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.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.     

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.     

N—O键解离焓的密度泛函理论研究

在高精度计算方法G3和G3B3的基础上,比较了密度泛函理论(DFT)十几种方法对N—O键解离焓(BDE)相对于实验值的计算精度,发现用B3P86方法计算15种化合物N—O键的BDE,均方根误差最小,仅为6.36kJ·mol-1,计算值与实验值的线性相关系数为0.991.在此基础上,用该方法分别计算了非芳香化合物及芳香化合物的N—O键BDE.通过自然键轨道分析,发现部分N—O键的BDE与N—O键的键长、原子电荷密度及键级之间存在定量关系.此外,在B3P86方法的基础上预测了几种典型的杂环芳香化合物N—O键BDE值.     

Assessment of theoretical methods for the calculation of methyl cation affinities

The methyl cation affinity (MCA; 298 K) of a variety of neutral and anionic bases has been examined computationally with a wide variety of theoretical methods. These include high-level composite procedures such as W1, G3, G3B3, and G2, conventional ab initio methods such as CCSD(T) and MP2, as well as a selection of density functional theory (DFT) methods. Experimental results for a variety of small model systems are well reproduced with practically all these methods, and the performance of DFT based methods are far superior in comparison to their MP2 analogs for these small models. For larger model, systems including motifs frequently encountered in organocatalysts, the performance deteriorates somewhat for DFT methods, while it improves significantly for MP2, rendering the former methods unreliable for common organic bases. Thus, MP2 calculations performed in combination with basis sets such as 6-31+G(2d, p) or larger, appear to offer a practical and reliable approach to compute MCAs of organic bases.     

An assessment of density functional methods for studying molecular adsorption in cluster models of zeolites

The performance of six density functional theory (DFT) methods has been tested for a zeolite cluster containing three tetrahedral atoms (3T) and the complexes it forms with water and methanol molecules. The DFT methods (BLYP, BP86, BPW91, B3LYP, B3P86, B3PW91) give results in good agreement with second-order perturbation theory (MP2). The results in this paper provide evidence of the suitability of DFT methods for studying hydrogen-bonded adsorption complexes in zeolites. Generally, the hybrid DFT methods are in closer agreement with experiment and MP2 than the pure DFT methods for geometrical parameters. The only exception is the Z⁻ geometry, perhaps due to its anionic character. All DFT methods give results in good overall agreement with MP2 for intramolecular geometrical parameters of the adsorption complexes, intramolecular vibrational frequencies, and adsorption energies. The B3LYP method gives intermolecular geometries and intermolecular vibrational frequencies which are closest to those obtained from the MP2 method. Thus, the B3LYP method seems to be the best choice for a density functional treatment of molecular adsorption in zeolite systems.     

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.     

A quantum chemistry study on C–H homolytic bond dissociation enthalpies of five-membered and six-membered heterocyclic compounds

The C–H homolytic bond dissociation enthalpies (BDEs) of 27 heterocyclic compounds of small systems (less than 8 non-hydrogen atoms) were evaluated by the composite ab initio methods of G4 and CBS-Q. In addition, the C–H BDEs of an extended database including 60 heterocyclic compounds were assessed by 16 DFT functionals. The correlation between the theoretical and experimental values reveals that the BMK functional provided the lowest root mean square error (RMSE) of 10.2 kJ/mol, and the correlation coefficient (R²) was 0.955. The mean deviation (MD), mean absolute deviation (MAD) of BMK are 0.1 kJ/mol and 7.9 kJ/mol separately. Therefore, we utilized BMK to research C–H BDEs together with the substituent effects of five-membered and six-membered heterocyclic compounds including large systems. The nature of C–H BDE change pattern was analyzed by the natural bond orbital (NBO).     

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.     

Accurate calculation of the heats of formation for large main group compounds with spin-component scaled MP2 methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-zeta quality) treatments become routinely possible for systems with 50-100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the "real" accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10-20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds.     

