Assessment of theoretical procedures for calculating barrier heights for a diverse set of water-catalyzed proton-transfer reactions

Accurate electronic barrier heights are obtained for a set of nine proton-transfer tautomerization reactions, which are either (i) uncatalyzed, (ii) catalyzed by one water molecule, or (iii) catalyzed by two water molecules. The barrier heights for reactions (i) and (ii) are obtained by means of the high-level ab initio W2.2 thermochemical protocol, while those for reaction (iii) are obtained using the W1 protocol. These three sets of benchmark barrier heights allow an assessment of the performance of more approximate theoretical procedures for the calculation of barrier heights of uncatalyzed and water-catalyzed reactions. We evaluate initially the performance of the composite G4 procedure and variants thereof (e.g., G4(MP2) and G4(MP2)-6X), as well as that of standard ab initio procedures (e.g., MP2, SCS-MP2, and MP4). We find that the performance of the G4(MP2)-type thermochemical procedures deteriorates with the number of water molecules involved in the catalysis. This behavior is linked to deficiencies in the MP2-based basis-set-correction term in the G4(MP2)-type procedures. This is remedied in the MP4-based G4 procedure, which shows good performance for both the uncatalyzed and the water-catalyzed reactions, with mean absolute deviations (MADs) from the benchmark values lying below the threshold of "chemical accuracy" (arbitrarily defined as 1 kcal mol(-1) ≈ 4.2 kJ mol(-1)). We also examine the performance of a large number of density functional theory (DFT) and double-hybrid DFT (DHDFT) procedures. We find that, with few exceptions (most notably PW6-B95 and B97-2), the performance of the DFT procedures that give good results for the uncatalyzed reactions deteriorates with the number of water molecules involved in the catalysis. The DHDFT procedures, on the other hand, show excellent performance for both the uncatalyzed and catalyzed reactions. Specifically, almost all of them afford MADs below the "chemical accuracy" threshold, with ROB2-PLYP and B2K-PLYP showing the best overall performance.     

Computational s-block thermochemistry with the correlation consistent composite approach

The correlation consistent composite approach (ccCA) is a model chemistry that has been shown to accurately compute gas-phase enthalpies of formation for alkali and alkaline earth metal oxides and hydroxides (Ho, D. S.; DeYonker, N. J.; Wilson, A. K.; Cundari, T. R. J. Phys. Chem. A 2006, 110, 9767).The ccCA results contrast to more widely used model chemistries where calculated enthalpies of formation for such species can be in error by up to 90 kcal mol-1. In this study, we have applied ccCA to a more general set of 42 s-block molecules and compared the ccCA DeltaHf values to values obtained using the G3 and G3B model chemistries. Included in this training set are water complexes such as Na(H2O)n+ where n = 1 - 4, dimers and trimers of ionic compounds such as (LiCl)2 and (LiCl)3, and the largest ccCA computation to date: Be(acac)2, BeC10H14O4. Problems with the G3 model chemistries seem to be isolated to metal-oxygen bonded systems and Be-containing systems, as G3 and G3B still perform quite well with a 2.7 and 2.6 kcal mol-1 mean absolute deviation (MAD), respectively, for gas-phase enthalpies of formation. The MAD of the ccCA is only 2.2 kcal mol-1 for enthalpies of formation (DeltaHf) for all compounds studied herein. While this MAD is roughly double that found for a ccCA study of >350 main group (i.e., p-block) compounds, it is commensurate with typical experimental uncertainties for s-block complexes. Some molecules where G3/G3B and ccCA computed DeltaHf values deviate significantly from experiment, such as (LiCl)3, NaCN, and MgF, are inviting candidates for new experimental and high-level theoretical studies.     

