DFT and ab initio calculations on two reactions between hydrogen atoms and the fire suppressants 2-H heptafluoropropane and CF3Br

Reaction enthalpies and barrier heights of the reactions CF3Br+H-->CF3+HBr {reaction (1)} and CF3CHFCF3+H-->CF3CFCF3+H2 {reaction (2)} have been calculated at the near state-of-the-art ab initio level, and also by employing the B3LYP, BH&HLYP, BB1K, MPW1K, MPWB1K and TPSS1KCIS functionals. In addition, the integrated molecular orbital+molecular orbital (IMOMO) method has been used to study reaction (2). The ab initio benchmark values of the reaction enthalpy (298 K) and barrier height (0 K) of reaction (2) are reported for the first time {-(0.7+/-0.7) and 13.3+/-0.5 kcal/mole respectively}. When density functional theory (DFT) results are compared with ab initio benchmarks for both reactions (1) and (2), the MPWB1K functional is found to have the best performance of the six functionals used. The IMOMO method with the RCCSD/aug-cc-pVTZ and/or RCCSD(T)/aug-cc-pVTZ levels, as the high levels of calculation on the model system, gives reaction enthalpies and barrier heights of reaction (2), which agree with ab initio benchmark values to within 1 kcal/mole. Computed key geometrical parameters and imaginary vibrational frequencies of the transition state structures of reactions (1) and (2) obtained at different levels of calculation are compared. The magnitudes of the computed imaginary vibrational frequencies of the transition states of both reactions considered are found to be very sensitive to the levels of calculation used to obtain them. The heat of formation (298 K) of CF3CFCF3 calculated at the near state-of-the-art level has a value of -(318+/-3) kcal/mole.     

Benchmark database of barrier heights for heavy atom transfer, nucleophilic substitution, association, and unimolecular reactions and its use to test theoretical methods

A benchmark database of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions has been developed by using Weizmann 1 calculations, and 29 DFT methods and 6 ab initio wave-function theory (WFT) methods have been tested against the new database as well as against an older database for hydrogen atom transfer reactions. Among the tested hybrid DFT methods without kinetic energy density, MPW1K is the most accurate model for calculations of barrier heights. Among the tested hybrid meta DFT methods, BB1K and MPWB1K are the two most accurate models for the calculations of barrier heights. Overall, the results show that BB1K and MPWB1K are the two best DFT methods for calculating barrier heights, followed in order by MPW1K, MPWKCIS1K, B1B95, MPW1B95, BH and HLYP, B97-2, mPW1PW91, and B98. The popular B3LYP method has a mean unsigned error four times larger than that of BB1K. Of the methods tested, QCISD(T) is the best ab initio WFT method for barrier height calculations, and QCISD is second best, but QCISD is outperformed by the BB1K, MPWB1K, MPWKCIS1K, and MPW1K methods.     

Comparative assessment of density functional methods for 3d transition-metal chemistry

In the present study, we comparatively assessed the newly developed M05 functional against a data set of reaction energies for transition-metal chemistry. The functionals to which we compare are BLYP, B3LYP, B97-2, MPWLYP1M, TPSS, and TPSSh. We draw the following conclusions: (1) TPSS gives the best performance for calculating the binding energies of three transition-metal dimers (Sc(2), Ni(2), and V(2)) that have severe multireference character, (2) B97-2 gives the best performance for calculating the binding energies of the nine metal-ligand diatomics (three monohydrides, three monoxide, and three monofluorides), and (3) M05 gives the overall best performance for all 18 data in the assessment, and it has a mean unsigned error 55% lower than the popular B3LYP functional. Since the M05 functional also gives good performance for main-group thermochemistry, for noncovalent chemistry, and for calculating barrier heights, M05 can be applied to a wide range of problems where nonhybrid functionals or functionals designed for kinetics fail.     