Vibrational frequencies of hydrazoic acid and methyl azide: density functional theory study

Harmonic vibrational frequencies of HN3 and CH3N3 molecules and their several isotopomers are calculated using HF, MP2 and five popular density functional theory (DFT) methods. On the basis of the comparison between calculated and experimental results, assignments of fundamental vibrational modes arc examined. HF and MP2 results are in bad agreement with experimental values. Of the five DFT methods, BLYP reproduces the observed fundamental frequencies the most satisfactorily. Two hybrid DFT methods are found to yield frequencies generally higher than the observed fundamental frequencies. The results indicate that BLYP calculation is a very promising approach for understanding the observed spectral features.     

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.     

Basis set convergence of explicitly correlated double-hybrid density functional theory calculations

The basis set convergence of explicitly correlated double-hybrid density functional theory (DFT) is investigated using the B2GP-PLYP functional. As reference values, we use basis set limit B2GP-PLYP-F12 reaction energies extrapolated from the aug(')-cc-pV(Q+d)Z and aug(')-cc-pV(5+d)Z basis sets. Explicitly correlated double-hybrid DFT calculations converge significantly faster to the basis set limit than conventional calculations done with basis sets saturated up to the same angular momentum (typically, one "gains" one angular momentum in the explicitly correlated calculations). In explicitly correlated F12 calculations the VnZ-F12 basis sets converge faster than the orbital A(')VnZ basis sets. Furthermore, basis set convergence of the MP2-F12 component is apparently faster than that of the underlying Kohn-Sham calculation. Therefore, the most cost-effective approach consists of combining the MP2-F12 correlation energy from a comparatively small basis set such as VDZ-F12 with a DFT energy from a larger basis set such as aug(')-cc-pV(T+d)Z.     

Accurate Prediction of IrH Bond Dissociation Enthalpies by Density Functional Theory Methods

The iridium hydride complexes have been extensively used in organic reactions, such as oxidation and hydrogenation reactions. In many of these reactions, the dissociation or formation of Ir? H bond plays an important role in determining the overall reaction rates and yields. In the present study, the accuracy of different theoretical methods for prediction of Ir? H bond strengths has been examined on the basis of the previously reported Ir? H BDEs of 17 different complexes. Comparing the performance of different DFT functionals (e.g. B3LYP, TPSS, M06), different basis sets (including the different effective core potentials (ECP) on Ir and I atoms, and the total electron basis sets on the other atoms), and different solvation models (SMD, CPCM, and IEFPCM) in solution phase single point calculations, we found that the gas‐phase calculation with TPSS/(LanL2DZ: 6‐31G(d)) method is relatively more accurate than the other gas‐phase calculation methods, and can well simulate the Ir? H BDEs in low‐polarity solvents (such as chlorobenzene and dichloroethane). Finally, efforts were put in analyzing the structure‐activity relationships between the ligand structure (around Ir center) and the Ir? H BDEs. We wish the present study could benefit future studies on the Ir‐H complexes involved organic reactions.     

Density Functional Theory Calculations on Ni-Ligand Bond Dissociation Enthalpies

The formation and breaking of Ni-L (L=N-heterocyclic carbene, tertiary phosphine etc.) bond is involved in many Ni-catalyzed/mediated reactions. The accurate prediction of Ni-L bond dissociation enthalpies (BDEs) is potentially important to understand these Ni-complex involving reactions. We assess the accuracy of diffierent DFT functionals (such as B3LYP, M06, MPWB1K, etc.) and diffierent basis sets, including both effective core potentials for Ni and the all electron basis sets for all other atoms in predicting the Ni-L BDE values reported recently by Nolan et al. [J. Am. Chem. Soc. 125, 10490 (2003) and Organometallics 27, 3181 (2008)]. It is found that the MPWB1K/LanL2DZ:6-31+G(d,p)//MPWB1K/LanL2DZ:6-31G(d) method gives the best correlations with the experimental results. Meanwhile, the solvent effect calculations (with CPCM, PCM, and SMD models) indicate that both CPCM and PCM perform well.     