The correlation-consistent composite approach: application to the G3/99 test set

The correlation-consistent composite approach (ccCA), an ab initio composite technique for computing atomic and molecular energies, recently has been shown to successfully reproduce experimental data for a number of systems. The ccCA is applied to the G3/99 test set, which includes 223 enthalpies of formation, 88 adiabatic ionization potentials, 58 adiabatic electron affinities, and 8 adiabatic proton affinities. Improvements on the original ccCA formalism include replacing the small basis set quadratic configuration interaction computation with a coupled cluster computation, employing a correction for scalar relativistic effects, utilizing the tight-d forms of the second-row correlation-consistent basis sets, and revisiting the basis set chosen for geometry optimization. With two types of complete basis set extrapolation of MP2 energies, ccCA results in an almost zero mean deviation for the G3/99 set (with a best value of -0.10 kcal mol(-1)), and a 0.96 kcal mol(-1) mean absolute deviation, which is equivalent to the accuracy of the G3X model chemistry. There are no optimized or empirical parameters included in the computation of ccCA energies. Except for a few systems to be discussed, ccCA performs as well as or better than Gn methods for most systems containing first-row atoms, while for systems containing second-row atoms, ccCA is an improvement over Gn model chemistries.     

The 6-31B(d) basis set and the BMC-QCISD and BMC-CCSD multicoefficient correlation methods

Three new multicoefficient correlation methods (MCCMs) called BMC-QCISD, BMC-CCSD, and BMC-CCSD-C are optimized against 274 data that include atomization energies, electron affinities, ionization potentials, and reaction barrier heights. A new basis set called 6-31B(d) is developed and used as part of the new methods. BMC-QCISD has mean unsigned errors in calculating atomization energies per bond and barrier heights of 0.49 and 0.80 kcal/mol, respectively. BMC-CCSD has mean unsigned errors of 0.42 and 0.71 kcal/mol for the same two quantities. BMC-CCSD-C is an equally effective variant of BMC-CCSD that employs Cartesian rather than spherical harmonic basis sets. The mean unsigned error of BMC-CCSD or BMC-CCSD-C for atomization energies, barrier heights, ionization potentials, and electron affinities is 22% lower than G3SX(MP2) at an order of magnitude less cost for gradients for molecules with 9-13 atoms, and it scales better (N6 vs N,7 where N is the number of atoms) when the size of the molecule is increased.     

Reaction barrier heights from an exact-exchange-based density-functional correlation model

A recent exact-exchange-based density-functional model of nondynamical and dynamical correlation [A.D. Becke, J. Chem. Phys. 122, 064101 (2005)] is tested on 70 barrier heights for a variety of reaction types: hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitutions, association reactions, and unimolecular rearrangements, including both even- and odd-electron systems. The mean absolute error with respect to accurate reference data is 1.4 kcal/mol. This is achieved without any refitting of the parameters of the model to the barrier height data.     

A pseudopotential-based composite method: the relativistic pseudopotential correlation consistent composite approach for molecules containing 4d transition metals (Y-Cd)

The correlation consistent composite approach (ccCA) has proven to be an effective first-principles-based composite approach for main group and first-row transition metal species. By combining relativistic pseudopotentials and ccCA, accurate energetic and thermodynamic data for heavier elements, including transition metals, is obtainable. Relativistic pseudopotential ccCA (rp-ccCA) was formulated and tested on 25 molecules from the G3∕05 set that contain 4p elements (Ga-Kr). A 32.5% time savings was obtained using rp-ccCA, relative to ccCA employing all-electron basis sets. When implementing rp-ccCA to compute dissociation energies and enthalpies of formation for molecules from the 4p block, rp-ccCA results in a mean absolute deviation of 0.89 kcal?mol(-1) from experimental data. rp-ccCA was also applied to a set of 30 4d transition metal-containing molecules, ranging from diatomics to Mo(CO)(6), and enthalpies of formation for these species were obtained with a mean absolute deviation of 2.89 kcal mol(-1) in comparison to experimental data. Based on quality of the experimentally available enthalpies of formation, where the average value of reported experimental error bars is 3.43 kcal mol(-1), rp-ccCA is within transition metal chemical accuracy for the 4d molecule set. rp-ccCA is a pseudopotential-based composite method for transition metals and is shown to yield accurate thermodynamic results for molecules containing heavy elements Ga-Kr and Y-Cd.     

