0 is only moderately sensitive to the level of theory, gef(T) exhibits more pronounced sensitivity. Once again, double hybrids acquit themselves very well. The effects of zero-point energy and nonfactorizable rovibrational partition functions have been considered.

Unrestricted Coupled Cluster and Brueckner Doubles Variations of W1 Theory.

Unrestricted coupled cluster spin contamination corrected [UCCSD(T)] and unrestricted Brueckner doubles [UBD(T)] variations of the Weizmann-1 theory (W1), denoted as W1U, W1Usc, and W1BD, respectively, are compared with the restricted open-shell W1 theory [W1(RO)]. The performances of the four W1 variants are assessed with 220 total atomization energies, electron affinities, ionization potentials, and proton affinities in the G2/97 test set, for consistency with the error analysis of the original W1(RO) study. The root-mean-square deviations from the experiment of W1U (0.65 ± 0.48 kcal/mol), W1Usc (0.57 ± 0.48 kcal/mol), W1BD (0.62 ± 0.48 kcal/mol), and W1(RO) (0.57 ± 0.48 kcal/mol) show that the four methods are virtually indistinguishable. This error analysis excludes the "singlet biradicals," C2 and O3, since single determinantal methods are not really adequate for these strongly multireference systems. The unrestricted W1 variants perform poorly for such highly spin-contaminated and multireference species (the largest deviation from experiment for W1Usc is -4.2 ± 0.1 kcal/mol for the O3 EA). W1(RO) performs much better than its unrestricted counterparts for these pathological cases (the deviation from experiment is reduced to -1.5 ± 0.1 kcal/mol for the O3 EA), though the errors are significantly larger than those for the overall test set. The examples of C2, O3, and the F2 potential energy curve indicate that an advantage to using W1BD is that the error in ⟨S(2)⟩ correlates with the magnitude of the error in energy, whereas W1(RO) loses accuracy without such a warning.

Atomization energies of the carbon clusters C n (n = 2−10) revisited by means of W4 theory as well as density functional, Gn, and CBS methods

The thermochemistry of the carbon clusters C n (n = 2−10) has been revisited by means of W4 theory and W3.2lite theory. Particularly, the larger clusters exhibit very pronounced post-CCSD(T) correlation effects. Despite this, our best calculated total atomization energies agree surprisingly well with the 1991 estimates obtained from scaled CCD(ST)/6-31G* data. Accurately reproducing the small singlet–triplet splitting in C2 requires inclusion of connected quintuple and sextuple excitations. Post-CCSD(T) correlation effects in C4 stabilize the linear form. Linear/cyclic equilibria in C6, C8, and C10 are not strongly affected by connected quadruples, but they are affected by higher-order triples, which favor polyacetylenic rings but disfavor cumulenic rings. Near the CCSD(T) basis set limit, C10 does undergo bond angle alternation in the bottom-of-the-well structure, although it is expected to be absent in the vibrationally averaged structure. The thermochemistry of these systems, and particularly the longer linear chains, is a particularly difficult test for density functional methods. Particularly for the smaller chains and the rings, double-hybrid functionals clearly outperform conventional DFT functionals for these systems. Among compound thermochemistry schemes, G4 clearly outperforms the other members of the Gn family. Our best estimates for total atomization energies at 0 K are: C2() 144.07, C2(3Πu) 142.39, C3() 315.83, C4() 429.16, C4(1Ag) 430.09, C5() 596.64, C6() 717.19, C6() 729.68, C7() 877.45, C8() 1001.86, C8(1A g ) 1014.97, C9() 1159.21, C10() 1288.22, and C10() 1355.54 kcal mol−1.

Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics

We present a number of near-exact, nonrelativistic, Born-Oppenheimer reference data sets for the parametrization of more approximate methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochemistry protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small molecules that cover varying degrees of nondynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calculated DFT values with experimental atomization energies is hampered by comparatively large experimental uncertainties in many experimental values and compounds errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. We find that the optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimolecular and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x, y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochemistry and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochemistry and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochemistry, B2GP-PLYP appears to be the more robust toward nondynamical correlation and strongly polar character. We additionally find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.

Basis set convergence of post-CCSD contributions to molecular atomization energies

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, proportional to L(-5/2). Quasiperturbative connected quadruple excitations, (Q), converge smoothly as proportional to 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)(Lambda) 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 "3sigma <or=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.

Heats of Formation of Beryllium, Boron, Aluminum, and Silicon Re-examined by Means of W4 Theory

Benchmark total atomization energies (TAE0 values) were obtained, by means of our recent W4 theory [Karton, A.; Rabinowitz, E.; Martin, J. M. L.; Ruscic, B. J. Chem. Phys. 2006, 125, 144108], for the molecules Be2, BeF2, BeCl2, BH, BF, BH3, BHF2, B2H6, BF3, AlF, AlF3, AlCl3, SiH4, Si2H6, and SiF4. We were then able to deduce "semi-experimental" heats of formation for the elements beryllium, boron, aluminum, and silicon by combining the calculated TAE0 values with experimental heats of formation obtained from reactions that do not involve the species Be(g), B(g), Al(g), and Si(g). The elemental heats of formation are fundamental thermochemical quantities that are required whenever a molecular heat of formation has to be derived from a calculated binding energy. Our recommended DeltaH degrees f,0 [A(g)] values are Be 76.4+/-0.6 kcal/mol, B 135.1+/-0.2 kcal/mol, Al 80.2+/-0.4 kcal/mol, and Si 107.2+/-0.2 kcal/mol. (The corresponding values at 298.15 K are 77.4, 136.3, 80.8, and 108.2 kcal/mol, respectively.) The Be value is identical to the CODATA recommendation (but with half of the uncertainty), while the B, Al, and Si values represent substantial revisions from established earlier reference data. The revised B and Si values are in agreement with earlier semi-ab initio derivations but carry much smaller uncertainties.

Benchmark atomization energy of ethane: Importance of accurate zero-point vibrational energies and diagonal Born–Oppenheimer corrections for a ‘simple’ organic molecule

A benchmark calculation of the atomization energy of the ‘simple’ organic molecule C 2H 6 (ethane) has been carried out by means of W4 theory. While the molecule is straightforward in terms of one-particle and n-particle basis set convergence, its large zero-point vibrational energy (and anharmonic correction thereto) and nontrivial diagonal Born–Oppenheimer correction (DBOC) represent interesting challenges. For the W4 set of molecules and C 2H 6, we show that DBOCs to the total atomization energy are systematically overestimated at the SCF level, and that the correlation correction converges very rapidly with the basis set. Thus, even at the CISD/cc-pVDZ level, useful correlation corrections to the DBOC are obtained. When applying such a correction, overall agreement with experiment was only marginally improved, but a more significant improvement is seen when hydrogen-containing systems are considered in isolation. We conclude that for closed-shell organic molecules, the greatest obstacles to highly accurate computational thermochemistry may not lie in the solution of the clamped-nuclei Schrödinger equation, but rather in the zero-point vibrational energy and the diagonal Born–Oppenheimer correction.