Benchmark study of DFT functionals for late-transition-metal reactions

The performance of a wide variety of DFT exchange-correlation functionals for a number of late-transition-metal reaction profiles has been considered. Benchmark ab-initio reference data for the prototype reactions Pd + H2, Pd + CH4, Pd + C2H6 (both C-C and C-H activation), and Pd + CH3Cl are presented, while ab-initio data of lesser quality were obtained for the catalytic hydrogenation of acetone and for the low-oxidation-state and high-oxidation-state mechanisms of the Heck reaction. "Kinetics" functionals such as mPW1K, PWB6K, BB1K, and BMK clearly perform more poorly for late-transition-metal reactions than for main-group reactions, as well as compared to general-purpose functionals. There is no single "best functional" for late-transition-metal reactions, but rather a cluster of several functionals (PBE0, B1B95, PW6B95, and TPSS25B95) that perform about equally well; if main-group thermochemical performance is additionally considered, then B1B95 and PW6B95 emerge as the best performers. TPSS25B95 and TPSS33B95 offer attractive performance compromises if weak interactions and main-group barrier heights, respectively, are also important. In the ab-initio calculations, basis set superposition errors (BSSE) can be greatly reduced by ensuring that the metal spd shell has sufficient radial flexibility in the high-exponent range. Optimal HF percentages in hybrid functionals depend on the class of systems considered, increasing from anions to neutrals to cations to main-group barrier heights; transition-metal barrier heights represent an intermediate situation. The use of meta-GGA correlation functionals appears to be quite beneficial.     

DFT and ab initio calculations on the reaction between fluorine atoms and the fire suppressant, 2-H heptafluoropropane

Benchmark values for the reaction enthalpy (298 K) and the barrier height (0 K) of the reaction, CF₃CHFCF₃ + F → CF₃CFCF₃ + HF, have been calculated at state-of-the-art ab initio level to be −34.7 ± 1.0 and −0.9 ± 0.9 kcal/mole, respectively. The B3LYP, BH&HLYP, BB1K, MPW1K, MPWB1K and TPSS1KCIS functionals and the model method, the integrated molecular orbital + molecular orbital (IMOMO) method, have also been used to study this reaction.     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.     

A direct ab initio dynamics study of the water-assisted tautomerization of formamide

Direct ab initio dynamics calculations based on a canonical variational transition-state theory with several multidimensional semiclassical tunneling approximations were carried out to obtain rate constants for the water-assisted tautomerization of formamide. The accuracy of the density functionals, namely, B-LYP, B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yields the most accurate transition-state properties when comparing it to ab initio MP2 and QCISD results, whereas B-LYP and B3-LYP methods predict barrier heights too low. Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-LYP levels using the 6–31G(d,p) basis set. At the BH&H-LYP level, we found that the zero-point energy motion lowers the barrier to tautomerization in the formamide-water complex by 3.6 kcal/mol. When tunneling is considered, the activation energy at the BH&H-LYP level at 300 K is 17.1 kcal/mol. This is 3.4 kcal/mol below the zero-point-corrected barrier and 7.0 kcal/mol below the classical barrier. Excellent agreement between BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP for rate calculations of large systems. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 861–874, 1997     

Comparative DFT study on the <Emphasis Type="Italic">α</Emphasis>-glycosidic bond in reactive species of galactosyl diphosphates

Correct prediction of the structure and energetics along the reaction pathway of the formation or dissociation of the glycosidic bond in sugar phosphates is crucial for the understanding of catalytic mechanism and for the determination of transition state structures of sugar-phosphate processing enzymes. The performance of seven density functional theory (DFT) methods (BLYP, B3LYP, MPW1PW91, MPW1K, MPWB1K, M05 and M05-2X) and two wave function methods (HF and MP2) was tested using four structural models with the activated sugar-phosphate α-glycosidic linkage. The models were chosen based on the crystal structure of the retaining glycosyltransferase LgtC complex with methyl α-d-galactopyranose diphosphate and its 2-fluoro derivative. Results of the MP2 method were used as a benchmark for the other methods. Two structural trends were observed in the calculations: predicted length of the activated C1-O1 glycosidic bond of 1.49–1.63 Å was significantly larger than values of a standard C1-O1 glycosidic bond in crystal structures of carbohydrates (1.39–1.48 Å), and the calculated value depended on the DFT method used. The MPW1K, M05 and M05-2X functionals provided results in closest agreement with those from the MP2 method, the difference being less than 0.02 Å in the calculated glycosidic bond lengths. On the contrary, the BLYP and B3LYP functionals failed to predict sugar diphosphate in the (-sc) conformation as a stable structure. Instead, the only stationary points localized along the C1-O1 dissociation coordinate were oxocarbenium ions at the distance of approximately 2.8 Å. The M05-2X, MPW1K and MPWB1K functionals gave the most reasonable prediction of the thermochemical kinetic parameters, where the formation of the oxocarbenium ion has a slightly endothermic character (0.4–1.7 kJ mol^?1) with an activation barrier of 7.9–9.2 kJ mol^?1.     

