Amir Karton

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 Truhlars 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.

W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions

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 (T4), inclusion of connected quintuple excitations (T5), 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 T4, but is insufficient by itself if the molecule exhibits some nondynamical correlation. The latter considerably slows down basis set convergence for T4, 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+CCSDTQcc-pVDZ-CCSDT(Q)cc-pVDZ] offers a very reliable as well as fairly cost-effective estimate of the basis set limit T4 contribution. The T5 contribution converges very rapidly with the basis set, and even a simple double-zeta basis set appears to be adequate. The largest T5 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.

Model for the exceptional reactivity of peroxiredoxins 2 and 3 with hydrogen peroxide: a kinetic and computational study.

Peroxiredoxins (Prx) are thiol peroxidases that exhibit exceptionally high reactivity toward peroxides, but the chemical basis for this is not well understood. We present strong experimental evidence that two highly conserved arginine residues play a vital role in this activity of human Prx2 and Prx3. Point mutation of either ArgI or ArgII (in Prx3 Arg-123 and Arg-146, which are ∼3–4 Å or ∼6–7 Å away from the active site peroxidative cysteine (Cp), respectively) in each case resulted in a 5 orders of magnitude loss in reactivity. A further 2 orders of magnitude decrease in the second-order rate constant was observed for the double arginine mutants of both isoforms, suggesting a cooperative function for these residues. Detailed ab initio theoretical calculations carried out with the high level G4 procedure suggest strong catalytic effects of H-bond-donating functional groups to the Cp sulfur and the reactive and leaving oxygens of the peroxide in a cooperative manner. Using a guanidinium cation in the calculations to mimic the functional group of arginine, we were able to locate two transition structures that indicate rate enhancements consistent with our experimentally observed rate constants. Our results provide strong evidence for a vital role of ArgI in activating the peroxide that also involves H-bonding to ArgII. This mechanism could explain the exceptional reactivity of peroxiredoxins toward H2O2 and may have wider implications for protein thiol reactivity toward peroxides.

Borane–Lewis Base Complexes as Homolytic Hydrogen Atom Donors

Radical stabilization energies (RSE)s have been calculated for a variety of boryl radicals complexed to Lewis bases at the G3(MP2)-RAD level of theory. These are referenced to the B-H bond dissociation energy (BDE) in BH(3) determined at W4.3 level. High RSE values (and thus low BDE(B-H) values) have been found for borane complexes of a variety of five- and six-membered ring heterocycles. Variations of RSE values have been correlated with the strength of Lewis acid-Lewis base complex formation at the boryl radical stage. The analysis of charge- and spin-density distributions shows that spin delocalization in the boryl radical complexes constitutes one of the mechanisms of radical stabilization.

Accurate reaction barrier heights of pericyclic reactions: Surprisingly large deviations for the CBS-QB3 composite method and their consequences in DFT benchmark studies

Accurate barrier heights are obtained for the 26 pericyclic reactions in the BHPERI dataset by means of the high‐level Wn‐F12 thermochemical protocols. Very often, the complete basis set (CBS)‐type composite methods are used in similar situations, but herein it is shown that they in fact result in surprisingly large errors with root mean square deviations (RMSDs) of about 2.5 kcal mol−1. In comparison, other composite methods, particularly G4‐type and estimated coupled cluster with singles, doubles, and quasiperturbative triple excitations [CCSD(T)/CBS] approaches, show deviations well below the chemical‐accuracy threshold of 1 kcal mol−1. With the exception of SCS‐MP2 and the herein newly introduced MP3.5 approach, all other tested Møller‐Plesset perturbative procedures give poor performance with RMSDs of up to 8.0 kcal mol−1. The finding that CBS‐type methods fail for barrier heights of these reactions is unexpected and it is particularly troublesome given that they are often used to obtain reference values for benchmark studies. Significant differences are identified in the interpretation and final ranking of density functional theory (DFT) methods when using the original CBS‐QB3 rather than the new Wn‐F12 reference values for BHPERI. In particular, it is observed that the more accurate Wn‐F12 benchmark results in lower statistical errors for those methods that are generally considered to be robust and accurate. Two examples are the PW6B95‐D3(BJ) hybrid‐meta‐general‐gradient approximation and the PWPB95‐D3(BJ) double‐hybrid functionals, which result in the lowest RMSDs of the entire DFT study (1.3 and 1.0 kcal mol−1, respectively). These results indicate that CBS‐QB3 should be applied with caution in computational modeling and benchmark studies involving related systems.

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.

A computational chemist's guide to accurate thermochemistry for organic molecules

Composite ab initio methods are multistep theoretical procedures specifically designed to obtain highly accurate thermochemical and kinetic data with confident sub‐kcal mol−1 or sub‐kJ mol−1 accuracy. These procedures include all energetic terms that contribute to the molecular binding energies at these levels of accuracy (e.g., CCSD(T), post‐CCSD(T), core–valence, relativistic, spin‐orbit, Born–Oppenheimer, and zero‐point vibrational energy corrections). Basis‐set extrapolations (and other basis‐set acceleration techniques) are used for obtaining these terms at sufficiently high levels of accuracy. Major advances in computer hardware and theoretical methodologies over the past two decades have enabled the application of these procedures to medium‐sized organic systems (e.g., ranging from benzene and hexane to amino acids and DNA bases). With these advances, there has been a proliferation in the number of developed composite ab initio methods. We give an overview of the accuracy and applicability of the various types of composite ab initio methods that were developed in recent years. General recommendations to guide selection of the most suitable method for a given problem are presented, with a special emphasis on organic molecules. WIREs Comput Mol Sci 2016, 6:292–310. doi: 10.1002/wcms.1249

