Performance of Density Functional Theory for Transition Metal Oxygen Bonds

The accuracy of density functional theory (DFT) limits predictions in theoretical catalysis, and strong chemical bonds between transition metals and oxygen pose a particular challenge. We benchmarked 30 diverse density functionals against the bond dissociation enthalpies (BDE) of the 30 MO and 30 MO⁺ diatomic systems of all the 3d, 4d, and 5d metals, to test universality across the d-block as required in comparative studies. Seven functionals, B98, B97-1, B3P86, B2PLYP, TPSSh, B3LYP, and B97-2, display mean absolute errors (MAE) <30 kJ/mol. In contrast, many commonly used functionals such as PBE and RPBE overestimate M−O bonding by +30 kJ/mol and display MAEs from 48–76 kJ/mol. RPBE and OPBE reduce the over-binding of PBE but remain very inaccurate. We identify a linear relationship (p-value 7.6 ⋅ 10⁻⁵) between the precision and accuracy of DFT, i. e. inaccurate functionals tend to produce larger, unpredictable random errors. Some functionals commonly deviate from this relationship: Thus, M06-2X is very precise but not very accurate, whereas B3LYP* and MN15-L are more accurate but less precise than M06-2X. The best-performing hybrids have 10–30 % HF exchange, but this can be relieved by double hybrids (B2PLYP). Most functionals describe trends well, but errors comparing 5d to 4d/3d are ∼10 kJ/mol larger than group-wise errors, due to uncertainties in the spin-orbit coupling corrections for effective core potentials, affecting e. g. Pt/Pd or Au/Ag comparisons.     

Theoretical Study of the N-NO2 Bond Dissociation Energies for Energetic Materials with Density Functional Theory

The N-NO2 bond dissociation energies （BDEs） for 7 energetic materials were computed by means of accurate density functional theory （B3LYP, B3PW91 and B3P86） with 6-31G＊＊ and 6-311G＊＊ basis sets. By comparing the computed energies and experimental results, we find that the B3P86/6-311G＊＊ method can give good results of BDE, which has the mean absolute deviation of 1.30kcal/mol. In addition, substituent effects were also taken into account. It is noted that the Hammett constants of substituent groups are related to the BDEs of the N-NO2 bond and the bond dissociation energies of the energetic materials studied decrease when increasing the number of NO2 group.     

1, 4-Pyrone Effects on O-H Bond Dissociation Energies of Catechols in Flavonoids: A Density Functional Theory Study

In recent years, there has been growing interest in selecting efficient antioxidants with low toxicity to reduce the damage of free radicals. Among these antioxidants, flavonoids have been paid much attention, owing to their excellent antioxidative and pharmacological activities1. Up to now, many efforts have been given to summarize the structure-activity relationships (SAR) for flavonoids. It has been widely accepted that two structural factors are critical for flavonoids to enhance the…     

Density Functional Calculations of C–NO_2 Bond Dissociation Energies for Nitroalkanes Molecules

Bond dissociation energies for the removal of nitrogen dioxide group in some nit- roalkane energetic materials have been calculated by using the three hybrid density functional theory (DFT) methods B3LYP, B3PW91 and B3P86 with 6-31g** and 6-311g** basis sets. The computed BDEs have been compared with the available experimental results. It is found that the B3P86 method with 6-31g** and 6-311g** basis sets can obtain satisfactory bond dissociation energies (BDEs), which are in extraordinary agreement with the experimental data. Considering the smaller mean absolute deviation and maximum difference, the reliable B3P86/6-311g** method was recommended to compute the BDEs for the removal of nitrogen dioxide group in the nitroalkane energetic materials. Using the method, the BDEs of 8 other nitroalkane energetic materials have been calculated and the maximum difference from experimental value is 1.76 kcal·mol-1 (for the BDE of tC4H9–NO2), which further proves the reliability of B3P86/6-311g** method. In addition, it is noted that the BDEs of C–NO2 bond change slightly for main chain nitroalkane compounds with the maximum difference of only 3.43 kcal mol-1.     