A theoretical study of the interactions between N, N-dimethylformamide and aromatic hydrocarbons

The B3LYP and MP2 methods with 6-31G* basis set were used to predict the geometries of N, N-dimethylformamide (DMF) dimer and DMF–aromatic hydrocarbons interaction systems. A total of 10 conformers were obtained with no imaginary frequencies, respectively. The interaction energies of these binary mixtures have been obtained. The analyses of chelpg charge distribution and the atoms in molecules theory (AIM) were used to analyze the nature of the interaction. The results show the presence of hydrogen bonds between DMF and aromatic hydrocarbons. The interaction between DMF and benzonitrile is the strongest with the interaction energy of −21.58 kJ mol⁻¹ (BSSE corrected), and the intensity order of interactions is DMF–benzonitrile: d2 > DMF–DMF: a2 > DMF–toluene: c1 > DMF–benzene: b2.     

Theoretical studies of bond dissociation energies for removal of the nitrile group in some nitrile compounds

The CCN bond distances and bond dissociation energies (BDEs) are estimated by utilizing quantum chemical calculations for 16 nitrile compounds. Since DFT methods have been researched to have low basis sets sensitivity for small and medium molecules in our earlier work [Jun Zhao, Xinlu Cheng, Xiangdong. Yang, J. Mol. Struct. (Theochem) 766 (2006) 87] 16 nitrile compounds are studied by employing the hybrid density functional theory (B3LYP, B3PW91, B3P86) and the complete basis set (CBS-Q) method in conjunction with the 6-311G^** basis set. The obtained results are compared with the available experimental data. It is demonstrated that CBS-Q method, which can produce reasonable BDEs for some systems, seems unable to predict accurate BDEs here. While, the B3P86 calculated results agree very well with the experimental values. So B3P86 method is suitable for computing the reliable BDEs of CCN bond for nitrile compounds.     

Consequences of spin contamination in unrestricted calculations on open-shell species: effect of Hartree-Fock and Møller-Plesset contributions in hybrid and double-hybrid density functional theory approaches

The extent of spin contamination in unrestricted versions of pure, hybrid and double-hybrid density functional theory (DFT) methods, and its consequences, as manifested in the difference between unrestricted and restricted energies (U - R), has been investigated for 22 homolytic bond dissociation reactions. In accordance with previous studies, increasing the amount of Hartree-Fock (HF) exchange in unrestricted hybrid DFT procedures leads to an increase in the extent of spin contamination. However, in unrestricted double-hybrid DFT procedures, which include both a proportion of HF exchange and a perturbative correlation contribution (MP2), the opposing behavior of UHF and UMP2 with respect to spin contamination leads to smaller differences between the energies predicted by unrestricted and restricted variants. For example, for the most spin-contaminated radicals, a 30-100 kJ mol(-1) |U - R| difference at the HF and MP2 levels is reduced to just 0-5 kJ mol(-1) with the double-hybrid functionals. The double-hybrid UDFT procedures can thus benefit from the inclusion of UHF and UMP2 contributions without incurring to the same extent the problems associated with spin contamination.     

Halogen‐Bonding Interactions with π Systems: CCSD(T), MP2, and DFT Calculations

Halogen bonding is a noncovalent interaction between a halogen atom and a nucleophilic site. Interactions involving the π electrons of aromatic rings have received, up to now, little attention, despite the large number of systems in which they are present. We report binding energies of the interaction between either NCX or PhX (X=F, Cl, Br, I) and the aromatic benzene system as determined with the coupled cluster with perturbative triple excitations method [CCSD(T)] extrapolated at the complete basis set limit. Results are compared with those obtained by Møller–Plesset perturbation theory to second order (MP2) and density functional theory (DFT) calculations by using some of the most common functionals. Results show the important role of DFT in studying this interaction.