Accurate bond dissociation enthalpies by using doubly hybrid XYG3 functional

In this work, we examine the performance of XYG3, a newly developed doubly hybrid density functional (Zhang, Xu, and Goddard III, Proc Natl Acad Sci USA 2009, 106, 4963), to calculate covalent bond dissociation enthalpy (BDE). We use 5 atoms, 32 molecular radicals, and 116 closed-shell molecules to set up 142 bond dissociation reactions. For the total of 148 heats of formation (HOFs) and 142 BDEs, XYG3 leads to mean absolute deviations (MADs) of 1.45 and 1.87 kcal/mol, respectively. In comparison with some other functionals, MADs for HOFs are 2.31 (M06-2X), 2.98 (B2PLYP-D), 3.04 (BMK), 3.96 (B3LYP), 4.47 (B2PLYP), 5.42 (B2GP-PLYP), 6.46 (PBE0), and 29.93 kcal/mol (B3P86), and the corresponding errors for BDEs are 2.06 (M06-2X), 2.25 (BMK), 2.51 (B2PLYP-D), 2.89 (B2GP-PLYP), 3.30 (B3P86), 3.44 (B2PLYP), 3.87 (PBE0), and 6.14 kcal/mol (B3LYP).     

Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Calculations of ionization energies and electron affinities for atoms and molecules: A comparative study with different methods

In the present work, we examined the performance of 36 density functionals, including the newly developed doubly hybrid density functional XYG3 (Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Natl. Acad. Sci, USA, 2009, 106, 4963), to calculate ionization energies (IEs) and electron affinities (EAs). We used the well-established G2-1 set as reference, which contains 14 atoms and 24 molecules for IE, along with 7 atoms and 18 molecules for EA. XYG3 leads to mean absolute deviations (MADs) of 0.057 and 0.080 eV for IEs and EAs, respectively, using the basis set of 6-311 + G (3df,2p). In comparison with some other functionals, MADs for IEs are 0.109 (B2PLYP), 0.119 (M06-2X), 0.159 (X3LYP), 0.161 (PBE), 0.162 (B3LYP), 0.165 (PBE0), 0.173 (TPSS), 0.200 (BLYP), and 0.215 eV (LC-BLYP). MADs for EAs are 0.090 (X3LYP), 0.090 (B2PLYP), 0.102 (PBE), 0.103 (M06-2X), 0.104 (TPSS), 0.105 (BLYP), 0.106 (B3LYP), 0.126 (LC-BLYP), and 0.128 eV (PBE0).     

Nickel-catalyzed alkyl coupling reactions: evaluation of computational methods

The B3LYP, M06, M06L, M062X, MPW1K, and PBE1PBE DFT methods were evaluated for modeling nickel-catalyzed coupling reactions. The reaction consists of a nucleophilic attack by a carbanion equivalent on the nickel complex, S(N)2 attack by the anionic nickel complex on an alkyl halide, and reductive elimination of the coupled alkane product, regenerating the nickel catalyst. On the basis of CCSD(T)//DFT single-point energies, the B3LYP, M06, and PBE1PBE functionals were judged to generate the best ground state geometries. M06 energies are generally comparable or superior to B3LYP and PBE1PBE energies for transition state calculations. The MP2 and CCSD methods were also evaluated for single-point energies at the M06 geometries. The rate-determining step of this reaction was found to be nucleophilic attack of a L(2)NiR anion on the alkyl halide.     

Ring-opening radical clock reactions: many density functionals have difficulty keeping time

The ability of several density-functional theory methods to describe the kinetics and energetics of a series of ring-opening reactions of cyclopropyl and cyclobutyl-type radicals was explored. PBE, B971 and B3LYP perform quite well in their ability to replicate experiment, based upon the ring opening of cyclopropylcarbinyl, two α-trialkylsilyloxycyclopropylmethyl radicals, pentamethylcyclopropylcarbinyl, cyclobutylcarbinyl and 1-cyclobutylethylcarbinyl. The other functionals tested, which includes BLYP, CAM-B3LYP, BHandHLYP, B2PLYP and B2PLYP-D, as well as functionals designed for kinetics applications, namely MPW1K, BMK and M06-2X, all perform poorly. The latter of these functionals display some integration grid dependencies.     

Assessment of a composite method based on selected density functional theory methods and complete basis set extrapolation formulas

Extrapolation formulas based on power and exponential formulas, as well as alternatives from a Taylor series, were tested and used with density functional theory (DFT) for the calculation of enthalpies of formation. The following four functionals were analyzed: B3LYP, BMK, M06-2X, and B2PLYP. Preliminary tests pointed to B2PLYP and B3LYP as the best and worst functionals, respectively. Taylor series expressions were as accurate as the power formulas and presented better performance than the exponential equation. The power formula (Equation (2)) and one of the simplest Taylor expressions (Equation (13)) were selected for the calculations with B3LYP and B2PLYP, with further empirical adjustments based on the higher level correction (HLC) and scaling of the experimental atomization energies used to calculate enthalpies of formation. HLC improved the B3LYP mean absolute error (MAE) from approximately 4.3 to 3.5 kcal mol⁻¹ using both extrapolation alternatives. For B2PLY, the MAEs were improved from 2.7 to 2.6 kcal mol⁻¹. Regarding the G3/05 test set, a significant improvement in the MAEs around 2.5 and 1.5 kcal mol⁻¹ were achieved using B3LYP and B2PLYP, respectively. The accuracy obtained from these empirical corrections was equivalent to other composite methods. The MAEs from B3LYP and B2PLYP may be suggested as ranges for the possible accuracy to be achieved by some DFT methods. The empirical corrections suggested in this work are improvements that may be considered to provide acceptable accuracy for enthalpies of formation and possibly other properties.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Vibrational frequency scale factors for density functional theory and the polarization consistent basis sets