碳氟键均裂解离能的密度泛函理论研究

运用6种密度泛函方法(B3LYP, B3P86, B3PW91, PBE1PBE, MPW1B95, MPW1K)对15个含氟有机化合物的碳氟键均裂解离能进行理论计算, 得到的理论值与实验值比较, 发现B3P86方法用于碳氟键均裂解离能的计算相对可靠. 使用验证后的理论方法对含氟杂环有机化合物和卤氟烃中的碳氟键均裂解离能进行了预测和分析, 并进一步讨论了α-取代基效应以及Hammett型取代基效应对碳氟键均裂解离能的影响.     

Density Functional Theory Study on the Adsorption of CN on Transition Metal M（100） （M = Ni,Pd, Pt,Cu, Ag and Au） Surfaces

The adsorption of cyanide on the top site of a series of transition metal M（100） （M = Cu, Ag, Au, Ni, Pd, Pt） surfaces via carbon and nitrogen atoms respectively, with the CN axis perpendicular to the surface, has been studied by means of density functional theory and cluster model. Geometry, adsorption energy and vibrational frequencies have been determined, and the present calculations show that the adsorption of CN through C-end on metal surface is more favorable than that via N-end for the same surface. The vibrational frequencies of CN for C-down configuration on surface are blue-shifted with respect to the free CN, which is contrary to the change of vibrational frequencies when CN is adsorbed by N-down structure. Furthermore, the charge transfer from surface to CN causes the increase of surface work function.     

密度泛函法计算C1-C14正构烃生成焓及C-C键裂解能

采用密度泛函理论(DFT)方法研究了费托石脑油裂解反应中涉及到C₁-C₁₄正构烃和自由基中间体的生成焓及其C-C键解离能(BDE)。 结果表明,在所有评价的密度泛函理论方法（B97-1、BB1K、B1B95、MPWB1K和MPW1B95）中,MPW1B95/6-311G(d,p)方法计算最精确。 以此方法为基准,进一步对高碳烃及其裂解产物的标准生成焓和C-C键解离能进行了预测。 与可得到的实验数据相比,MPW1B95/6-311G(d,p)方法预测的烃和自由基的平均生成焓分别为0.8和2.7 kJ/mol,C-C键解离能的平均绝对误差只有3.1 kJ/mol,表明此方法不仅可准确计算正构烃标准生成焓和C-C键解离能,而且还能正确预测C-C键解离能变化趋势。     

5-氟胞嘧啶互变异构的密度泛函理论计算

采用BH-HLYP/6-311＋G**方法对10种气相和水相中可能存在的5-氟胞嘧啶互变异构体进行了几何全优化, 并计算出它们的总能量和吉布斯自由能. Onsager反应场溶剂模型用于水相的计算. 计算结果表明, 5-氟胞嘧啶在气相中主要以烯醇式-氨基式形式存在, 在水相中主要以酮式-氨基式形式存在. 溶剂化自由能与异构体的气相偶极矩存在相关性．进一步求得互变异构化以及构象异构化和顺反异构化的过渡态, 探讨异构化过程中的几何结构和能量的变化.     

烃类化合物碳氢键解离焓的密度泛函理论研究

通过比较10种密度泛函方法对烃类化合物碳氢键解离焓的计算精度, 发现新型密度泛函BMK方法具有最高的计算精度. 利用该方法计算了包含饱和链烃,、不饱和链烃、脂环烃和芳香烃在内的172个烃类化合物的碳氢键解离焓,计算均方根误差仅为7.95 kJ•mol^－1, 线性拟合常数为0.985. 通过自然键轨道法分析发现, 烃类物质的碳氢键解离焓与母体的碳氢键杂化轨道成分p%, 自由基奇电子轨道杂化成分p%及自由基的自旋密度三个参数之间存在较好的定量关系. 此外, 饱和链烷烃及不饱和链烃的碳氢键解离焓与碳氢键键长之间也存在较好的线性关系.     

