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.     

The shape of gaseous n-butylbenzene: assessment of computational methods and comparison with experiments

Conformational landscape of neutral and ionized n-butylbenzene has been examined. Geometries have been optimized at the B3LYP/6-31G(d), B3LYP/6-31+G(d,p), B3LYP-D/6-31+G(d,p), B2PLYP/6-31+G(d,p), B2PLYP-D/6-31+G(d,p), B97-D/6-31+G(d,p), and M06-2X/6-31+G(d,p) levels. This study is complemented by energy computations using 6-311++G(3df,2p) basis set and CBS-QB3 and G3MP2B3 composite methods to obtain accurate relative enthalpies. Five distinguishable conformers have been identified for both the neutral and ionized systems. Comparison with experimentally determined rotational constants shows that the best geometrical parameters are provided by B3LYP-D and M06-2X functionals, which include an explicit treatment of dispersion effects. Composite G3MP2B3 and CBS-QB3 methods, and B2PLYP-D, B3LYP-D, B97-D, and M06-2X functionals, provide comparable relative energies for the two sets of neutral and ionized conformers of butyl benzene. An exception is noted however for conformer V(+) the stability of which being overestimated by the B3LYP-D and B97-D functionals. The better stability of neutral conformers I, III, and IV, and of cation I(+) , demonstrated by our computations, is in perfect agreement with conclusions based on micro wave, fluorescence, and multiphoton ionization experiments.     

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.     

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.     

Harmonic vibrational frequencies: scale factors for pure, hybrid, hybrid meta, and double-hybrid functionals in conjunction with correlation consistent basis sets

Scale factors for (a) low (<1000 cm(-1)) and high harmonic vibrational frequencies, (b) thermal contributions to enthalpy and entropy, and (c) zero-point vibrational energies have been determined for five hybrid functionals (B3P86, B3PW91, PBE1PBE, BH&HLYP, MPW1K), five pure functionals (BLYP, BPW91, PBEPBE, HCTH93, and BP86), four hybrid meta functionals (M05, M05-2X, M06, and M06-2X) and one double-hybrid functional (B2GP-PLYP) in combination with the correlation consistent basis sets [cc-pVnZ and aug-cc-pVnZ, n = D(2),T(3),Q(4)]. Calculations for vibrational frequencies were carried out on 41 organic molecules and an additional set of 22 small molecules was used for the zero-point vibrational energy scale factors. Before scaling, approximately 25% of the calculated frequencies were within 3% of experimental frequencies. Upon application of the derived scale factors, nearly 90% of the calculated frequencies deviated less than 3% from the experimental frequencies for all of the functionals when the augmented correlation consistent basis sets were used.     

Comparison of some dispersion-corrected and traditional functionals as applied to peptides and conformations of cyclohexane derivatives

We compare the energetic and structural properties of fully optimized α-helical and antiparallel β-sheet polyalanines and the energetic differences between axial and equatorial conformations of three cyclohexane derivatives (methyl, fluoro, and chloro) as calculated using several functionals designed to treat dispersion (B97-D, ωB97x-D, M06, M06L, and M06-2X) with other traditional functionals not specifically parametrized to treat dispersion (B3LYP, X3LYP, and PBE1PBE) and with experimental results. Those functionals developed to treat dispersion significantly overestimate interaction enthalpies of folding for the α-helix and predict unreasonable structures that contain Ramachandran φ and ψ and C = O[ellipsis (horizontal)]N H-bonding angles that are out of the bounds of databases compiled the β-sheets. These structures are consistent with overestimation of the interaction energies. For the cyclohexanes, these functionals overestimate the stabilities of the axial conformation, especially when used with smaller basis sets. Their performance improves when the basis set is improved from D95?? to aug-cc-pVTZ (which would not be possible with systems as large as the peptides).     

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     

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     

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.     

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.     