Benchmark calculations of reaction energies, barrier heights, and transition-state geometries for hydrogen abstraction from methanol by a hydrogen atom

We report benchmark calculations of reaction energies, barrier heights, and transition-state geometries for the reaction of CH(3)OH with H to produce CH(2)OH and H(2). Highly accurate composite methods, such as CBS, G2, G3S, G3X, G3SX, and multi-coefficient correlation methods (MCCMs), are used to calibrate lower-cost methods. We also performed single-level CCSD(T) calculations extrapolated to the infinite-basis limit on the basis of aug-cc-pVXZ (X = 3, 4) correlation consistent basis sets. The benchmark high-level calculations give consensus values of the forward reaction barrier height and the reaction energy of 9.7 kcal/mol and - 6.4 kcal/mol, respectively. To evaluate the accuracy of cost-efficient methods that are potentially useful for dynamics studies of the title reaction, we further include the results obtained by hybrid density functional theory methods and hybrid meta density functional theory methods that have recently been designed for chemical kinetics. Results obtained by popular semiempirical methods are also given for comparison. On the basis of the benchmark gas-phase results, we suggest MC-QCISD/3, MC3BB, and BB1K as reasonably accurate and affordable electronic structure methods for calculating dynamics for the title reaction.     

Reactions of hydrogen atom with hydrogen peroxide

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 structure calculations. Transition state geometries are optimized by multireference perturbation theory (MRMP2) with a variety of one-electron basis sets, and by a multireference coupled cluster (MR-AQCCSD) method. A variety of single-reference benchmark-level calculations have also been carried out; included among them are BMC-CCSD, G3SX(MP3), G3SX, G3, G2, MCG3, CBS-APNO, CBS-Q, CBS-QB3, and CCSD(T). Our data obtained at the MRMP2 level are the most complete; the barrier height for (1a) using MRMP2 at the infinite basis set limit is 4.8 kcal/mol. Results are also obtained with midlevel single-reference multicoefficient correlation methods, such as MC3BB, MC3MPW, MC-QCISD/3, and MC-QCISD-MPWB, and with a variety of hybrid density functional methods, which are compared with high-level theory. On the basis of the evaluated experimental values and the benchmark calculations, two possible recommended values are given for the rate coefficients.     

Multilayer formulation of the fragment molecular orbital method (FMO)

The fragment molecular orbital method (FMO) has been generalized to allow for multilayer structure. Fragments are assigned to layers, and each layer can be described with a different basis set and/or level of electron correlation. Interlayer boundaries are treated in the general spirit of the FMO method since they also coincide with some interfragment boundaries. The question of the one- and two-layer FMO accuracy dependence upon the fragmentation scheme is also addressed. The new method has been applied to predict the reaction barrier and the reaction heat for the Diels-Alder reaction with a representative set of reactants based on dividing fragments in two layers. The 6-31G* basis set has been used for the active site and the 6-31G*, 6-31G, 3-21G, and STO-3G basis sets have been used for the substituents. Different levels of electron correlation (RHF, B3LYP, and MP2) have been applied to layers in systematic fashion. The one-layer FMO errors in the reaction barrier and the reaction heat were 2.0 kcal/mol or less for all levels applied (RHF, B3LYP, and MP2), relative to full ab initio methods. For the two-layer method the error was found to be several kcal/mol. Benchmark calculations of the activation barrier for the decarboxylation of phenylcyanoacetate by beta-cyclodextrin demonstrated that the two-layer calculations are efficient, being 36 times faster than the regular DFT, as well as accurate, with the error being 1.0 kcal/mol.     

Agreement between experiment and hybrid DFT calculations for O--H bond dissociation enthalpies in manganese complexes

Information on the accuracy of DFT functionals for redox reactions in transition metal systems is rather limited. To analyze the performance of some popular functionals for redox reactions in manganese systems, calculated O--H bond dissociation enthalpies for Mn-ligands in six different complexes are compared to experimental results. In this benchmark, B3LYP performs well with a mean absolute error of 3.0 kcal/mol. B98 gives similar results to B3LYP (error of 3.8 kcal/mol). B3LYP* gives lower O--H bond strengths than B3LYP and has a mean error of 5.0 kcal/mol. Compared to B98 and B3LYP, B3LYP* has an error trend for the manganese ligands that is more similar to the error for a free water molecule. The nonhybrid functional BLYP consistently and significantly underestimates the O--H bond strengths by approximately 20 kcal/mol. HCTH407 has a rather large mean error of 9.4 kcal/mol and shows no consistent trend. The results support the use of hybrid functionals and the present computational method for large model systems containing manganese. An example is the oxygen evolving complex in photosystem II where hybrid functionals predict the appearance of a Mn(IV)-oxyl radical before the O--O bond formation step.     