多组态二级微扰理论计算CH3O2激发光谱以及CH3O2→CH3＋O2解离反应

在C_s对称性和aug-cc-pVTZ基组水平下, 采用全活化空间自洽场方法(CASSCF)研究了CH₃O₂自由基基态及其阴阳离子的12个低激发态. 为了进一步考虑动态电子相关效应, 采用二级多组态微扰理论(CASPT2)获得更加精确的能量值. 所有计算得到的电子态都是价电子态, 而且所得绝热激发能和电子亲和势与实验值非常接近.在CASPT2//CASSCF理论水平下计算了CH₃O₂从²A"和²A'电子态的CH₃O₂→CH₃＋O₂的解离反应的势能曲线(PECs). 优化得到的裂解产物的几何结构和能量与分别优化CH₃和O₂得到的结果进行比较, 从而确定裂解产物的电子态. 结果表明, 从²A"和²A'电子态的解离反应分别对应产物CH₃(²A")＋O₂(³A")和CH₃(²A")＋O₂(¹A").     

Tris(Butadiene) Compounds versus Butadiene Oligomerization in Second-Row Transition Metal Chemistry: Effects of Increased Ligand Fields

The geometries, energetics, and preferred spin states of the second-row transition metal tris(butadiene) complexes (C₄H₆)₃M (M = Zr–Pd) and their isomers, including the experimentally known very stable molybdenum derivative (C₄H₆)₃Mo, have been examined by density functional theory. Such low-energy structures are found to have low-spin singlet and doublet spin states in contrast to the corresponding derivatives of the first-row transition metals. The three butadiene ligands in the lowest-energy (C₄H₆)₃M structures of the late second-row transition metals couple to form a C₁₂H₁₈ ligand that binds to the central metal atom as a hexahapto ligand for M = Pd but as an octahapto ligand for M = Rh and Ru. However, the lowest-energy (C₄H₆)₃M structures of the early transition metals have three separate tetrahapto butadiene ligands for M = Zr, Nb, and Mo or two tetrahapto butadiene ligands and one dihapto butadiene ligand for M = Tc. The low energy of the experimentally known singlet (C₄H₆)₃Mo structure contrasts with the very high energy of its experimentally unknown singlet chromium (C₄H₆)₃Cr analog relative to quintet (C₁₂H₁₈)Cr isomers with an open-chain C₁₂H₁₈ ligand.     

Density Functional Calculations of C-NO2 Bond Dissociation Energies for Nitroalkanes Molecules

Bond dissociation energies for the removal of nitrogen dioxide group in some nitroalkane energetic materials have been calculated by using the three hybrid density functional theory （DFT） methods B3LYP, B3PW91 and B3P86 with 6-31g^＊＊ and 6-311g^＊＊ basis sets. The computed BDEs have been compared with the available experimental results. It is found that the B3P86 method with 6-31g^＊＊ and 6-311g^＊＊ basis sets can obtain satisfactory bond dissociation energies （BDEs）, which are in extraordinary agreement with the experimental data. Considering the smaller mean absolute deviation and maximum difference, the reliable B3P86/6-311g^＊＊ method was recommended to compute the BDEs for the removal of nitrogen dioxide group in the nitroalkane energetic materials. Using the method, the BDEs of 8 other nitroalkane energetic materials have been calculated and the maximum difference from experimental value is 1.76 kcal.mo1^-1 （for the BDE of tC4Hg-NOz）, which further proves the reliability of B3P86/6-311g^＊＊ method. In addition, it is noted that the BDEs of C-NO2 bond change slightly for main chain nitroalkane compounds with the maximum difference of only 3.43 kcal mo1^-1.     