Assessment of ab initio MP2 and density functionals for characterizing the potential energy profiles of the SN2 reactions at N center

The potential energy profiles of five selected bimolecular nucleophilic substitution (S_N2) reactions at nitrogen (N) center have been reinvestigated with the CCSD(T), G3[MP2,CCSD(T)], MP2, and some density functional methods. The basis sets of 6‐31+G(d,p) and 6‐311+G(3d,2p) are used for the MP2 and density functional calculations. Taking the relative energies at the CCSD(T)/CBS level of theory as benchmarks, we recommend the MP2, B97‐K, B2K‐PLYP, BMK, ωB97X‐D, M06‐2X, M05‐2X, CAM‐B3LYP, M08‐SO, and ωB97X methods to generally characterize the potential energy profiles for the S_N2 reactions at N center. Furthermore, these recommended methods with the relatively small 6‐31+G(d,p) basis set may also be used to perform direct classical trajectory simulations to uncover the dynamic behaviors of the S_N2 reactions at N center. © 2012 Wiley Periodicals, Inc.     

Halogen bonds with benzene: An assessment of DFT functionals

The performance of an extensive set of density functional theory functionals has been tested against CCSD(T) and MP2 results, extrapolated to the complete basis set (CBS) limit, for the interaction of either DCl or DBr (D = H, HCC, F, and NC) with the aromatic system of benzene. It was found that double hybrid functionals explicitly including dispersion, that is, B2PLYPD and mPW2PLYPD, provide the better agreement with the CCSD(T)/CBS results on both energies and equilibrium geometry, indicating the importance of dispersive contributions in determining this interaction. Among the less expensive functionals, the better performance is provided by the ωB97X and M062X functionals, while the ωB97XD and B97D functionals are shown to work very well for bromine complexes but not so well for chlorine complexes. © 2013 Wiley Periodicals, Inc.     

Assessment of new meta and hybrid meta density functionals for predicting the geometry and binding energy of a challenging system: the dimer of H2S and benzene

Noncovalent interactions of a hydrogen bond donor with an aromatic pi system present a challenge for density functional theory, and most density functionals do not perform well for this kind of interaction. Here we test seven recent density functionals from our research group, along with the popular B3LYP functional, for the dimer of H 2S with benzene. The functionals considered include the four new meta and hybrid meta density functionals of the M06 suite, three slightly older hybrid meta functionals, and the B3LYP hybrid functional, and they were tested for their abilities to predict the dissociation energies of three conformations of the H 2S-benzene dimer and to reproduce the key geometric parameters of the equilibrium conformation of this dimer. All of the functionals tested except B3LYP correctly predict which of the three conformations of the dimer is the most stable. The functionals that are best able to reproduce the geometry of the equilibrium conformation of the dimer with a polarized triple-zeta basis set are M06-L, PWB6K, and MPWB1K, each having a mean unsigned relative error across the two experimentally verifiable geometric parameters of only 8%. The success of M06-L is very encouraging because it is a local functional, which reduces the cost for large simulations. The M05-2X functional yields the most accurate binding energy of a conformation of the dimer for which a binding energy calculated at the CCSD(T) level of theory is available; M05-2X gives a binding energy for the system with a difference of merely 0.02 kcal/mol from that obtained by the CCSD(T) calculation. The M06 functional performs well in both categories by yielding a good representation of the geometry of the equilibrium structure and by giving a binding energy that is only 0.19 kcal/mol different from that calculated by CCSD(T). We conclude that the new generation of density functionals should be useful for a variety of problems in biochemistry and materials where aromatic functional groups can serve as hydrogen bond acceptors.     

Developing a computational model that accurately reproduces the structural features of a dinucleoside monophosphate unit within B-DNA

The ability of a dinucleoside monophosphate to mimic the conformation of B-DNA was tested using a combination of different phosphate models (anionic, neutral, counterion), environments (gas, water), and density functionals (B3LYP, MPWB1K, M06-2X) with the 6-31G(d,p) basis set. Three sequences (5'-GX(Py)-3', where X(Py) = T, U or (Br)U) were considered, which vary in the (natural or modified) 3' pyrimidine nucleobase (X(Py)). These bases were selected due to their presence in natural DNA, structural similarity to T and/or applications in radical-initiated anti-tumour therapies. The accuracy of each of the 54 model, method and sequence combinations was judged based on the ability to reproduce key structural features of natural B-DNA, including the stacked base-base orientation and important backbone torsion angles. B3LYP yields distorted or tilted relative base-base orientations, while many computational challenges were encountered for MPWB1K. Despite wide use in computational studies of DNA, the neutral (protonated) phosphate model could not consistently predict a stacked arrangement for all sequences. In contrast, stacked base-base arrangements were obtained for all sequences with M06-2X in conjunction with both the anionic and (sodium) counterion phosphate models. However, comparison of calculated and experimental backbone conformations reveals the charge-neutralized counterion phosphate model best mimics B-DNA. Structures optimized with implicit solvent (water) are comparable to gas-phase structures, which suggests similar results should be obtained in an environment of intermediate polarity. We recommend the use of either gas-phase or water M06-2X optimizations with the counterion phosphate model to study the structure and/or reactivity of natural or modified DNA with a dinucleoside monophosphate.     

