Bond dissociation energies and radical stabilization energies: an assessment of contemporary theoretical procedures

Various contemporary theoretical procedures have been tested for their accuracy in predicting the bond dissociation energies (BDEs) and the radical stabilization energies (RSEs) for a test set of 22 monosubstituted methyl radicals. The procedures considered include the high-level W1, W1', CBS-QB3, ROCBS-QB3, G3(MP2)-RAD, and G3X(MP2)-RAD methods, unrestricted and restricted versions of the double-hybrid density functional theory (DFT) procedures B2-PLYP and MPW2-PLYP, and unrestricted and restricted versions of the hybrid DFT procedures BMK and MPWB1K, as well as the unrestricted DFT procedures UM05 and UM05-2X. The high-level composite procedures show very good agreement with experiment and are used to evaluate the performance of the comparatively less expensive DFT procedures. RMPWB1K and both RBMK and UBMK give very promising results for absolute BDEs, while additionally restricted and unrestricted X2-PLYP methods and UM05-2X give excellent RSE values. UM05, UB2-PLYP, UMPW2-PLYP, UM05-2X, and UMPWB1K are among the less well performing methods for BDEs, while UMPWB1K and UM05 perform less well for RSEs. The high-level theoretical results are used to recommend alternative experimental BDEs for propyne, acetaldehyde, and acetic acid.     

An assessment of theoretical procedures for predicting the thermochemistry and kinetics of hydrogen abstraction by methyl radical from benzene

The reaction enthalpy (298 K), barrier (0 K), and activation energy and preexponential factor (600-800 K) have been examined computationally for the abstraction of hydrogen from benzene by the methyl radical, to assess their sensitivity to the applied level of theory. The computational methods considered include high-level composite procedures, including W1, G3-RAD, G3(MP2)-RAD, and CBS-QB3, as well as conventional ab initio and density functional theory (DFT) methods, with the latter two classes employing the 6-31G(d), 6-31+G(d,p) and/or 6-311+G(3df,2p) basis sets, and including ZPVE/thermal corrections obtained from 6-31G(d) or 6-31+G(d,p) calculations. Virtually all the theoretical procedures except UMP2 are found to give geometries that are suitable for subsequent calculation of the reaction enthalpy and barrier. For the reaction enthalpy, W1, G3-RAD, and URCCSD(T) give best agreement with experiment, while the large-basis-set DFT procedures slightly underestimate the endothermicity. The reaction barrier is slightly more sensitive to the choice of basis set and/or correlation level, with URCCSD(T) and the low-cost BMK method providing values in close agreement with the benchmark G3-RAD value. Inspection of the theoretically calculated rate parameters reveals a minor dependence on the level of theory for the preexponential factor. There is more sensitivity for the activation energy, with a reasonable agreement with experiment being obtained for the G3 methods and the hybrid functionals BMK, BB1K, and MPW1K, especially in combination with the 6-311+G(3df,2p) basis set. Overall, the high-level G3-RAD composite procedure, URCCSD(T), and the cost-effective DFT methods BMK, BB1K, and MPW1K give the best results among the methods assessed for calculating the thermochemistry and kinetics of hydrogen abstraction by the methyl radical from benzene.     

BDE261: a comprehensive set of high-level theoretical bond dissociation enthalpies

We have used the high-level W1w protocol to compile a comprehensive collection of 261 bond dissociation enthalpies (BDEs) for bonds connecting hydrogen, first-row and second-row p-block elements. Together they cover 45 bond types, and we term this the BDE261 set. We have used these benchmark values to assess the performance of computationally less demanding theoretical procedures, including density functional theory (DFT), double-hybrid DFT (DHDFT), and high-level composite procedures. We find that the M06-2X (DFT), ROB2-PLYP and DuT-D3 (DHDFT), and G3X(MP2)-RAD and G4(MP2)-6X (composite) procedures yield absolute BDEs with satisfactory to excellent accuracy. Overall, we recommend G4(MP2)-6X as an accurate and relatively cost-effective procedure for the direct computation of BDEs. One important finding is that the deviations for DFT and (especially) DHDFT procedures are often quite systematic. This allows an alternative approach to obtaining accurate absolute BDEs, namely, to evaluate accurate relative BDEs (RBDEs) using a computationally less demanding procedure, and to use these RBDEs in combination with appropriate and accurate reference BDEs to give accurate absolute BDEs. We recommend DuT-D3 for this purpose. For a still less computationally demanding approach, we introduce the deviation from additivity of the RBDE (DARBDE), and demonstrate that the combination of lower-level DARBDEs for larger systems and higher-level (W1w) reference RBDEs and BDEs for small systems can be utilized to obtain improved RBDEs for multiply substituted systems at low cost.     

