High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification

The recently developed high-accuracy extrapolated ab initio thermochemistry method for theoretical thermochemistry, which is intimately related to other high-precision protocols such as the Weizmann-3 and focal-point approaches, is revisited. Some minor improvements in theoretical rigor are introduced which do not lead to any significant additional computational overhead, but are shown to have a negligible overall effect on the accuracy. In addition, the method is extended to completely treat electron correlation effects up to pentuple excitations. The use of an approximate treatment of quadruple and pentuple excitations is suggested; the former as a pragmatic approximation for standard cases and the latter when extremely high accuracy is required. For a test suite of molecules that have rather precisely known enthalpies of formation {as taken from the active thermochemical tables of Ruscic and co-workers [Lecture Notes in Computer Science, edited by M. Parashar (Springer, Berlin, 2002), Vol. 2536, pp. 25-38; J. Phys. Chem. A 108, 9979 (2004)]}, the largest deviations between theory and experiment are 0.52, -0.70, and 0.51 kJ mol(-1) for the latter three methods, respectively. Some perspective is provided on this level of accuracy, and sources of remaining systematic deficiencies in the approaches are discussed.     

Ab initio thermal rate coefficients for H + NH3 ⇌ H2 + NH2

The reversible reaction NH₃ + H ⇌ H₂ + NH₂, which plays an important role in NH₃ fuel combustion, is studied with a theoretical approach that combines the high-accuracy extrapolated ab initio thermochemistry (HEAT) protocol with semiclassical transition state theory (SCTST). The calculated forward reaction is endothermic by 11.8 ± 1 kJ/mol, in nearly perfect agreement with the active thermochemical tables (ATcT) value of 11.5 ± 0.2 kJ/mol. Using this improved thermochemistry yields better rate constants, especially at low temperatures. Experimental rate constants available from 400 to 2000 K for the forward and reverse reaction pathways can be reproduced (within 20%) by the calculations from first principles.     

Towards highly accurate ab initio thermochemistry of larger systems: benzene

The high accuracy extrapolated ab initio thermochemistry (HEAT) protocol is applied to compute the total atomization energy (TAE) and the heat of formation of benzene. Large-scale coupled-cluster calculations with more than 1500 basis functions and 42 correlated electrons as well as zero-point energies based on full cubic and (semi)diagonal quartic force fields obtained with the coupled-cluster singles and doubles with perturbative treatment of the triples method and atomic natural orbital (ANO) triple- and quadruple-zeta basis sets are presented. The performance of modifications to the HEAT scheme and the scaling properties of its contributions with respect to the system size are investigated. A purely quantum-chemical TAE and associated conservative error bar of 5463.0 ± 3.1 kJ mol(-1) are obtained, while the corresponding 95% confidence interval, based on a statistical analysis of HEAT results for other and related molecules, is ± 1.8 kJ mol(-1). The heat of formation of benzene is determined to be 101.5 ± 2.0 kJ mol(-1) and 83.9 ± 2.1 kJ mol(-1) at 0 K and 298.15 K, respectively.     

Accurate thermochemistry from quantum chemical calculations?

The answer to the title question is definitely “yes” – at least for fairly small molecules. Computational procedures, namely the Weizmann (Wn) and Gaussian-3 (G3) family of methods, the complete basis set extrapolation scheme (CBS-x), the “high accuracy extrapolated ab initio thermochemistry” (HEAT) as well as the “correlation consistent composite approach” (ccCA), aimed at energies with chemical accuracy or even better (sub kJ?mol^?1) are described and several applications illustrating the level of accuracy that can be achieved are presented.     

High-accuracy extrapolated ab initio thermochemistry of vinyl chloride

Applying a modified "high accuracy extrapolated ab initio thermochemistry" (HEAT) scheme, the standard heat of formation of vinyl chloride at 0 K is computed to be 29.79 +/- 1 kJ/mol and at 298.15 K to be 20.9 +/- 2 kJ/mol, thus resolving earlier discrepancies among the available experimental values, which span a range from 21 up to 38 kJ/mol. The enthalpies of the reactions C2H4 + Cl2 --> CH2CHCl + HCl and C2H2 + HCl --> CH2CHCl at 298.15 K are determined to be -123.0 and -113.9 +/- 2 kJ/mol, respectively.     