Quantitative computational thermochemistry of transition metal species

The correlation consistent Composite Approach (ccCA), which has been shown to achieve chemical accuracy (+/-1 kcal mol-1) for a large benchmark set of main group and s-block metal compounds, is used to compute enthalpies of formation for a set of 17 3d transition metal species. The training set includes a variety of metals, ligands, and bonding types. Using the correlation consistent basis sets for the 3d transition metals, we find that gas-phase enthalpies of formation can be efficiently calculated for inorganic and organometallic molecules with ccCA. However, until the reliability of gas-phase transition metal thermochemistry is improved, both experimentally and theoretically, a large experimental training set where uncertainties are near +/-1 kcal mol-1 (akin to commonly used main group benchmarking sets) remains an ambitious goal. For now, an average deviation of +/-3 kcal mol-1 appears to be the initial goal of "chemical accuracy" for ab initio transition metal model chemistries. The ccCA is also compared to a more robust but relatively expensive composite approach primarily utilizing large basis set coupled cluster computations. For a smaller training set of eight molecules, ccCA has a mean absolute deviation (MAD) of 3.4 kcal mol-1 versus the large basis set coupled-cluster-based model chemistry, which has a MAD of 3.1 kcal mol-1. However, the agreement for transition metal complexes is more system dependent than observed in previous benchmark studies of composite methods and main group compounds.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

Thinking out of the black box: accurate barrier heights of 1,3-dipolar cycloadditions of ozone with acetylene and ethylene

Accurate barriers for the 1,3-dipolar cycloadditions of ozone with acetylene and ethylene have been determined via the systematic extrapolation of ab initio energies within the focal point approach of Allen and co-workers. Electron correlation has been accounted for primarily via coupled cluster theory, including single, double, and triple excitations, as well as a perturbative treatment of connected quadruple excitations [CCSD, CCSD(T), CCSDT, and CCSDT(Q)]. For the concerted [4 + 2] cycloadditions, the final recommended barriers are DeltaH(0K) = 9.4 +/- 0.2 and 5.3 +/- 0.2 kcal mol(-1) for ozone adding to acetylene and ethylene, respectively. These agree with recent results of Cremer et al. and Anglada et al., respectively. The reaction energy for O3 + C2H2 exhibits a protracted convergence with respect to inclusion of electron correlation, with the CCSDT/cc-pVDZ and CCSDT(Q)/cc-pVDZ values differing by 2.3 kcal mol-1. Recommended enthalpies of formation (298 K) for cycloadducts 1,2,3-trioxole and 1,2,3-trioxolane are +32.8 and -1.6 kcal mol(-1), respectively. Popular composite ab initio approaches [CBS-QB3, CBS-APNO, G3, G3B3, G3(MP2)B3, G4, G4(MP3), and G4(MP2)] predict a range of barrier heights for these systems. The CBS-QB3 computed barrier for ozone and acetylene, DeltaH(0K) = 4.4 kcal mol(-1), deviates by 5 kcal mol(-1) from the focal point value. CBS-QB3 similarly underestimates the barrier for the reaction of ozone and ethylene, yielding a prediction of only 0.7 kcal mol(-1). The errors in the CBS-QB3 results are significantly larger than mean errors observed in application to the G2 test set. The problem is traced to the nontransferability of MP2 basis set effects in the case of these reaction barriers. The recently published G4 and G4(MP2) approaches perform substantially better for O3 + C2H2, predicting enthalpy barriers of 9.0 and 8.4 kcal mol(-1), respectively. For the prediction of these reaction barriers, the additive corrections applied in the majority of the composite approaches considered lead to worse agreement with the reference focal point values than would be obtained relying only on single point energies evaluated at the highest level of theory utilized within each composite method.     