X-H (X = C, N, O, Si, P, S) 键离解能计算的密度泛函方法研究

使用了不同密度泛函方法计算X-H (X = C, N, O, Si, P, S) 键离解能，并分析不同密度泛函方法的计算精度。研究发现大多数密度泛函方法包括B3LYP, B3P86, B3PW91, G96LYP, PBE1PBE，和BH&HLYP都明显低估键离解能13-25 kJ/mol。该现象与是否使用无限基组无关，因为即使使用无限基组键离解能仍然被低估。因此密度泛函方法不适合用于键离解能的估算。其中B3P86方法的偏差最小。进一步分析表明，使用限制性开壳层计算并无任何优势，在大多数情况下非限制性开壳层计算实际上比限制性开壳层计算要好。最后，我们发现了密度泛函方法对键离解能的低估是系统的，因此建议利用校准后的UDFT/6-311++G(d, p)方法计算化学键离解能。     

两态反应Ni2+与c-C6H12的机理及自旋-轨道耦合研究

在密度泛函理论的B3LYP方法下, 对两态反应Ni₂⁺与环己烷体系进行了较为系统的研究. 结果表明, 反应分别在第一个氢迁移(⁴IM1→⁴TS1/2), 第三个氢迁移(⁴TS15/16→⁴IM15)以及 翻转过程(⁴IM5→⁴TS5/6, ²TS11/12→²IM12)发生了二、四重态势能面的交叉, 本文运用内禀反应坐标单点垂直激发计算的方法得到势能面大致的交叉点(CP), 进一步利用Crossing2004程序获得精确的最低能量交叉点(MECP). 对MECP附近的自旋轨道耦合(SOC)常数进行了计算. MECP1～MECP4处的SOC值分别为318.01, 396.89, 268.74和306.67 cm^-1. 较大的SOC值说明不同势能面间发生了有效地跃迁并使反应沿着最低反应通道进行. 对反应通道的研究发现, 反应中同面脱氢是主要反应通道. 异面脱氢由于翻转过程中决速步骤势垒为33 kcal/mol(吸热3 kcal/mol), 只生成少量的异面脱氢产物. 计算结果解释了实验现象.     

Theoretical Study of Remote Substituent Effects on X-H （X=CH2, NH,O） Bond Dissociation Energies of Azulene

In the study, the X-H （X=CH2, NH, O） bond dissociation energies （BDE） of para-substituted azulene （Y-C10H8X-H） were predicted theoretically for the first time using Density Functronal Theory （DFT） methods at UB3LYP/6-311 ＋ ＋g（2df,2p）//UB3LYP/6-31 ＋g（d） level. It was found that the substituents exerted similar effects on the X-H BDE of azulene as those on benzene, except for 6-substituted 2-methylazulene. Owing to the substituent-dipole interaction, the reaction constants （ρ^＋） of 2- and 6-Y-CIoHsX-H （X=NH and O only） varied violently. The origin of the substituent effects on the X-H BDE of azulene was found, by both GE/RE and SIE theory, to be directly associated with variation of the radical effects, although the ground effects also played a modest role in determining the net. substituent effects.     

Benchmark Study of the Performance of Density Functional Theory for Bond Activations with (Ni,Pd)-Based Transition-Metal Catalysts

