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.     

Performance of the M06 family of exchange-correlation functionals for predicting magnetic coupling in organic and inorganic molecules

The performance of the M06 family of exchange-correlation potentials for describing the electronic structure and the Heisenberg magnetic coupling constant (J) is investigated using a set of representative open-shell systems involving two unpaired electrons. The set of molecular systems studied has well defined structures, and their magnetic coupling values are known experimentally. As a general trend, the M06 functional is about equally as accurate as B3LYP or PBE0. The performance of local functionals is important because of their economy and convenience for large-scale calculations; we find that M06-L local functional of the M06 family largely improves over the local spin density approximation and the generalized gradient approximation.     

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.     

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.     

Improved description of nuclear magnetic resonance chemical shielding constants using the M06-L meta-generalized-gradient-approximation density functional

The performance of the M06-L density functional has been tested for four databases of NMR isotropic chemical shielding constants. Comparison with the B3LYP, BLYP, HCTH, KT1, KT2, LSDA, OPBE, OLYP, PBE, TPSS, and VSXC functionals shows that M06-L has improved performance for calculating NMR chemical shielding constants, especially for highly correlated systems. We also found that VSXC and M06-L have encouraging accuracy for calculating (13)C chemical shielding constants, and both functionals perform very well for the chemical shielding constants in the o-benzyne molecule.     

The prediction of Fe Mössbauer parameters by the density functional theory: a benchmark study

We report the performance of eight density functionals (B3LYP, BPW91, OLYP, O3LYP, M06, M06-2X, PBE, and SVWN5) in two Gaussian basis sets (Wachters and Partridge-1 on iron atoms; cc-pVDZ on the rest of atoms) for the prediction of the isomer shift (IS) and the quadrupole splitting (QS) parameters of M?ssbauer spectroscopy. Two sources of geometry (density functional theory-optimized and X-ray) are used. Our data set consists of 31 iron-containing compounds (35 signals), the M?ssbauer spectra of which were determined at liquid helium temperature and where the X-ray geometries are known. Our results indicate that the larger and uncontracted Partridge-1 basis set produces slightly more accurate linear correlations of electronic density used for the prediction of IS and noticeably more accurate results for the QS parameter. We confirm and discuss the earlier observation of Noodleman and co-workers that different oxidation states of iron produce different IS calibration lines. The B3LYP and O3LYP functionals have the lowest errors for either IS or QS. BPW91, OLYP, PBE, and M06 have a mixed success whereas SVWN5 and M06-2X demonstrate the worst performance. Finally, our calibrations and conclusions regarding the best functional to compute the M?ssbauer characteristics are applied to candidate structures for the peroxo and Q intermediates of the enzyme methane monooxygenase hydroxylase (MMOH), and compared to experimental data in the literature.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Quantum-chemical DFT calculations of the energies of the O—H bond of phenols

The energies of homolytic cleavage of the O—H bonds in 36 phenols with various structures were calculated within the scope of density functional theory using a series of exchange-correlation functionals and basis sets. The best agreement between the calculated and experimental data is given by the M06-2X/6-311++G(2d,2p)//B3LYP/6-31G(d) method.     

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).     

Optical absorption and emission properties of fluoranthene, benzo[k]fluoranthene, and their derivatives. A DFT study

Fluoranthene and benzo[k]fluoranthene-based oligoarenes are good candidates for organic light-emitting diodes (OLEDs). In this work, the electronic structure and optical properties of fluoranthene, benzo[k]fluoranthene, and their derivatives have been studied using quantum chemical methods. The ground-state structures were optimized using the density functional theory (DFT) methods. The lowest singlet excited state was optimized using time-dependent density functional theory (TD-B3LYP) and configuration interaction singles (CIS) methods. On the basis of ground- and excited-state geometries, the absorption and emission spectra have been calculated using the TD-DFT method with a variety of exchange-correlation functionals. All the calculations were carried out in chloroform medium. The results show that the absorption and emission spectra calculated using the B3LYP functional is in good agreement with the available experimental results. Unlikely, the meta hybrid functionals such as M06HF and M062X underestimate the absorption and emission spectra of all the studied molecules. The calculated absorption and emission wavelength are more or less basis set independent. It has been observed that the substitution of an aromatic ring significantly alters the absorption and emission spectra.     

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.     

Quantum mechanical modeling of Zn-based spinel oxides: Assessing the structural,vibrational, and electronic properties

The structural, electronic, and vibrational properties of two leading representatives of the Zn-based spinel oxides class, normal ZnX₂O₄ (X = Al, Ga, In) and inverse Zn₂MO₄ (M = Si, Ge, Sn) crystals, were investigated. In particular, density functional theory (DFT) was combined with different exchange-correlation functionals: B3LYP, HSE06, PBE0, and PBESol. Our calculations showed good agreement with the available experimental data, showing a mean percentage error close to 3% for structural parameters. For the electronic structure, the obtained HSE06 band-gap values overcome previous theoretical results, exhibiting a mean percentage error smaller than 10.0%. In particular, the vibrational properties identify the significant differences between normal and inverse spinel configurations, offering compelling evidence of a structure-property relationship for the investigated materials. Therefore, the combined results confirm that the range-separated HSE06 hybrid functional performs the best in spinel oxides. Despite some points that cannot be directly compared to experimental results, we expect that future experimental work can confirm our predictions, thus opening a new avenue for understanding the structural, electronic, and vibrational properties in spinel oxides.     