Density functional theory investigation of the reactions of isodihalomethanes (CH(2)X-X where X = Cl, Br, or I) with ethylene: substituent effects on the carbenoid behavior of the CH(2)X-X species

We investigated the chemical reactions of isodihalomethane (CH(2)X-X) and CH(2)X radical species (where X = Cl, Br, or I) with ethylene and the isomerization reactions of CH(2)X-X using density functional theory calculations. The CH(2)X-X species readily reacts with ethylene to give the cyclopropane product and an X(2) product via a one-step reaction with barrier heights of approximately 2.9 kcal/mol for CH(2)I-I, 6.8 kcal/mol for CH(2)Br-Br, and 8.9 kcal/mol for CH(2)Cl-Cl. The CH(2)X reactions with ethylene proceed via a two-step reaction mechanism to give a cyclopropane product and X atom product with much larger barriers to reaction. This suggests that photocyclopropanation reactions using ultraviolet excitation of dihalomethanes most likely occurs via the isodihalomethane species and not the CH(2)X species. The isomerization reactions of CH(2)X-X had barrier heights of approximately 14.4 kcal/mol for CH(2)I-I, 11.8 kcal/mol for CH(2)Br-Br, and 9.1 kcal/mol for CH(2)Cl-Cl. We compare our results for the CH(2)X-X carbenoids to results from previous calculations of the Simmons-Smith-type carbenoids (XCH(2)ZnX) and Li-type carbenoids (LiCH(2)X) and discuss their differences and similarities as methylene transfer agents.     

Assessment of density functionals for pi systems: Energy differences between cumulenes and poly-ynes; proton affinities, bond length alternation, and torsional potentials of conjugated polyenes; and proton affinities of conjugated Shiff bases

Woodcock et al. [J. Phys. Chem. A 2002, 106, 11923] pointed out that no density functional was able to obtain the correct sign of the relative energies of the allene and propyne isomers of C3H4 and that density functional theory (DFT) predicts that poly-ynes are insufficiently stabilized over cumulenes for higher homologues. In the present work, we show that the recent M05 density functional predicts the correct ordering of allene and propyne and gives a mean unsigned error (MUE) of only 1.8 kcal/mol for the relative energies of the two isomers of C3H4, C5H4, and C7H4. Two other recent functionals, M05-2X and PWB6K, also give reasonably low MUEs, 2.7 and 3.0 kcal/mol, respectively, as compared to 6.2 kcal/mol for the popular B3LYP functional. Another challenging problem for density functionals has been a tendency to overpolarize conjugated pi systems. We test this here by considering proton affinities of conjugated polyenes and conjugated Schiff bases. Again M05-2X performs quite well, with MUEs of 2.1 and 3.9 kcal/ mol, respectively, as compared to 5.8 and 5.9 kcal/mol for B3LYP. Averaged over the three problems, M05-2X has a MUE of 3.0 kcal/mol, the BMK functional of Boese et al. has an MUE of 3.2 kcal/mol, and M05 has an MUE of 5.1 kcal/mol. Twenty-two other tested functionals have MUEs of 5.2-8.1 kcal/mol averaged over the three test problems. Both M05 and M05-2X do quite well, compared to other density functionals, for torsion potentials in butadiene and styrene, and M05 does very well for bond length alternation in conjugated polyenes. Since the M05 functional has broad accuracy for main group and transition metal chemistry and M05-2X has broad accuracy for main group chemistry, we conclude that significant progress is being made in improving the performance of DFT across a wide range of problem types.     

Theoretical studies of proton-transfer reactions of 2-hydroxypyridine--(H2O)n (n = 0-2) in the ground and excited states

The potential energy profiles for proton-transfer reactions of 2-hydroxypyridine and its complexes with water were determined by MP2, CASSCF and MR-CI calculations with the 6-31G** basis set. The tautomerization reaction between 2-hydroxypyridine (2HP) and 2-pyridone (2PY) does not take place at room temperature because of a barrier of approximately 35 kcal/mol for the ground-state pathway. The water-catalyzed enol-keto tautomerization reactions in the ground state proceed easily through the concerted proton transfer, especially for the two-water complex. The S1 tautomerization between the 2HP and 2PY monomers has a barrier of 18.4 kcal/mol, which is reduced to 5.6 kcal/mol for the one-water complex and 6.4 kcal/mol for the two-water complex. The results reported here predict that the photoinduced tautomerization reaction between the enol and keto forms involves a cyclic transition state having one or two water molecules as a bridge.     

Reactions of the alkoxy radicals formed following OH-addition to alpha-pinene and beta-pinene. C-C bond scission reactions.