Variable trends in R-X bond dissociation energies (R = Me, Et, i-Pr, t-Bu)

[structure: see text] High level ab initio molecular orbital calculations confirm experimental indications that the effect of alkyl substituents (R = Me, Et, i-Pr, t-Bu) on R-X bond dissociation energies varies considerably according to the nature of X. A simple qualitative explanation in terms of valence-bond theory is presented, highlighting the increasing importance of the stabilization of R-X by the ionic R(+)X(-) configuration for electronegative X substituents (such as F, OH, and OCH(3)).     

环境污染物中碳氯键离解能的理论研究

利用六种密度泛函理论方法（B3LYP, B3P86, MPW1K, TPSS1KCIS, X3LYP, BMK）对碳氯键离解能进行理论计算,结果发现几种新发展的密度泛函(DFT)方法用于碳氯键离解能的计算比传统的B3LYP有较大的改善,其中对能量估算相对准确的B3P86方法对碳氯键离解能的计算精度最高,对17个分子中碳氯键离解能计算的平均绝对偏差为6.58 kJ/mol。最后运用B3P86方法对一系列环境危害较大,但可通过光化学降解和生物降解的氯代有机物的碳氯键离解能值进行预测,并讨论了影响碳氯键离解能的结构性质关系。     

S=O homolytic bond dissociation enthalpies in sulfoxides

The S=O bond dissociation enthalpies (BDE) were calculated using high-level ab initio methods including G3, G3B3, CBS-Q, CBS-4M, CCSD(T), and MP2. Based on the comparison of these theoretical values and experimental ones, the performances of a number of density functional theory (DFT) methods were then assessed. It was found that the B3P86 method gave the lowest root of mean square error. We therefore used this method to calculate the S=O BDEs of a number of substituted sulfoxides. The electronic effect of the substituents and the remote substituents effect of aryl-substituted sulfoxides on S=O BDE were investigated. In addition, a molecular orbital analysis of typical molecules was conducted in order to investigate the electronic effect on S=O BDEs. We also predicted several S=O BDE values of heteroaromatic substituted sulfoxides using the B3P86 method.     

Reliable low-cost theoretical procedures for studying addition-fragmentation in RAFT polymerization

Enthalpies for the beta-scission reactions, R'SC(*)(Z)SR --> R'SC(Z)=S + (*)R (for R, R' = CH(3), CH(2)CH(3), CH(2)CN, C(CH(3))(2)CN, CH(2)COOCH(3), CH(CH(3))COOCH(3), CH(2)OCOCH(3), CH(2)Ph, C(CH(3))(2)Ph, and CH(CH(3))Ph and Z = CH(3), H, Cl, CN, CF(3), NH(2), Ph, CH(2)Ph, OCH(3), OCH(2)CH(3), OCH(CH(3))(2), OC(CH(3))(3), and F) have been calculated using a variety of DFT, MP2, and ONIOM-based methods, as well as G3(MP2)-RAD, with a view to identifying an accurate method that can be practically applied to larger systems. None of the DFT methods examined can reproduce the quantitative, nor qualitative, values of the fragmentation enthalpy; in most cases the relative errors are over 20 kJ mol(-1) and in some cases as much as 55 kJ mol(-1). The ROMP2 methods fare much better, but fail when the leaving group radical (R(*)) is substituted with a group (such as phenyl or CN) that delocalizes the unpaired electron. However, provided the primary substituents on the leaving group radical are included in the core system, an ONIOM-based approach in which the full system is studied via ROMP2 (or SCS- or SOS-MP2) calculations with the 6-311+G(3df,2p) basis set and the core system is studied at G3(MP2)-RAD can reproduce the corresponding G3(MP2)-RAD values of the full systems within 5 kJ mol(-1) and is a practical method for use on larger systems.     