Calculated harmonic vibrational frequencies systematically deviate from experimental vibrational frequencies. The observed deviation can be corrected by applying a scale factor. Scale factors for: (i) harmonic vibrational frequencies [categorized into low (<1000 cm^?1) and high (>1000 cm^?1)], (ii) vibrational contributions to enthalpy and entropy, and (iii) zero‐point vibrational energies (ZPVEs) have been determined for widely used density functionals in combination with polarization consistent basis sets (pc‐n, n = 0,1,2,3,4). The density functionals include pure functionals (BP86, BPW91, BLYP, HCTH93, PBEPBE), hybrid functionals with Hartree‐Fock exchange (B3LYP, B3P86, B3PW91, PBE1PBE, mPW1K, BH&HLYP), hybrid meta functionals with the kinetic energy density gradient (M05, M06, M05‐2X, M06‐2X), a double hybrid functional with Møller‐Plesset correlation (B2GP‐PLYP), and a dispersion corrected functional (B97‐D). The experimental frequencies for calibration were from 41 organic molecules and the ZPVEs for comparison were from 24 small molecules (diatomics, triatomics). For this family of basis sets, the scale factors for each property are more dependent on the functional selection than on basis set level, and thus allow for a suggested scale factor for each density functional when employing polarization consistent basis sets (pc‐n, n = 1,2,3,4). A separate scale factor is recommended when the un‐polarized basis set, pc‐0, is used in combination with the density functionals. © 2012 Wiley Periodicals, Inc.     

Reactivity of cycloalkanes in hydrogen abstraction with different acceptors

The reactions of some acceptors (^?CH₃, ^?OOH, ^?CCl₃, O₃, and Br^?) with saturated cyclic hydrocarbons, viz., cyclohexane, cycloheptane, and cyclooctane were studied by the DFT methods based on B3LYP and PBE0 functionals, the method based on the double hybrid functional B2PLYP, a combined ONIOM approach (CCSD:B3LYP)) and the coupled-cluster method (CCSD) using the 6-31+G**, aug-cc-pVDZ, Midi-X, and SVP basis sets. A specific feature of these reactions is that their rates depend on the excess ring energy, although no ring opening occurs in all cases.     

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.     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.     

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.     

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.     

A DFT study on Cu(I) coordination in Cu‐ZSM‐5: Effects of the functional choice and tuning of the ONIOM approach

The coordination of Cu⁺ at the T1 and T7 positions of the M7 ring of Cu‐ZSM‐5, and the interaction of NO with coordinated Cu⁺ were investigated by means of DFT/ONIOM calculations. The B3LYP, BLYP, PBE1PBE, PBE, M06, and M062X functionals with the def2‐TZVP (def2‐QZVP for Cu) basis set were used in the high‐level part of ONIOM calculations, with the HF/3‐21G, B3LYP/LANL2DZ, M06/LANL2DZ, and M062X/LANL2DZ methods in the low‐level part. The ability of suitable combinations of the above methods to reproduce (i) the crystallographic structure of purely siliceous ZSM‐5, (ii) the tendency of Cu⁺ to be twofold or fourfold coordinated by framework oxygen atoms of Cu‐ZSM‐5, and (iii) the interaction energy and the N? O stretching frequency of adsorbed nitrogen oxide are discussed, showing that different results are obtained depending on the adopted computational approach. With reference to above properties, some considerations about the employment of the ONIOM approximations are also included. © 2015 Wiley Periodicals, Inc.     

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.     

Broken symmetry density functional study of a mixed‐valence unsymmetrical dinuclear iron complex

Density functional theory (DFT) calculations with different exchange‐correlation functionals were performed for a mixed valence Fe(II)/Fe(III) binuclear complex with μ‐methoxo and two μ‐carboxylate bridging ligands, (1) with geometry optimizations being performed for all possible spin multiplicities (M_S = 2, 4, 6, 8, and 10). Within the exchange‐correlation functionals studied, only the hybrid GGA functionals B3P and B3LYP and also the pure GGA functional RPBE, predicts the geometry with high spin (S = 9/2) to be more stable than the geometry with low spin state (S = 1/2) by 20 kcal/mol, in agreement with the experimental findings. These functionals also predict the same stability order for the different spin states, being M_S = 10>8>6>2>4. The meta‐GGA functionals TPSS and TPSSh and also the pure GGA functionals BLYP and BP86 predict different stability orders. The computed average EPR g‐tensor, g_av, of 2.03, at the B3LYP level, is in good agreement with the experimental findings. Heisenberg exchange coupling constants, J, were calculated within the broken‐symmetry formalism, at the B3LYP level, showing that the two iron centers are antiferromagnetic coupling, with a very weak coupling constant of about ?7 cm^?1, in good agreement with the experimental value. Additionally, the effect of using different multiplicities of the reference geometries on the computed J value is discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010