Post-CCSD(T) ab Initio Thermochemistry of Halogen Oxides and Related Hydrides XOX,XOOX, HOX, XOn, and HXOn (X = F, Cl), and Evaluation of DFT Methods for These Systems

Benchmark-quality W4 (and related) thermochemical data were obtained for the fluorine and chlorine oxides and some related hydrides, all of which are of interest for computational modeling of atmospheric processes. Our best available estimates for total atomization energies at 0 K are the following: HO2 165.97 +/- 0.14, H2O2 252.08 +/- 0.14, HOF 149.24 +/- 0.14, FO 51.17 +/- 0.10, F2O 89.43 +/- 0.14, FO2 130.15 +/- 0.16, F2O2 146.00 +/- 0.16, ClO 63.40 +/- 0.10, HOCl 156.73 +/- 0.14, Cl2O 96.93 +/- 0.16, OClO 122.33 +/- 0.16, ClOO 121.88 +/- 0.32, Cl2O2 142.9 +/- 0.3, ClO3 159.9 +/- 0.4, HClO2 192.0 +/- 0.4, HClO3 258.1 +/- 0.3, and HClO4 313.4 +/- 1 kcal/mol. For several of these species, the total atomization energy contains unusually large components from correlation effects beyond CCSD(T). The geometry of FOOF is significantly affected by connected quadruple excitations. A large variety of DFT exchange-correlation functionals have been evaluated for these systems and observations on their performance are offered. Our best available estimates for deltaHf,0o are the following: HO2 3.65 +/- 0.14, H2O2 -30.82 +/- 0.14, HOF -20.15 +/- 0.14, FO 26.28 +/- 0.11, F2O 6.48 +/- 0.14, FO2 6.30 +/- 0.16, F2O2 8.90 +/- 0.18, ClO 24.19 +/- 0.10, HOCl -17.51 +/- 0.14, Cl2O 19.24 +/- 0.16, OClO 24.26 +/- 0.16, ClOO 24.69 +/- 0.16, Cl2O2 32.3 +/- 0.3, ClO3 45.7 +/- 0.4, HClO2 6.2 +/- 0.4, HClO3 -0.9 +/- 0.3, and HClO4 2.9 +/- 1.0 kcal/mol. (The corresponding values at 298.15 K are 2.96 +/- 0.14, -32.24 +/- 0.14, -20.84 +/- 0.14, 26.43 +/- 0.11, 5.94 +/- 0.14, 5.87 +/- 0.16, 7.84 +/- 0.18, 24.18 +/- 0.10, -18.20 +/- 0.14, 18.82 +/- 0.16, 23.67 +/- 0.16, 24.30 +/- 0.16, 31.5 +/- 0.3, 44.3 +/- 0.4, 5.0 +/- 0.4, -2.6 +/- 0.3, and -0.1 +/- 1.0 kcal/mol, respectively.)

Economical Post-CCSD(T) Computational Thermochemistry Protocol and Applications to Some Aromatic Compounds

To achieve a kilojoules-per-mole level of accuracy consistently in computational thermochemistry, the inclusion of post-CCSD(T) correlation effects cannot be avoided. Such effects are included in the W4 and HEAT computational thermochemistry protocols. The principal bottleneck in carrying out such calculations for larger systems is the evaluation of the T(3)-(T) term. We propose a cost-effective empirical approximation for this term that does not entail any reliance on experimental data. For first-row molecules, our W3.2lite protocol yields atomization energies with a 95% confidence interval of approximately 0.4 kcal/mol at the expense of introducing two such parameters. W3.2lite has been successfully applied to aromatic and aliphatic hydrocarbons such as benzene, fulvene, phenyl radical, pyridine, furan, benzyne isomers, trans-butadiene, cyclobutene, [1.1.1]propellane, and bicyclo[1.1.1]pentane. The W3.2lite predictions for fulvene, phenyl radical, cyclobutene, and [1.1.1]propellane are impossible to reconcile with experiment and suggest that remeasurement may be in order.

Determination of Barrier Heights for Proton Exchange in Small Water, Ammonia, and Hydrogen Fluoride Clusters with G4(MP2)- Type, MPn, and SCS-MPn Procedures-A Caveat

Calculation of accurate water-water interaction energies is of fundamental importance in computational modeling of many biological and chemical phenomena. We have obtained benchmark barrier heights for proton-exchange reactions and complexation energies in water clusters (H2O)n (n = 1-6) by means of the high-level W1-F12 procedure. We find that lower-cost composite procedures (e.g., G4(MP2) and G4(MP2)-6X), as well as MP2 and SCS-MP2, exhibit surprisingly poor performance for the barrier heights of reactions involving multiple proton exchanges. Moreover, the performance significantly deteriorates with increasing size of the clusters. Similar observations apply to complexation energies in water clusters, and to barrier heights for proton exchange in ammonia and hydrogen fluoride clusters. We propose a modified version of G4(MP2)-6X (denoted G4(MP2)-6X+) that includes sp- and d-diffuse functions in the CCSD(T) term, which gives excellent proton-exchange barrier heights at a computational cost only slightly greater than that of standard G4(MP2). G4(MP2)-6X+ also leads to a substantial improvement over G4(MP2) and G4(MP2)-6X for the calculation of electron affinities.