How to compute isomerization energies of organic molecules with quantum chemical methods

The reaction energies for 34 typical organic isomerizations including oxygen and nitrogen heteroatoms are investigated with modern quantum chemical methods that have the perspective of also being applicable to large systems. The experimental reaction enthalpies are corrected for vibrational and thermal effects, and the thus derived "experimental" reaction energies are compared to corresponding theoretical data. A series of standard AO basis sets in combination with second-order perturbation theory (MP2, SCS-MP2), conventional density functionals (e.g., PBE, TPSS, B3-LYP, MPW1K, BMK), and new perturbative functionals (B2-PLYP, mPW2-PLYP) are tested. In three cases, obvious errors of the experimental values could be detected, and accurate coupled-cluster [CCSD(T)] reference values have been used instead. It is found that only triple-zeta quality AO basis sets provide results close enough to the basis set limit and that sets like the popular 6-31G(d) should be avoided in accurate work. Augmentation of small basis sets with diffuse functions has a notable effect in B3-LYP calculations that is attributed to intramolecular basis set superposition error and covers basic deficiencies of the functional. The new methods based on perturbation theory (SCS-MP2, X2-PLYP) are found to be clearly superior to many other approaches; that is, they provide mean absolute deviations of less than 1.2 kcal mol-1 and only a few (<10%) outliers. The best performance in the group of conventional functionals is found for the highly parametrized BMK hybrid meta-GGA. Contrary to accepted opinion, hybrid density functionals offer no real advantage over simple GGAs. For reasonably large AO basis sets, results of poor quality are obtained with the popular B3-LYP functional that cannot be recommended for thermochemical applications in organic chemistry. The results of this study are complementary to often used benchmarks based on atomization energies and should guide chemists in their search for accurate and efficient computational thermochemistry methods.     

Bioinorganic chemistry modeled with the TPSSh density functional

In this work, the TPSSh density functional has been benchmarked against a test set of experimental structures and bond energies for 80 transition-metal-containing diatomics. It is found that the TPSSh functional gives structures of the same quality as other commonly used hybrid and nonhybrid functionals such as B3LYP and BP86. TPSSh gives a slope of 0.99 upon linear fitting to experimental bond energies, whereas B3LYP and BP86, representing 20% and 0% exact exchange, respectively, give linear fits with slopes of 0.91 and 1.07. Thus, TPSSh eliminates the large systematic component of the error in other functionals, reducing rms errors from 46-57 to 34 kJ/mol. The nonhybrid version of the functional, TPSS, gives a slope of 1.08, similar to BP86, implying that using 10% exact exchange is the main reason for the success of TPSSh. Typical bioinorganic reactions were then investigated, including spin inversion and electron affinity in iron-sulfur clusters, and breaking or formation of bonds in iron proteins and cobalamins. The results show that differences in reaction energies due to exact exchange can be much larger than the usually cited approximately 20 kJ/mol, sometimes exceeding 100 kJ/mol. The TPSSh functional provides energies approximately halfway between nonhybrids BP86 and TPSS, and 20% exact exchange hybrid B3LYP: Thus, a linear correlation between the amount of exact exchange and the numeric value of the reaction energy is observed in all these cases. For these reasons, TPSSh stands out as a most promising density functional for use and further development within the field of bioinorganic chemistry.     

Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.     

Theoretical study of the competitive decomposition and isomerization of 1-hexyl radical

The ground-state potential energy surface of the 1-hexyl system, including the main decomposition and isomerization processes, has been calculated with the MPW1K, BB1K, MPWB1K, MPW1B95, BMK, M05-2X and CBS-QB3 methods. On the basis of these data, thermal rate coefficients of different reaction channels and branching ratios were then calculated using the master equation formulation at 250–2,500 K. The results clearly point out that the 1,5 H atom transfer reaction of 1-hexyl radical with exothermicity proceeds through the lowest reaction barrier, whereas the decomposition processes are thermodynamically unfavorable with large endothermicity. The temperature effect is important on the relative importance of different reactions in the 1-hexyl system. In the low-temperature range of 250–900 K, isomerization reactions, especially 1,5 H atom transfer reaction of 1-hexyl radical, are dominating and responsible for over 82.17% of all the reactions, due to their smaller reaction barriers than those of the decomposition reactions. Furthermore, an equilibrium process involving the isomeric forms of the hexyl radicals appearing at relative low temperature was validated theoretically. However, isomerization and decomposition processes are kinetically competitive and simultaneously important under normal pyrolysis conditions.     