Accurate prediction of vertical electronic transitions of Ni(II) coordination compounds via time dependent density functional theory

Time dependent density functional theory calculations are completed for five Ni(II) complexes formed by polydentate peptides to predict the electronic absorption spectrum. The ligands examined were glycyl‐glycyl‐glycine (GGG), glycyl‐glycyl‐glycyl‐glycine (GGGG), glycyl‐glycyl‐histidine (GGH), glycyl‐glycyl‐cysteine (GGC), and triethylenetetramine (trien). Fifteen functionals and two basis sets were tested. On the basis of the mean absolute percent deviation (MAPD), the ranking among the functionals is: HSE06 ∼ MPW1PW91 ∼ PBE0 > ω‐B97x‐D ∼ B3P86 ∼ B3LYP ∼ CAM‐B3LYP > PBE ∼ BLYP ∼ BP86 > TPSS > TPSSh > BHandHLYP > M06 ≫ M06‐2X. Concerning the basis sets, the triple‐ζ def2‐TZVP performs better than the double‐ζ LANL2DZ. With the functional HSE06 and basis set def2‐TZVP the MAPD with respect to the experimental λ_max is 1.65% with a standard deviation of 1.26%. The absorption electronic spectra were interpreted in terms of vertical excitations between occupied and virtual MOs based on Ni‐d atomic orbitals. The electronic structure of the Ni(II) species is also discussed.     

Electron localization function study on intramolecular electron transfer in the QTTFQ and DBTTFI radical anions

The unsymmetrical distribution of the unpaired electron in the ground state of the DBTTFI(?-) radical anion (bi(6-n-butyl-5,7-dioxo-6,7-dihydro-5H-[1,3]dithiolo[4,5-f]isoindole-2-ylidene) is theoretically predicted using the M06-2X/6-31+G(d,p) level of calculations. The results are additionally confirmed by single point calculations at B3LYP/aug-cc-pVTZ, LC-ωPBE/aug-cc-pVTZ, and M06-2X/aug-cc-pVTZ levels. DBTTFI, containing the TTF (tetrathiafulvalene) fragment, may be used in the construction of organic microelectronic devices, similarly to the radical anion of QTTFQ. The unsymmetrical distribution of spin density in (QTTFQ)(?-) has been confirmed using M06-2X/aug-cc-pVTZ calculations, with subsequent study using topological analysis of electron localization function (ELF). The reorganization of the chemical bonds during intramolecular electron transfer in (QTTFQ)(?-) and (DBTTFI)(?-) has been analyzed using bonding evolution theory (BET). The reaction path has been simulated by the IRC procedure, and the evolution of valence basins has been described using catastrophe theory. The simple mechanisms: (QTTFQ)(?-): η-1-3-CC(+)-0: (-?)(QTTFQ) and (DBTTFI)(?-): η-1-3-[F](4)[F(+)](4)-0: (-?)(DBTTFI), each consisting of three steps, have been observed. Two cusp or 4-fold catastrophes occur immediately after the TS. Our study shows that potential future microelectronic devices, constructed on the basis of the (QTTFQ)(?-) and (DBTTFI)(?-) systems, should exploit the properties of the C═C bond.     

Systematic investigation on the geometric dependence of the calculated nuclear magnetic shielding constants

We perform a systematic examination on the dependence of the calculated nuclear magnetic shielding constants on the chosen geometry for a selective set of density functional methods of B3LYP, PBE0, and OPBE. We find that the OPBE exchange-correlation functional performs remarkably well when either the optimized geometries or the experimental geometries are used. The popular B3LYP and PBE0 functionals have a clear tendency of deshielding, giving shieldings that are usually too low and shifts that are usually too high, at the experimental geometries. Combined with the Hartree-Fock geometries, however, much improved magnetic constants are obtained for B3LYP and PBE0, due to the compensation effect from the systematic underestimation of bond lengths by the Hartree-Fock method.     

Theoretical investigation of the EPR hyperfine coupling constants in amino derivatives

The HFCCs of the radical cations of a series of amines have been determined at different levels of approximation including the CISD, QCISD, and CCSD ab initio correlated methods and density functional theory approaches employing the B3LYP, PBE0, BHandHLYP, TPSS, and BLYP exchange-correlation functionals. Although quantitative differences with respect to experimental data have been noticed, these are mostly systematic within a given class of N and H atoms. As a consequence, these different levels of theory are reliable in most cases to account for the substituent and structure effects on the HFCCs of amines. Linear regression fits have then been performed to reach quantitative agreement between the theoretical and experimental values. This has finally been substantiated by considering the EPR signal of the recently synthesized radical cations of two derivatives of [10-(4-aminophenyl)-9-anthryl]aniline as well as in confirming a recent assignment of the EPR signal of n-propylamine.