O-H bond dissociation enthalpies of oximes: a theoretical assessment and experimental implications

By using a multilayer composite ab initio method ONION-G3B3, we calculated O-H bond dissociation enthalpies (BDEs) of 58 oximes that were measured experimentally. Experimental BDEs derived from thermal decomposition kinetics and calorimetric measurements were found to be consistent with the theory. However, the electrochemical method was found to give questionably high BDEs possibly due to errors in the measurement of pKa's or redox potentials. Subsequently, the performances of a variety of DFT functionals including B3LYP, B3P86, B3PW91, BHandH, BHandHLYP, BMK, PBE1PBE, MPW1KCIS, mPWPW91, MPW1B95, and MPW1K were tested to calculate oxime O-H BDEs, where ROBHandHLYP was found to be the most accurate. By using this method, we calculated O-H BDEs of over 140 oximes in a systematic fashion. All of the calculated O-H BDEs fell in the range from 76.8 to 89.8 kcal/mol. An amino group on the azomethine carbon was found to strengthen the O-H bond, whereas bulky alkyl substituents on oximes decreased O-H BDEs due to their large steric-strain-relieving effects in the process of O-H bond cleavage. Para substituents had little effect on the BDEs of benzaldoximes and phenyl methyl ketoximes. Finally, on the basis of a spin distribution calculation, aryl-, alkyl-, and carbonyl-substituted iminoxyl radicals were found to be sigma-radicals, whereas amino-substituted iminoxyl radicals were of pi-structure.     

Bond dissociation energies and radical stabilization energies associated with model peptide-backbone radicals

Bond dissociation energies (BDEs) and radical stabilization energies (RSEs) have been calculated for a series of models that represent a glycine-containing peptide-backbone. High-level methods that have been used include W1, CBS-QB3, U-CBS-QB3, and G3X(MP2)-RAD. Simpler methods used include MP2, B3-LYP, BMK, and MPWB1K in association with the 6-311+G(3df,2p) basis set. We find that the high-level methods produce BDEs and RSEs that are in good agreement with one another. Of the simpler methods, RBMK and RMPWB1K achieve good accuracy for BDEs and RSEs for all the species that were examined. For monosubstituted carbon-centered radicals, we find that the stabilizing effect (as measured by RSEs) of carbonyl substituents (CX=O) ranges from 24.7 to 36.9 kJ mol(-1), with the largest stabilization occurring for the CH=O group. Amino groups (NHY) also stabilize a monosubstituted alpha-carbon radical, with the calculated RSEs ranging from 44.5 to 49.5 kJ mol(-1), the largest stabilization occurring for the NH2 group. In combination, NHY and CX=O substituents on a disubstituted carbon-centered radical produce a large stabilizing effect ranging from 82.0 to 125.8 kJ mol(-1). This translates to a captodative (synergistic) stabilization of 12.8 to 39.4 kJ mol(-1). For monosubstituted nitrogen-centered radicals, we find that the stabilizing effect of methyl and related (CH2Z) substituents ranges from 25.9 to 31.7 kJ mol(-1), the largest stabilization occurring for the CH3 group. Carbonyl substituents (CX=O) destabilize a nitrogen-centered radical relative to the corresponding closed-shell molecule, with the calculated RSEs ranging from -30.8 to -22.3 kJ mol(-1), the largest destabilization occurring for the CH=O group. In combination, CH2Z and CX=O substituents at a nitrogen radical center produce a destabilizing effect ranging from -19.0 to -0.2 kJ mol(-1). This translates to an additional destabilization associated with disubstitution of -18.6 to -7.8 kJ mol(-1).     

A computational study of C?S bond dissociation enthalpies in petroleum chemistry

High‐level theoretical methods (BMK, B3LYP, B98, B3P86, B3PW91, PBE1PBE, PBE1KIS, MPWPW91, MPW1KCIS, TPSS1KCIS, G3, G3//BMK, and CBS‐Q) were utilized to study the carbon–sulfur bond dissociation enthalpies (BDEs) of hydrocarbons in petroleum chemistry. The performance of these methods was evaluated on the basis of a training set including the available experimental BDEs, and it was found that the BMK (Boese‐Martin for Kinetics) method had the best agreement with experimental values. By using the BMK method to calculate C S BDEs of saturated hydrocarbon, the main factors, which determine the changing trend of BDE values, were discussed. Results revealed that the repulsive energies played an important role in determining a change in the trend of BDEs as well as the radical effect. Good agreements were obtained between further calculated BDEs and the experimental ones for C S and C O bonds. Moreover, the same calculation method was applied to predict C S BDEs for which the experimental values were still unavailable. A range of predicted bond dissociation enthalpy values were provided according to the calculations. © 2010 Wiley Periodicals, Inc. Heteroatom Chem 22:97–105, 2011; View this article online at wileyonlinelibrary.com . DOI 10.1002/hc.20662     