The performance of 23 density functionals, including one LDA, four GGAs, three meta-GGAs, three hybrid GGAs, eight hybrid meta-GGAs, and ten double-hybrid functionals, was investigated for the computation of activation energies of various covalent main-group single bonds by four catalysts: Pd, PdCl⁻, PdCl₂, and Ni (all in the singlet state). A reactant complex, the barrier, and reaction energy were considered, leading to 164 energy data points for statistical analysis. Extended Gaussian AO basis sets were used in all calculations. The best functional for the complete benchmark set relative to estimated CCSD(T)/CBS reference data is PBE0-D3, with an MAD value of 1.1 kcal mol⁻¹ followed by PW6B95-D3, the double hybrid PWPB95-D3, and B3LYP-D3 (1.9 kcal mol⁻¹ each). The other tested hybrid meta-GGAs perform less well (M06-HF: 7.0 kcal mol⁻¹; M06-2X: 6.3 kcal mol⁻¹; M06: 4.9 kcal mol⁻¹) for the investigated reactions. In the Ni case, some double hybrids show larger errors due to partial breakdown of the perturbative treatment for the correlation energy in cases with difficult electronic structures (partial multi-reference character). Only double hybrids either with very low amounts of perturbative correlation (e.g., PBE0-DH) or that use the opposite-spin correlation component only (e.g., PWPB95) seem to be more robust. We also investigated the effect of the D3 dispersion correction. While the barriers are not affected by this correction, significant and mostly positive results were observed for reaction energies. Furthermore, six very recently proposed double-hybrid functionals were analyzed regarding the influence of the amount of Fock exchange as well as the type of perturbative correlation treatment. According to these results, double hybrids with <50–60 % of exact exchange and ∼30 % perturbative correlation perform best.     

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.     

Manganese,Iron, Cobalt,and Nickel Oxo‐, Peroxo‐, and Superoxoclusters: A Density Functional Theory Study

The 3d‐transition‐metal dioxo‐, peroxo‐, and superoxoclusters with the general composition MO₂, M(O₂), and MOO (M=Mn, Fe, Co, and Ni) were studied by DFT by the B1LYP functional. The dioxides in their ground states represent the global minima for the M+O₂ system. Both ground‐state dioxides and the lowest‐energy peroxides are in their (d‐only) highest spin states. The ⁶A₁ state of Co(O₂) exceeds the d‐only spin‐multiplicity value (quartet), being nearly isoenergetic with the ⁴A₁ state of Co(O₂). The energy gain on transforming the peroxides to the corresponding dioxides decreases in the order Mn(O₂)>Fe(O₂)>Co(O₂)>Ni(O₂) and varies in the range 0.27–1.8 eV. The dissociation energy to M+O₂ for all studied peroxides is less than 1 eV being the lowest (0.47 eV) for Mn(O₂). The Mn and Fe peroxides need less than 0.3 eV to rupture one of the MO bonds to form the corresponding superoxide. Mn and Fe superoxides are less stable than the corresponding peroxides; the superoxide of Co is more stable than its peroxide, while Ni superoxide is unstable—its energy is above the limit of dissociation to Ni+O₂. According to the electrostatic potential maps, the oxygen atoms in the peroxides are more nucleophilic than those in the dioxides and superoxides, in which the terminal oxygen atom is more nucleophilic than the M‐bonded oxygen atom. This result differs from the expectations based on charge‐distribution analysis.     

Gold Behaves as Hydrogen in the Intermolecular Self‐Interaction of Metal Aurides MAu4 (M=Ti,Zr, and Hf)

We performed density functional calculations to examine the intermolecular self‐interaction of metal tetraauride MAu₄ (M=Ti, Zr, and Hf) clusters. We found that the metal auride clusters have strong dimeric interactions (2.8–3.1 eV) and are similar to the metal hydride analogues with respect to structure and bonding nature. Similarly to (MH₄)₂, the (μ‐Au)₃ C_s structures with three three‐center two‐electron (3c–2e) bonds were found to be the most stable. Natural orbital analysis showed that greater than 96 % of the Au 6s orbital contributes to the 3c–2e bonds, and this predominant s orbital is responsible for the similarity between metal aurides and metal hydrides (>99 % H 1s). The favorable orbital interaction between occupied Au 6s and unoccupied metal d orbitals leads to a stronger dimeric interaction for MAu₄‐MAu₄ than the interaction for MH₄‐MH₄. There is a strong relationship between the dimeric interaction energy and the chemical hardness of its monomer for (MAu₄)₂ and (MH₄)₂.