Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Stacking of Metal Chelates with Benzene: Can Dispersion‐Corrected DFT Be Used to Calculate Organic–Inorganic Stacking?

CCSD(T)/CBS energies for stacking of nickel and copper chelates are calculated and used as benchmark data for evaluating the performance of dispersion‐corrected density functionals for calculating the interaction energies. The best functionals for modeling the stacking of benzene with the nickel chelate are M06HF‐D3 with the def2‐TZVP basis set, and B3LYP‐D3 with either def2‐TZVP or aug‐cc‐pVDZ basis set, whereas for copper chelate the PBE0‐D3 with def2‐TZVP basis set yielded the best results. M06L‐D3 with aug‐cc‐pVDZ gives satisfying results for both chelates. Most of the tested dispersion‐corrected density functionals do not reproduce the benchmark data for stacking of benzene with both nickel (no unpaired electrons) and copper chelate (one unpaired electron), whereas a number of these functionals perform well for interactions of organic molecules.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

How computational methods and relativistic effects influence the study of chemical reactions involving Ru‐NO complexes?

Two treatments of relativistic effects, namely effective core potentials (ECP) and all‐electron scalar relativistic effects (DKH2), are used to obtain geometries and chemical reaction energies for a series of ruthenium complexes in B3LYP/def2‐TZVP calculations. Specifically, the reaction energies of reduction ( A ‐ F ), isomerization ( G‐I ), and Cl⁻ negative trans influence in relation to NH₃ ( J ‐ L ) are considered. The ECP and DKH2 approaches provided geometric parameters close to experimental data and the same ordering for energy changes of reactions A ‐ L . From geometries optimized with ECP, the electronic energies are also determined by means of the same ECP and basis set combined with the computational methods: MP2, M06, BP86, and its derivatives, so as B2PLYP, LC‐wPBE, and CCSD(T) (reference method). For reactions A ‐ I , B2PLYP provides the best agreement with CCSD(T) results. Additionally, B3LYP gave the smallest error for the energies of reactions J ‐ L . © 2017 Wiley Periodicals, Inc.     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Mechanistic insights into triterpene synthesis from quantum mechanical calculations. Detection of systematic errors in B3LYP cyclization energies

Most quantum mechanical studies of triterpene synthesis have been done on small models. We calculated mPW1PW91/6-311+G(2d,p)//B3LYP/6-31G* energies for many C30H51O+ intermediates to establish the first comprehensive energy profiles for the cationic cyclization of oxidosqualene to lanosterol, lupeol, and hopen-3beta-ol. Differences among these 3 profiles were attributed to ring strain, steric effects, and proton affinity. Modest activation energy barriers and the ample exothermicity of most annulations indicated that the cationic intermediates rarely need enzymatic stabilization. The course of reaction is guided by hyperconjugation of the carbocationic 2p orbital with parallel C-C and C-H bonds. Hyperconjugation for cations with a horizontal 2p orbital (in the plane of the ABCD ring system) leads to annulation and ring expansion. If the 2p orbital becomes vertical, hyperconjugation fosters 1,2-methyl and hydride shifts. Transition states leading to rings D and E were bridged cyclopropane/carbonium ions, which allow ring expansion/annulation to bypass formation of undesirable anti-Markovnikov cations. Similar bridged species are also involved in many cation rearrangements. Our calculations revealed systematic errors in DFT cyclization energies. A spectacular example was the B3LYP/6-311+G(2d,p)//B3LYP/6-31G* prediction of endothermicity for the strongly exothermic cyclization of squalene to hopene. DFT cyclization energies for the 6-311+G(2d,p) basis set ranged from reasonable accuracy (mPW1PW91, TPSSh with 25% HF exchange) to underestimation (B3LYP, HCTH, TPSS, O3LYP) or overestimation (MP2, MPW1K, PBE1PBE). Despite minor inaccuracies, B3LYP/6-31G* geometries usually gave credible mPW1PW91 single-point energies. Nevertheless, DFT energies should be used cautiously until broadly reliable methods are established.     

COS与O2反应的密度泛函理论研究

用量子化学密度泛函理论（DFT）方法，对COS与O2的反应进行了理论研究．在UB3LYP／6—31G^＊，UB3LYP／6—311＋＋G^＊＊水平上，优化了反应势能面上各驻点（反应物、产物、中间体和过渡态）的几何构型，在UB3LYP／6—31G^＊水平上通过内禀反应坐标（IRC）计算和振动分析，对过渡态进行了确认．在CCSD（T）／6—311＋＋G（2d，2p）水平上进行了单点能量计算，并确定了反应机理．研究结果表明，反应主要产物为CO2和SO.     