Activation energies of pericyclic reactions: performance of DFT, MP2, and CBS-QB3 methods for the prediction of activation barriers and reaction energetics of 1,3-dipolar cycloadditions, and revised activation enthalpies for a standard set of hydrocarbon pericyclic reactions

Activation barriers and reaction energetics for the three main classes of 1,3-dipolar cycloadditions, including nine different reactions, were evaluated with the MPW1K and B3LYP density functional methods, MP2, and the multicomponent CBS-QB3 method. The CBS-QB3 values were used as standards for 1,3-dipolar cycloaddition activation barriers and reaction energetics, and the density functional theory (DFT) and MP2 methods were benchmarked against these values. The MPW1K/6-31G* method and basis set performs best for activation barriers, with a mean absolute deviation (MAD) value of 1.1 kcal/mol. The B3LYP/6-31G* method and basis set performs best for reaction enthalpies, with a MAD value of 2.4 kcal/mol, while the MPW1K method shows large errors for reaction energetics. The MP2 method gives the expected systematic underestimation of barriers. Concerted and nearly synchronous transition structures are predicted by all DFT and MP2 methods. Also reported are revised estimated 0 K experimental activation enthalpies for a standard set of hydrocarbon pericyclic reactions and updated comparisons to experiment for DFT, ab initio, and multicomponent methods. B3LYP and MPW1K methods with MAD values of 1.5 and 2.1 kcal/mol, respectively, fortuitously outperform the multicomponent CBS-QB3 method, which has a MAD value of 2.3. The MAD value of the O3LYP functional improves to 2.4 kcal/mol from the previously reported 3.0 kcal/mol.     

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.     

Accurate ab initio prediction of propagation rate coefficients in free-radical polymerization: Acrylonitrile and vinyl chloride

A systematic methodology for calculating accurate propagation rate coefficients in free-radical polymerization was designed and tested for vinyl chloride and acrylonitrile polymerization. For small to medium-sized polymer systems, theoretical reaction barriers are calculated using G3(MP2)-RAD. For larger systems, G3(MP2)-RAD barriers can be approximated (to within 1 kJ mol⁻¹) via an ONIOM-based approach in which the core is studied at G3(MP2)-RAD and the substituent effects are modeled with ROMP2/6-311+G(3df,2p). DFT methods (including BLYP, B3LYP, MPWB195, BB1K and MPWB1K) failed to reproduce the correct trends in the reaction barriers and enthalpies with molecular size, though KMLYP showed some promise as a low cost option for very large systems. Reaction rates are calculated via standard transition state theory in conjunction with the one-dimensional hindered rotor model. The harmonic oscillator approximation was shown to introduce an error of a factor of 2–3, and would be suitable for “order-of-magnitude” estimates. A systematic study of chain length effects indicated that rate coefficients had largely converged to their long chain limit at the dimer radical stage, and the inclusion of the primary substituent of the penultimate unit was sufficient for practical purposes. Solvent effects, as calculated using the COSMO model, were found to be relatively minor. The overall methodology reproduced the available experimental data for both of these monomers within a factor of 2.     

A theoretical study of the thermodynamics and kinetics of small organosulfur compounds

The performance of a large set of ab initio procedures in predicting geometries, thermochemical and kinetic data of small sulfur compounds is assessed. Geometries and thermochemical data for H₂S, (CH₃)₂S, H₂S₂, (CH₃)₂S₂ and H₂C=S are studied using the HF method, density functional theory methods (B3LYP, BHandHLYP, MPW1PW91 and BMK), post-HF methods [MP2, MP3, MP4, CCSD, CCSD(T) and QCISD] and composite techniques (G3, G3B3, CBS-QB3 and W1U). A set of five reactions involving these small organosulfur compounds is studied and the influence of the level of theory on transition state geometries, reaction barriers and rate coefficients is assessed. Independent of the level of theory used, accurate geometries are obtained with the 6-311G(2d,d,p) and cc-pVTZ basis sets, both reproducing experimental bond lengths and bond angles within 2 pm and 0.5°. Besides composite methods, the BMK/cc-pVTZ method is the only studied method that succeeds to predict standard enthalpies of formation within 10 kJ mol^?1 of the experimental data. The best agreement with experimental rate coefficients is obtained with the BHandHLYP/cc-pVTZ method, closely followed by the composite methods and the BMK/cc-pVTZ method. All these methods succeed to reproduce the experimental rate coefficients within a factor 4. To obtain an accurate prediction of both thermochemical and kinetic data for organosulfur compounds, the commonly used composite methods G3B3 and CBS-QB3 and the BMK/cc-pVTZ method prove to be valuable tools.     