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

Previously, master equation (ME) simulations using semiclassical transition state theory (SCTST) and high-accuracy extrapolated ab initio thermochemistry (HEAT) predicted rate constants in excellent agreement with published experimental data over a wide range of pressure and temperatures ≳250 K, but the agreement was not as good at lower temperatures. Possible reasons for this reduced performance are investigated by (a) critically evaluating the published experimental data and by investigating; (b) three distinct ME treatments of angular momentum, including one that is exact at the zero- and infinite-pressure limits; (c) a hindered-rotor model for HOCO that implicitly includes the cis- and trans-conformers; (d) possible empirical adjustments of the thermochemistry; (e) possible empirical adjustments to an imaginary frequency controlling tunneling; (f) including or neglecting the prereaction complex PRC1; and (g) its possible bimolecular reactions. Improvements include better approximations to factors in SCTST and using the Hill and van Vleck treatment of angular momentum coupling. Evaluation of literature data does not reveal any specific shortcomings, but the stated uncertainties may be underestimated. All ME treatments give excellent fits to experimental data at T ≥ 250 K, but the discrepancy at T < 250 K persists. Note that each ME model requires individual empirical energy transfer parameters. Thermochemical adjustments were unable to match the experimental H/D kinetic isotope effects. Adjusting an imaginary frequency can achieve good fits, but the adjustments are unacceptably large. Whether PRC1 and its possible bimolecular reactions are included had little effect. We conclude that none of the adjustments is an improvement over the unadjusted theory. Note that only one set of experimental data exists in the regime of the discrepancy with theory, and data for DO + CO are scanty.     

Influence of coadsorbates on the NO dissociation on a rhodium(311) surface.

Density functional theory (DFT) studies were performed to investigate the influence of coadsorbates on the nitrogen oxide dissociation on the vicinal rhodium(311) surface. This study amplifies prior studies on the dissociation of oxygen and nitrogen oxide on the (111) facet of rhodium. The influence of coadsorbates on the kinetic parameters and thermochemistry of the NO dissociation on Rh311 was studied. In addition, the activation energy and thermochemistry of this reaction were determined as a function of oxygen preoccupation/initial coverage. Steric and electronic effects and their influence on the dissociation reaction were examined. The results are discussed in the face of an NOx dissociation catalyst system proposed by Nakatsuji.     

Accurate thermochemistry and spectroscopy of the oxygen-protonated sulfur dioxide isomers

Despite the promising relevance of protonated sulfur dioxide in astrophysical and atmospheric fields, its thermochemical and spectroscopic characterization is very limited. High-level quantum-chemical calculations have shown that the most stable isomer is the cis oxygen-protonated sulfur dioxide, HOSO(+), while the trans form is about 2 kcal mol(-1) less stable; even less stable (by about 42 kcal mol(-1)) is the S-protonated isomer [V. Lattanzi et al., J. Chem. Phys., 2010, 133, 194305]. The enthalpy of formation for the cis- and trans-HOSO(+) is presented, based on the well tested HEAT protocol [A. Tajti et al., J. Chem. Phys., 2004, 121, 11599]. Systematically extrapolated ab initio energies, accounting for electron correlation through coupled cluster theory, including up to single, double, triple and quadruple excitations, have been corrected for core-electron correlation, anharmonic zero-point vibrational energy, diagonal Born-Oppenheimer and scalar relativistic effects. As a byproduct, proton affinity of sulfur dioxide and atomization energies have also been obtained at the same levels of theory. Vibrational and rotational spectroscopic properties have been investigated by means of composite schemes that allow us to account for truncation of basis set as well as core correlation. Where available, for both thermochemistry and spectroscopy, very good agreement with experimental data has been observed.     

