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.

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.

An experimental and detailed chemical kinetic modeling study of hydrogen and syngas mixture oxidation at elevated pressures

Laminar flame speeds and ignition delay times have been measured for hydrogen and various compositions of H2/CO (syngas) at elevated pressures and elevated temperatures. Two constant-volume cylindrical vessels were used to visualize the spherical growth of the flame through the use of a schlieren optical setup to measure the laminar flame speed of the mixture. Hydrogen experiments were performed at initial pressures up to 10 atm and initial temperatures up to 443 K. A syngas composition of 50/50 by volume was chosen to demonstrate the effect of carbon monoxide on H2−O2 chemical kinetics at standard temperature and pressures up to 10 atm. All atmospheric mixtures were diluted with standard air, while all elevated-pressure experiments were diluted with a He:O2 of 7:1 to minimize instabilities. The laminar flame speed measurements of hydrogen and syngas are compared to available literature data over a wide range of equivalence ratios where good agreement can be seen with several data sets. Additionally, an improved chemical kinetics model is shown for all conditions within the current study. The model and the data presented herein agree well, which demonstrates the continual, improved accuracy of the chemical kinetic model.A high-pressure shock tube was used to measure ignition delay times for several baseline compositions of syngas at three pressures across a wide range of temperatures. The compositions of syngas (H2/CO) by volume presented in this study included 80/20, 50/50, 40/60, 20/80, and 10/90, all of which are compared to previously published ignition delay times from a hydrogen-oxygen mixture to demonstrate the effect of carbon monoxide addition. Generally, an increase in carbon monoxide increases the ignition delay time, but there does seem to be a pressure dependency. At low temperatures and pressures higher than about 12 atm, the ignition delay times appear to be indistinguishable with an increase in carbon monoxide. However, at high temperatures the relative composition of H2 and CO has a strong influence on ignition delay times. Model agreement is good across the range of the study, particularly at the elevated pressures. Also, an increase in carbon monoxide causes the activation energy of the mixture to decrease.© 2012 ASME

Laminar Flame Speed and Ignition Delay Time Data for the Kinetic Modeling of Hydrogen and Syngas Fuel Blends

By combining the generalized valence bond ansatz of correlated participating orbitals (CPO) with the complete-active-space prescription for selecting configurations and with the use of multireference second order perturbation theory (MRMP2) for including dynamical correlation, we define three levels of multireference (MR) theoretical model chemistries for electronic structure calculations of chemical reaction energies and barrier heights. The three levels differ in their choice of which orbitals are considered to be participating; the choices are called nominal (nom-CPO), moderate (mod-CPO), and extended (ext-CPO). Combining any of these three choices with a method for treatment of dynamical correlation energy and a one-electron basis set yields a theoretical model chemistry. Unlike the full-valence choice of active orbitals, the CPO choices lead to active spaces that contain the orbitals needed to include important static correlation effects on chemical reactions but do not increase with the size of the nonparticipating portion of the system, and hence they remain viable computational options even for many large and complex reacting systems. The accuracies of the new levels, combined with the MG3S basis set (a partially augmented, multiply polarized valence triple-ζ basis with appropriately tight d functions for 3p-block elements) and with the fully augmented correlation-consistent aug-cc-pVTZ basis set, are assessed against a previously presented database of barrier heights for diverse reaction types. We find that nom-CPO level captures the bulk of the static correlation energy, and MRMP2/nom-CPO calculations have an average error of only 1.4 kcal/mol in barrier heights, which may be compared to 5.0 kcal/mol for single-reference MP2 theory, 2.5 kcal/mol for CCSD, and 4.1 and 1.0 kcal/mol for the B3LYP and M06-2X density functionals, respectively. The accuracy of MRMP2/CPO for transition structure bond lengths and donor-acceptor distances is excellent, with a mean unsigned error of only 0.007 A as compared to 0.018 A for CCSD, 0.019 A for M06-2X, and 0.039 A for MP2 and B3LYP. We also introduce a new multireference diagnostic, called the M diagnostic, that allows one to measure the importance of static correlation in a given reagent or transition state.

Multireference Model Chemistries for Thermochemical Kinetics.

The 1,3-dipolar cycloadditions of ozone to ethyne and ethene provide extreme examples of multireference singlet-state chemistry, and they are examined here to test the applicability of several approaches to thermochemical kinetics of systems with large static correlation. Four different multireference diagnostics are applied to measure the multireference characters of the reactants, products, and transition states; all diagnostics indicate significant multireference character in the reactant portion of the potential energy surfaces. We make a more complete estimation of the effect of quadruple excitations than was previously available, and we use this with CCSDT/CBS estimation of Wheeler et al. (Wheeler, S. E.; Ess, D. H.; Houk, K. N. J. Phys. Chem. A 2008, 112, 1798.) to make new best estimates of the van der Waals association energy, the barrier height, and the reaction energy to form the cycloadduct for both reactions. Comparing with these best estimates, we present comprehensive mean unsigned errors f...

Thermochemical Kinetics for Multireference Systems: Addition Reactions of Ozone

Rate coefficients are calculated using canonical variational transition state theory with multidimensional tunneling (CVT/SCT) for the reactions H + H2O2 → H2O + OH (1a) and H + H2O2 → HO2 + H2 (1b). Reaction barrier heights are determined using two theoretical approaches:  (i) comparison of parametrized rate coefficient calculations employing CVT/SCT to experiment and (ii) high-level ab initio methods. The evaluated experimental data reveal considerable variations of the barrier height for the first reaction:  although the zero-point-exclusive barrier for (1a) derived from the data by Klemm et al. (First Int. Chem. Kinet. Symposium 1975, 61) is 4.6 kcal/mol, other available measurements result in a higher barrier of 6.2 kcal/mol. The empirically derived zero-point-exclusive barrier for (1b) is 10.4 kcal/mol. The electronic structure of the system at transition state geometries in both reactions was found to have “multireference” character; therefore special care was taken when analyzing electronic struct...

Daniel P. Theis

Papers

Reactions of hydrogen atom with hydrogen peroxide.