DFT studies of the phosphinidene derivative HPNaF and its insertion reaction with R–H(R=F,OH, NH<Subscript>2</Subscript>, CH<Subscript>3</Subscript>)

The formations of the phosphinidene derivative HPNaF and its insertion reactions with R–H (R=F, OH, NH₂, CH₃) have been systematically investigated employing the density functional theory (DFT), such as the B3LYP and MPW1PW91 methods. A comparison with the results of MP2 calculations shows that MPW1PW91 underestimates the barrier heights for the four reactions considered. Similarly, the same is also true for the B3LYP method depending on the selected reactions, but by much less than MPW1PW91, where the barrier heights of the four reactions are 25.2, 85.7, 119.0, and 142.4 kJ/mol at the B3LYP/6-311+G* level of theory, respectively. All the mechanisms of the four reactions are identical to each other, i.e., an intermediate has been located during the insertion reaction. Then, the intermediate could dissociate to substituted phosphinidane(H₂RP) and NaF with a barrier corresponding to their respective dissociation energies. Correspondingly, the reaction energies for the four reactions are −92.2, −68.1, −57.2, and −44.3 kJ/mol at the B3LYP/6-311+G* level of theory, respectively, where both the B3LYP and MPW1PW91 methods underestimate the reaction energies compared with the MP2 results. The linear correlations between the calculated barrier heights and the reaction energies have also been observed. As a result, the relative reactivity among the four insertion reactions should be as follows: H–F > H–OH > H–NH₂ > H–CH₃.     

Assessment of Contemporary Theoretical Methods for Bond Dissociation Enthalpies

The density functional theory (DFT) is the most popular method for evaluating bond dis-sociation enthalpies (BDEs) of most molecules. Thus, we are committed to looking for alternative methods that can balance the computational cost and higher precision to the best for large systems. The performance of DFT, double-hybrid DFT, and high-level com-posite methods are examined. The tested sets contain monocyclic and polycyclic aromatic molecules, branched hydrocarbons, small inorganic molecules, etc. The results show that the mPW2PLYP and G4MP2 methods achieve reasonable agreement with the benchmark values for most tested molecules, and the mean absolute deviations are 2.43 and 1.96 kcal/mol after excluding the BDEs of branched hydrocarbons. We recommend the G4MP2 is the most appropriate method for small systems (atoms number ≤20); the double-hybrid DFT methods are advised for large aromatic molecules in medium size (20 ≤atoms number ≤50), and the double-hybrid DFT methods with empirical dispersion correction are recommended for long-chain and branched hydrocarbons in the same size scope; the DFT methods are advised to apply for large systems (atoms number ≥50), and the M06-2X and B3P86 methods are also favorable. Moreover, the di erences of optimized geometry of different methods are discussed and the effects of basis sets for various methods are investigated.     

Synthesis of zirconium, hafnium, and tantalum complexes with sterically demanding hydrazide ligands

The bulky hydrazine t-BuN(H)NMe2 was synthesized via hydrazone and t-BuN(H)N(H)Me intermediates as the major component in a 90:5:5 mixture consisting of t-BuN(H)NMe2, t-BuN(Me)N(H)Me, and t-BuN(Me)NMe2. Reacting the mixture with n-BuLi followed by distillation and fractional crystallization led to the isolation of the ligand precursor LiN(t-Bu)NMe2. Lithium hydrazides, LiN(R)NMe2, were reacted with metal chlorides to afford the hydrazide complexes M(N(Et)NMe2)4 (M = Zr or Hf), MCl(N(R)NMe2)3 (M = Zr, R = i-Pr or t-Bu; M = Hf, R = t-Bu), and TaCl3(N(i-Pr)NMe2)2. The X-ray crystal structures of [LiN(i-Pr)NMe2]4, [LiN(t-Bu)NMe2.THF]2, ZrCl(N(R)NMe2)3 (R = i-Pr or t-Bu), and TaCl3(N(i-Pr)NMe2)2 were determined. The structural analyses revealed that the hydrazide ligands in ZrCl(N(R)NMe2)3 (R = i-Pr or t-Bu) and TaCl3(N(i-Pr)NMe2)2 are eta2 coordinated.