Computational studies on ethylene addition to nickel bis(dithiolene)

The density functionals B3LYP, B3PW91, BMK, HSE06, LC-ωPBE, M05, M06, O3LYP, TPSS, ω-B97X, and ω-B97XD are used to optimize key transition states and intermediates for ethylene addition to Ni(edt)(2) (edt = S(2)C(2)H(2)). The efficacy of the basis sets 6-31G**, 6-31++G**, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ is also examined. The geometric parameters optimized with different basis sets and density functionals are similar and agree well with experimental values. The ω-B97XD functional gives relative energies closest to those from CCSD, while M06 and HSE06 yield results close to those from CCSD(T). CASSCF and CASSCF-PT2 calculation results are also given. Variation of the relative energies from different density functionals appears to arise, in part, from the multireference character of this system, as confirmed by the T1 diagnostic and CASSCF calculations.     

用GGA密度泛函及其长程、色散校正方法计算各类氢键的结合能

应用广义梯度近似(GGA) (PW91和PBE)、含动能密度的广义梯度近似(meta-GGA) (M06-L)、杂化泛函(hyper-GGA)(M06-2X、X3LYP和B3LYP)及其长程校正泛函LC-DFT(CAM-B3LYP、LC-ωPBE和ωB97X)和色散校正密度泛函(DFT-D)(ωB97X-D和B97-D),用多种基函数对15种不同强度的传统氢键和非传统氢键体系的结合能进行了系统的计算与分析.并与高精度的CCSD(T)/aug-cc-pVQZ结果比较发现:在上述各类泛函中,对于氢键结合能的计算M06-2X和ωB97X-D泛函较为精确与可靠,且没有必要使用过大的基函数,6-311++G(2d,2p)或aug-cc-pVDZ水平的基组就已足够,各类泛函所计算结合能的基组重叠误差(BSSE)均较小,除ωB97X和ωB97X-D外,其它9种泛函不经BSSE校正也能得到同样甚至更准确的结果.     

On the applicability of density functional theory to manganese‐based complexes with catalytic activity toward water oxidation

The present contribution assesses the performance of several popular and accurate density functionals, namely B3LYP, BP86, M06, MN12L, mPWPW91, PBE0, and TPSSh toward manganese‐based coordination complexes. These compounds show promising properties toward application to catalytic water oxidation. Although manganese with N‐ and O‐biding ligands tends to give rise to high spin complexes, the results show that BP86, mPWPW91, and specially MN12L, tend to yield low‐spin complexes. The usage of these functionals for such compounds is, thus, discouraged. All the functionals considered deliver accurate geometries. The present results show, however, that B3LYP delivers geometries deviating from experimental values when compared to the other functionals of the set. M06, PBE0, and TPSSh deliver geometries of similar accuracy, PBE0 outstanding slightly with respect to the other two. © 2017 Wiley Periodicals, Inc.     

Crystal structure and density functional theory study on structural properties and energies of a isonicotinohydrazide compound

An X-ray and a theoretical study of the structure of the isoniazid derivative N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate (1) are reported. In this work, we will report a combined experimental and theoretical study on the molecular structure, vibrational spectra and energies of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate. The calculated parameters are in good agreement with the corresponding X-ray diffraction values. The FTIR spectrum in the range of 400-4000 cm-1 of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate has been recorded. The molecular geometry and vibrational frequencies and energies in the ground state are calculated by using the DFT (B3LYP, PBE1PBE) methods with 6-311G** basis sets. The calculated HOMO and LUMO energies also confirm that charge transfer occurs within the molecule. The geometries and normal modes of vibrations obtained from B3LYP/PBE1PBE/6-311G** calculations are in good agreement with the experimentally observed data.     