Studies on the structure, stability, and spectral signatures of hydride ion-water clusters

The gas-phase structure, stability, spectra, and electron density topography of H(-)W(n) clusters (where n = 1-8) have been calculated using coupled-cluster CCSD(T) and M?ller-Plesset second-order perturbation (MP2) theory combined with complete basis set (CBS) approaches. The performance of various density functional theory (DFT) based methods such as B3LYP, M05-2X, M06, M06-L, and M06-2X using 6-311++G(d,p), and aug-cc-pVXZ (aVXZ, where X = D, T, and Q) basis sets has also been assessed by considering values calculated using CCSD(T)/CBS limit as reference. The performance of the functionals has been ranked based on the mean signed/unsigned error. The comparison of geometrical parameters elicits that the geometrical parameters predicted by B3LYP/aVTZ method are in good agreement with those values obtained at MP2/aVTZ level of theory. Results show that M05-2X functional outperform other functionals in predicting the energetics when compared to CCSD(T)/CBS value. On the other hand, values predicted by M06-2X, and M06 methods, are closer to those values obtained from MP2/CBS approach. It is evident from the calculations that H(-)W(n) (where n = 5-8) clusters adopt several interesting structural motifs such as pyramidal, prism, book, Clessidra, cubic, cage, and bag. The important role played by ion-water (O-H···H(-)) and water-water (O-H···O) interactions in determining the stability of the clusters has also been observed. Analysis of the results indicates that the most stable cluster is made up of minimum number of O-H···H(-) interaction in conjugation with the maximum number of O-H···O interactions. The Bader theory of atoms in molecules (AIM) and natural bond orbital (NBO) analyses has also been carried out to characterize the nature of interactions between hydride ion and water molecules. It can be observed from the vibrational spectra of H(-)W(n) clusters, the stretching frequencies involving ion-water interaction always exhibit larger redshift and intensities than that of water-water (inter solvent) interactions.     

Benchmark of density functional theory methods on the prediction of bond energies and bond distances of noble-gas containing molecules

We have tested three pure density functional theory (DFT) functionals, BLYP, MPWPW91, MPWB95, and ten hybrid DFT functionals, B3LYP, B3P86, B98, MPW1B95, MPW1PW91, BMK, M05-2X, M06-2X, B2GP-PLYP, and DSD-BLYP with a series of commonly used basis sets on the performance of predicting the bond energies and bond distances of 31 small neutral noble-gas containing molecules. The reference structures were obtained using the CCSD(T)∕aug-cc-pVTZ theory and the reference energies were based on the calculation at the CCSD(T)∕CBS level. While in general the hybrid functionals performed significantly better than the pure functionals, our tests showed a range of performance by these hybrid functionals. For the bond energies, the MPW1B95∕6-311+G(2df,2pd), BMK∕aug-cc-pVTZ, B2GP-PLYP∕aug-cc-pVTZ, and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 2.0-2.3 kcal∕mol per molecule. For the bond distances, the MPW1B95∕6-311+G(2df,2pd), MPW1PW91∕6-311+G(2df,2pd), and B3P86∕6-311+G(2df,2pd), DSD-BLYP∕6-311+G(2df,2pd), and DSD-BLYP∕aug-cc-pVTZ methods stood out with mean unsigned errors of 0.008-0.013 A? per bond. The current study showed that a careful selection of DFT functionals is very important in the study of noble-gas chemistry, and the most recommended methods are MPW1B95∕6-311+G(2df,2pd) and DSD-BLYP∕aug-cc-pVTZ.