W3 theory: robust computational thermochemistry in the kJ/mol accuracy range

We are proposing a new computational thermochemistry protocol denoted W3 theory, as a successor to W1 and W2 theory proposed earlier [Martin and De Oliveira, J. Chem. Phys. 111, 1843 (1999)]. The new method is both more accurate overall (error statistics for total atomization energies approximately cut in half) and more robust (particularly towards systems exhibiting significant nondynamical correlation) than W2 theory. The cardinal improvement rests in an approximate account for post-CCSD(T) correlation effects. Iterative T3 (connected triple excitations) effects exhibit a basis set convergence behavior similar to the T3 contribution overall. They almost universally decrease molecular binding energies. Their inclusion in isolation yields less accurate results than CCSD(T) nearly across the board: It is only when T4 (connected quadruple excitations) effects are included that superior performance is achieved. T4 effects systematically increase molecular binding energies. Their basis set convergence is quite rapid, and even CCSDTQ/cc-pVDZ scaled by an empirical factor of 1.2532 will yield a quite passable quadruples contribution. The effect of still higher-order excitations was gauged for a subset of molecules (notably the eight-valence electron systems): T5 (connected quintuple excitations) contributions reach 0.3 kcal/mol for the pathologically multireference X 1Sigmag+ state of C2 but are quite small for other systems. A variety of avenues for achieving accuracy beyond that of W3 theory were explored, to no significant avail. W3 thus appears to represent a good compromise between accuracy and computational cost for those seeking a robust method for computational thermochemistry in the kJ/mol accuracy range on small systems.     

The Thermochemistry of London Dispersion-Driven Transition Metal Reactions: Getting the ‘Right Answer for the Right Reason’

Reliable thermochemical measurements and theoretical predictions for reactions involving large transition metal complexes in which long-range intramolecular London dispersion interactions contribute significantly to their stabilization are still a challenge, particularly for reactions in solution. As an illustrative and chemically important example, two reactions are investigated where a large dipalladium complex is quenched by bulky phosphane ligands (triphenylphosphane and tricyclohexylphosphane). Reaction enthalpies and Gibbs free energies were measured by isotherm titration calorimetry (ITC) and theoretically ‘back-corrected’ to yield 0 K gas-phase reaction energies (ΔE). It is shown that the Gibbs free solvation energy calculated with continuum models represents the largest source of error in theoretical thermochemistry protocols. The (‘back-corrected’) experimental reaction energies were used to benchmark (dispersion-corrected) density functional and wave function theory methods. Particularly, we investigated whether the atom-pairwise D3 dispersion correction is also accurate for transition metal chemistry, and how accurately recently developed local coupled-cluster methods describe the important long-range electron correlation contributions. Both, modern dispersion-corrected density functions (e.g., PW6B95-D3(BJ) or B3LYP-NL), as well as the now possible DLPNO-CCSD(T) calculations, are within the ‘experimental’ gas phase reference value. The remaining uncertainties of 2–3 kcal mol⁻¹ can be essentially attributed to the solvation models. Hence, the future for accurate theoretical thermochemistry of large transition metal reactions in solution is very promising.     

Further evidence for the inseparability of the theoretical enthalpic terminal and penultimate unit effects in the radical copolymerization of styrene with acrylonitrile

The theoretical enthalpies of propagation reactions at 0 K without zero‐point vibrational energy corrections according to terminal and penultimate models of the radical copolymerization of styrene with acrylonitrile are reported from molecular orbital calculations at the following levels of theory and basis sets: HF/6‐31G(d); B3‐LYP/6‐31G(d); B3‐LYP/6‐311G(d,p) and B3‐LYP/6‐311+G(3df)//6‐311G(d,p). Both the enthalpic terminal and penultimate unit effects, determined according to the theoretical thermochemistry, depend on the level of theory and basis set used for the molecular orbital calculations. The best performing B3LYP/6‐311+G(3df)//B3LYP/6‐311G(d,p) procedure gives theoretical enthalpies for the addition of styrene and acrylonitrile to CH that differ from experimental values by 0.6 and 1.6 kcal mol^?1, respectively. An analysis of the results obtained here leads to the conclusion that at least for the styrene–acrylonitrile monomer system, that is, a monomer system known as one of the few systems that do not conform to terminal model composition and microstructure equations, the enthalpic terminal unit effects seem to depend on the penultimate units of the growing radical. This finding, together with the outcome from our previous work on the dependence of the penultimate effects on the terminal units in a growing macroradical, indicates the inseparability of the enthalpic terminal (implicit) and explicit penultimate unit effects on the radical copolymerization. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1778–1787, 2003     