Benchmark database on isolated small peptides containing an aromatic side chain: comparison between wave function and density functional theory methods and empirical force field

A detailed quantum chemical study on five peptides (WG, WGG, FGG, GGF and GFA) containing the residues phenylalanyl (F), glycyl (G), tryptophyl (W) and alanyl (A) -- where F and W are of aromatic character -- is presented. When investigating isolated small peptides, the dispersion interaction is the dominant attractive force in the peptide backbone-aromatic side chain intramolecular interaction. Consequently, an accurate theoretical study of these systems requires the use of a methodology covering properly the London dispersion forces. For this reason we have assessed the performance of the MP2, SCS-MP2, MP3, TPSS-D, PBE-D, M06-2X, BH&H, TPSS, B3LYP, tight-binding DFT-D methods and ff99 empirical force field compared to CCSD(T)/complete basis set (CBS) limit benchmark data. All the DFT techniques with a '-D' symbol have been augmented by empirical dispersion energy while the M06-2X functional was parameterized to cover the London dispersion energy. For the systems here studied we have concluded that the use of the ff99 force field is not recommended mainly due to problems concerning the assignment of reliable atomic charges. Tight-binding DFT-D is efficient as a screening tool providing reliable geometries. Among the DFT functionals, the M06-2X and TPSS-D show the best performance what is explained by the fact that both procedures cover the dispersion energy. The B3LYP and TPSS functionals-not covering this energy-fail systematically. Both, electronic energies and geometries obtained by means of the wave-function theory methods compare satisfactorily with the CCSD(T)/CBS benchmark data.     

羰基镍簇Ni(CO)n(n=1-4)的结构和Ni-CO键解离性质的密度泛函理论研究

在密度泛函理论框架下, 应用不同泛函计算了配合物Ni(CO)n(n=1~4)的平衡几何构型和振动频率. 考察了泛函和基组重叠误差对预测Ni—CO键解离能的影响. 计算结果表明, 用杂化泛函能得到与实验一致的优化几何构型和较合理的振动频率. 对Ni(CO)n(n=2~4)体系, 用“纯”泛函, 如BP86和BPW91, 可得到与CCSD(T)更符合、 并与实验值接近的解离能. 当解离产物出现单个金属原子或离子(如金属羰基配合物的完全解离)时, BSSE校正项的计算中应保持金属部分的电子结构一致. 只有考虑配体基组和不考虑配体基组两种情况下金属的电子构型与配合物中金属的构型一致时, 才能得到合理的BSSE校正, 从而预测合理的解离能.     

DFT,DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T₁ and T₂ diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.     

采用12种密度泛函理论方法表征三种三价铀复合物

比较了BP86、PBE、B3LYP、B3PW91、BHandHLYP、PBE0、X3LYP、CAM-B3LYP、TPSS、M06L、M06和M06-2X等12种采用了广义梯度近似(GGA、hybrid GGA、meta-GGA和hybrid meta-GGA)的密度泛函理论(DFT)方法在三个三价铀复合物表征中的应用. 研究模型采用铀复合物催化CO₂和CS₂官能团化反应中的三个中间体(Tp^*)₂U- η¹-CH₂Ph (Cpd2), (Tp^*)₂U- κ²-O₂CCH₂Ph (Cpd3) 和(Tp^*)₂U- κ²-S₂CCH₂Ph (Cpd4). 研究发现, B3LYP 和B3PW91 在几何结构和电子结构方面优于其它方法. 基于分子轨道理论的MP2 方法在Cpd2 和Cpd3 的表征中给出与DFT方法相近的结果, 而在Cpd4 的表征中表现出较大的差异. 这可能是由于同样是单参考态方法的MP2捕捉到了与DFT方法不同的电子结构. 同时, 通过对比分别采用小核赝势(5f-in-valence)和大核赝势(5f-in-core)基组处理铀原子的计算结果, 发现对测试的模型体系, 两种处理方法可获得相近的热力学能量. 与以往主要关注高价态锕系复合物的处理方法的评估工作不同, 本项工作适应逐渐增加的对低价态锕系分子体系的研究的需求, 对12 种常用的密度泛函理论方法在低价态锕系复合物研究中的应用进行了评估, 期望为处理类似体系的研究工作提供参考.     