Comparative analysis of the performance of commonly available density functionals in the determination of geometrical parameters for zinc complexes

A set of 44 Zinc‐ligand bond‐lengths and of 60 ligand‐metal‐ligand bond angles from 10 diverse transition‐metal complexes, representative of the coordination spheres of typical biological Zn systems, were used to evaluate the performance of a total of 18 commonly available density functionals in geometry determination. Five different basis sets were considered for each density functional, namely two all‐electron basis sets (a double‐zeta and triple‐zeta formulation) and three basis sets including popular types of effective‐core potentials: Los Alamos, Steven‐Basch‐Krauss, and Stuttgart‐Dresden. The results show that there are presently several better alternatives to the popular B3LYP density functional for the determination of Zn‐ligand bond‐lengths and angles. BB1K, MPWB1K, MPW1K, B97‐2 and TPSS are suggested as the strongest alternatives for this effect presently available in most computational chemistry software packages. In addition, the results show that the use of effective‐core potentials (in particular Stuttgart‐Dresden) has a very limited impact, in terms of accuracy, in the determination of metal‐ligand bond‐lengths and angles in Zinc‐complexes, and is a good and safe alternative to the use of an all‐electron basis set such as 6‐31G(d) or 6‐311G(d,p). © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

MPW1K Performs Much Better than B3LYP in DFT Calculations on Reactions that Proceed by Proton-Coupled Electron Transfer (PCET)

DFT calculations have been performed with the B3LYP and MPW1K functional on the hydrogen atom abstraction reactions of ethenoxyl with ethenol and of phenoxyl with both phenol and alpha-naphthol. Comparison with the results of G3 calculations shows that B3LYP seriously underestimates the barrier heights for the reaction of ethenoxyl with ethenol by both proton-coupled electron transfer (PCET) and hydrogen atom transfer (HAT) mechanisms. The MPW1K functional also underestimates the barrier heights, but by much less than B3LYP. Similarly, comparison with the results of experiments on the reaction of phenoxyl radical with alpha-naphthol indicates that the barrier height for the preferred PCET mechanism is calculated more accurately by MPW1K than by B3LYP. These findings indicate that the MPW1K functional is much better suited than B3LYP for calculations on hydrogen abstraction reactions by both HAT and PCET mechanisms.     

Trends in R-X bond dissociation energies (R = Me, Et, i-Pr, t-Bu; X = H, CH3, OCH3, OH, F): a surprising shortcoming of density functional theory

The performance of a variety of high-level composite procedures, as well as lower-cost density functional theory (DFT)- and second-order perturbation theory (MP2)-based methods, for the prediction of absolute and relative R-X bond dissociation energies (BDEs) was examined for R = Me, Et, i-Pr and t-Bu, and X = H, CH(3), OCH(3), OH and F. The methods considered include the high-level G3(MP2)-RAD and G3-RAD procedures, a variety of pure and hybrid DFT methods (B-LYP, B3-LYP, B3-P86, KMLYP, B1B95, MPW1PW91, MPW1B95, BB1K, MPW1K, MPWB1K and BMK), standard restricted (open-shell) MP2 (RMP2), and two recently introduced variants of MP2, namely spin-component-scaled MP2 (SCS-MP2) and scaled-opposite-spin MP2 (SOS-MP2). The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the lower-level DFT- and MP2-based procedures. The best DFT methods (KMLYP and particularly BMK) provide very reasonable predictions for the absolute heats of formation and R-X BDEs for the systems studied. However, all of the DFT methods overestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu, leading in some cases to incorrect qualitative behavior. In contrast, the MP2-based methods generally show larger errors (than the best DFT methods) in the absolute heats of formation and BDEs, but better behavior for the relative BDEs, although they do tend to underestimate the stabilizing effect on BDEs in going from R = Me to R = t-Bu. The potentially less computationally expensive SOS-MP2 method offers particular promise as a reliable method that might be applicable to larger systems.     

Harmonic vibrational frequencies: scale factors for pure, hybrid, hybrid meta, and double-hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.