The atmospheric degradation pathways of the atmospherically important terpenes alpha-pinene and beta-pinene are studied using density functional theory. We employ the correlation functional of Lee, Yang, and Parr and the three-parameter HF exchange functional of Becke (B3LYP) together with the 6-31G(d) basis set. The C-C bond scission reactions of the beta-hydroxyalkoxy radicals that are formed after OH addition to alpha-pinene and beta-pinene are investigated. Both of the alkoxy radicals formed from the alpha-pinene-OH adduct possess a single favored C-C scission pathway with an extremely low barrier (approximately 3 kcal/mol) leading to the formation of pinonaldehyde. Neither of these pathways produces formaldehyde, and preliminary computational results offer some support for suggestions that 1,5 or 1,6 H-shift (isomerization) reactions of alkoxy radicals contribute to formaldehyde production. In the case of the alkoxy radical formed following OH addition to the methylene group of beta-pinene, there exists two C-C scission reactions with nearly identical barrier heights (approximately 7.5 kcal/mol); one leads to known products (nopinone and formaldehyde) but the ultimate products of the competing reaction are unknown. The single C-C scission pathway of the other alkoxy radical from beta-pinene possesses a very low (approximately 4 kcal/mol) barrier. The kinetically favored C-C scission reactions of all four alkoxy radicals appear to be far faster than expected rates of reaction with O2. The rearrangement of the alpha-pinene-OH adduct, a key step in the proposed mechanism of formation of acetone from alpha-pinene, is determined to possess a barrier of 11.6 kcal/mol. This value is consistent with another computational result and is broadly consistent with the modest acetone yields observed in product yield studies.     

Polyfunctional methodology for improved DFT thermochemical predictions

Statistical error distributions for enthalpies of formation as predicted by 18 different density functionals have been analyzed using a test set of 675 molecules. Systematic errors, dependent on the number of valence electrons, have been identified for some functionals. A simple empirical correction makes a significant improvement in the prediction error for these single functionals. Linear combinations of enthalpy estimates from different density functionals are identified that exploit the error correlations among the functionals and allow for further improvements in the accuracy of thermodynamic predictions. A good compromise between accuracy and computational efforts is achieved by the BLUE (best linear unbiased estimator) combination of three functionals, B3LYP, BLYP, and VSXC (polyfunctional 3 or PF3). The PF3 method has a mean absolute deviation (MAD) from experiment of 2.4 kcal/mol on the G3 set of 271 molecules. This can be compared to the MAD of 4.9 kcal/mol for B3LYP and 1.2 kcal/mol for the more costly G3 method. On the larger set of 675 molecules, the MAD for PF3 is 3.0 kcal/mol. Opportunities for further improvements in the accuracy of this method are discussed.     

Barrier heights of hydrogen‐transfer reactions with diffusion quantum monte carlo method

Hydrogen‐transfer reactions are an important class of reactions in many chemical and biological processes. Barrier heights of H‐transfer reactions are underestimated significantly by popular exchange–correlation functional with density functional theory (DFT), while coupled‐cluster (CC) method is quite expensive and can be applied only to rather small systems. Quantum Monte‐Carlo method can usually provide reliable results for large systems. Performance of fixed‐node diffusion quantum Monte‐Carlo method (FN‐DMC) on barrier heights of the 19 H‐transfer reactions in the HTBH38/08 database is investigated in this study with the trial wavefunctions of the single‐Slater–Jastrow form and orbitals from DFT using local density approximation. Our results show that barrier heights of these reactions can be calculated rather accurately using FN‐DMC and the mean absolute error is 1.0 kcal/mol in all‐electron calculations. Introduction of pseudopotentials (PP) in FN‐DMC calculations improves efficiency pronouncedly. According to our results, error of the employed PPs is smaller than that of the present CCSD(T) and FN‐DMC calculations. FN‐DMC using PPs can thus be applied to investigate H‐transfer reactions involving larger molecules reliably. In addition, bond dissociation energies of the involved molecules using FN‐DMC are in excellent agreement with reference values and they are even better than results of the employed CCSD(T) calculations using the aug‐cc‐pVQZ basis set. © 2017 Wiley Periodicals, Inc.