Benchmarking of density functionals for the kinetics and thermodynamics of the hydrolysis of glycosidic bonds catalyzed by glycosidases

In recent years, there has been an increased interest in understanding the enzymatic mechanism of glycosidases resorting mostly to DFT and DFT/MM calculations. However, the performance of density functionals (DFs) is well known to be system and property dependent. Trends drawn from general studies, despite important to evaluate the quality of the DFs and to pave the way for the development of new DFs, may be misleading when applied to a single specific system/property. To overcome this issue, we carried out a benchmarking study of 40 DFs applied to the geometry optimization and to the electronic barrier height (E _Barrier) and electronic energy of reaction (E _R) of prototypical glycosidase‐catalyzed reactions. Additionally, we report calculations with SCC‐DFTB and four semiempirical MO methods applied to the same problem. We have used a universal molecular model for retaining glycosidases, comprising only a 22‐atoms system that mimics the active site and substrate. High accuracy reference geometries and energies were calculated at the CCSD(T)/CBS//MP2/aug‐cc‐pVTZ level of theory. Most DFs reproduce the reference geometries extremely well, with mean unsigned errors (MUE) smaller than 0.05 Å for bond lengths and 3° for bond angles. Among the DFs, wB97X‐D, CAM‐B3LYP, B3P86, and PBE1PBE have the best performance in geometry optimizations (MUE = 0.02 Å). Conversely, semiempirical MO and SCC‐DFTB methods yielded less accurate geometries (MUE between 0.09 and 0.17 Å). The inclusion of D3 correction has a small, but still relevant, influence in the geometry predicted by some DFs. Regarding E _Barrier, 11 DFs (MPW1B95, CAM‐B3LYP, M06 ‐ 2X, PBE1PBE, wB97X ‐ D, B1B95, BMK, MN12 – SX, M05, M06, and M11) presented errors below 1 kcal.mol^?1, in relation to the reference energy. Most of these functionals belong to the family of hybrid functionals (H‐GGA, HH‐GGA, and HM‐GGA), which shows a positive influence of HF exchange in the determination of E _Barrier. The inclusion of D3 correction has not affected significantly the E _Barrier and E _R. The use of geometries at the accurate but expensive MP2/aug‐cc‐pVTZ level of theory has a small, albeit not insignificant, influence in the E _Barrier when compared with energies calculated with geometries determined with the DFs (usually a few tenths of kcal.mol^?1, with exceptions). In general, semiempirical MO methods and DFTB are associated with larger errors in the determination of E _Barrier, with unsigned errors from 6.9 to 24.7 kcal.mol^?1.     

Electronic spectroscopy of UO2(2+), NUO(+) and NUN: an evaluation of time-dependent density functional theory for actinides

The performance of the time-dependent density functional theory (TDDFT) approach has been evaluated for the electronic spectrum of the UO(2)(2+), NUO(+) and NUN molecules. Different exchange-correlation functionals (LDA, PBE, BLYP, B3LYP, PBE0, M06, M06-L, M06-2X, CAM-B3LYP) and the SAOP model potential have been investigated, as has the relative importance of the adiabatic local density approximation (ALDA) to the exchange-correlation kernel. The vertical excitation energies have been compared with reference data obtained using accurate wave-function theory (WFT) methods.     

Energy landscapes of nucleophilic substitution reactions: a comparison of density functional theory and coupled cluster methods

We have carried out a detailed evaluation of the performance of all classes of density functional theory (DFT) for describing the potential energy surface (PES) of a wide range of nucleophilic substitution (SN2) reactions involving, amongst others, nucleophilic attack at carbon, nitrogen, silicon, and sulfur. In particular, we investigate the ability of the local density approximation (LDA), generalized gradient approximation (GGA), meta-GGA as well as hybrid DFT to reproduce high-level coupled cluster (CCSD(T)) benchmarks that are close to the basis set limit. The most accurate GGA, meta-GGA, and hybrid functionals yield mean absolute deviations of about 2 kcal/mol relative to the coupled cluster data, for reactant complexation, central barriers, overall barriers as well as reaction energies. For the three nonlocal DFT classes, the best functionals are found to be OPBE (GGA), OLAP3 (meta-GGA), and mPBE0KCIS (hybrid DFT). The popular B3LYP functional is not bad but performs significantly worse than the best GGA functionals. Furthermore, we have compared the geometries from several density functionals with the reference CCSD(T) data. The same GGA functionals that perform best for the energies (OPBE, OLYP), also perform best for the geometries with average absolute deviations in bond lengths of 0.06 A and 0.6 degrees, even better than the best meta-GGA and hybrid functionals. In view of the reduced computational effort of GGAs with respect to meta-GGAs and hybrid functionals, let alone coupled cluster, we recommend the use of accurate GGAs such as OPBE or OLYP for the study of SN2 reactions.