Reactivity and core-ionization energies in conjugated dienes. Carbon 1s photoelectron spectroscopy of 1,3-pentadiene

The high-resolution carbon 1s photoelectron spectrum of trans-1,3-pentadiene has been resolved into contributions from the five inequivalent carbon atoms, and carbon 1s ionization energies have been assigned to each of these atoms. Spectra have also been measured for propene and 1,3-butadiene at better resolution than has previously been available. The ionization energies for the sp2 carbons are found to correlate well with activation energies for electrophilic addition and with proton affinities. Comparing the results for 1,3-pentadiene with those for ethene, propene, and 1,3-butadiene as well as with results of theoretical calculations makes it is possible to assess the effect of the terminal methyl group in 1,3-pentadiene. As in propene, the methyl group contributes electrons to the beta carbon through the pi system. In addition, there is a significant (though smaller) contribution from the methyl group to the terminal (delta) CH2 carbon, also through the pi system. Most of the effect of the methyl group is present in the ground-state molecule. There are only relatively small contributions from the methyl group to the ionization energies from redistribution of charge in the pi system in response to the removal of a core electron. In addition to these specific effects, there is an overall decrease in average ionization energy as the size of the molecule increases as well as effects that are specific to the conjugated systems in 1,3-butadiene and 1,3-pentadiene. The results provide insight into the reactivity and regioselectivity of conjugated dienes.     

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.     

Some observations on the kinetics and thermochemistry of the reactions of HO2 radicals with aldehydes and ketones

The rapid, gas phase equilibrium addition of HO₂ radicals to CH₂O to form the peroxy radical HOCH₂OO^? is in agreement with the known thermochemistry of these species. The recent study of the similar addition of HO₂^? to ketones shows no significant reaction, which is again in agreement with known thermochemistry. All these reactions are notable for significant dipole attraction between the reactants ranging from 3 to 7 kcal/mol. The thermochemistry shows that the hydroperoxyl alkoxy species, the primary possible adduct, is not favored by the free energy change for direct addition. This and the observed kinetics favor a concerted addition, H‐atom transfer, as the transition state for the reactions. Kinetic estimates for forward and reverse reactions are in good agreement with observations. A thermochemical examination of the step‐wise addition of HO₂^? to the carbonyl shows that the reaction proceeds through a concerted, cyclic transition state involving simultaneous H‐transfer, 3 + 2 cyclo‐addition of HO₂^? to the carbonyl group. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 509–512, 2001     

Organic nitriles from acid chlorides: an isovalent N for (O)CL exchange reaction mediated by a tungsten nitride complex

Nitride NW(N[i-Pr]Ar)3 (1, Ar = 3,5-C6H3Me2) was synthesized in two steps from known NW(O-t-Bu)3 (41% overall yield). Complex 1 is the tungsten congener of NMo(N[i-Pr]Ar)3, a known molecule that has been synthesized using N2 as the nitrido nitrogen source, but which undergoes no reaction with pivaloyl chloride. Compound 1 undergoes metathesis with pivaloyl chloride at 25 degrees C to form the corresponding nitrile in 97% yield. Another substrate examined in this work was the labeled acid chloride 1-Ad13C(O)Cl (Ad = adamantyl). The "(O)Cl" moiety is transferred to tungsten forming an oxo-chloride, (Ar[i-Pr]N)3W(O)Cl (3), as the final tungsten product; both 1 and 3 were characterized structurally by X-ray diffraction. An intermediate observed in the nitrile-forming reaction was characterized spectroscopically to be a tungsten acylimido complex. The latter assignment was substantiated by the synthesis and structural characterization of the compound (Ar[i-Pr]N)3W(NC(O)CF3)(O2CCF3) (2m). In addition, density functional theory calculations performed using ADF lent insight into the thermochemistry of the overall process.     

Ring-Polymer Molecular Dynamics Studies of Thermal Rate Coefficients for Reaction F+H2O→HF+OH

The prototype tetra-atomic reaction F+H₂O→HF+OH plays a significant role in both atmospheric and astronomical chemistry. In this work, thermal rate coefficients of this reaction are determined with the ring polymer molecular dynamics (RPMD) method on a full-dimensional potential energy surface (PES). This PES is the most accurate one for the title reaction, as demonstrated by the correct barrier height and reaction energy, compared to the benchmark calculations by the focal point analysis and the high accuracy extrapolated ab initio thermochemistry methods. The RPMD rate coefficients are in excellent agreement with those calculated by the semiclassical transition state theory and a two-dimensional master equation technique, and some experimental measurements. As has been found in many RPMD applications, quantum effects, including tunneling and zeropoint energy effects, can be efficiently and effectively captured by the RPMD method. In addition, the convergence of the results with respect to the number of beads is rapid, which is also consistent with previous RPMD applications.     

Examining the performance of DFT methods in uranium chemistry: does core size matter for a pseudopotential?

We have investigated the performance of DFT in U(VI) chemistry. A large, representative selection of functionals has been tested, in combination with two ECPs developed in Stuttgart that have different-sized cores (60 and 78 electrons for U). In addition, several tests were undertaken with another 14 electron pseudopotential, which was developed in Los Alamos. The experimental database contained vibrational wavenumbers, thermochemical data, and (19)F chemical shifts for molecules of the type UF(6-n)Cl(n). For the prediction of vibrational wavenumbers, the large-core RECP (14 electrons) gives results that are at least as good as those obtained with the small-core RECP (32 electrons). GGA functionals are as successful as hybrid GGA for vibrational spectroscopy; typical errors are only a few percent with the Stuttgart pseudopotentials. For thermochemistry, hybrid versions of DFT are more successful than GGA, LDA, or meta-GGA. Marginally better results are obtained with a 32 electron ECP than with 14; since the experimental uncertainties are at least 25 kJ/mol for each reaction, the best functionals give results that are essentially indistinguishable from experiment. However, large-basis CCSD(T) results match experiment better than any DFT that we examined. Our findings for NMR spectroscopy are rather disappointing; no combination of pseudopotential, functional, and basis yields even a qualitatively correct prediction of trends in the (19)F chemical shifts of UF(6-n)Cl(n) species. Results yielded by the large-core RECP are, in general, slightly less bad than those obtained with the small core. We conclude that DFT cannot be recommended for predictions of NMR spectra in this series of compounds, though this conclusion should not be generalized. Our most important result concerns the good performance of the large-core Stuttgart pseudopotential. Given its computational efficiency, we recommend that it be used with DFT methods for the prediction of molecular geometries, vibrational frequencies, and thermochemistry of a given oxidation state. The hybrid GGA functionals MPW1PW91 and PBE0 give the best results overall.     

Thermochemistry of the reaction catalyzed by lactate dehydrogenase

The thermochemistry of the reduction of pyruvate to lactate, in the presence of nicotinamide adenine dinucleotide (reduced form); catalyzed by the enzyme lactate dehydrogenase, has been studied. After approximately 120 experiments, a best value for the enthalpy of reaction has been determined to be ?14.80±0.30 kcal mol^?1. This reveals that the driving force for the reaction is almost completely enthalpic in nature. In addition, using the current methodology, it is possible to determine lactate dehydrogenase activity as low as 0.15 international units (325 Wroblewski units) per sample.     

环糊精高分子

环糊精以其独特的包合特性而引入注目，已被广泛地应用于化学分离及分析、药物控制释放、食品加工和环境保护等领域。环糊精高分子亦被证实具有包含、缓释及催化的能力，以及良好的机械强度和化学稳定性。本文综述了国内外关于环糊精高分子的类型、合成方法及实际应用的最新研究进展。