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.     

非共价作用对气相中B-DNA双螺旋结构稳定性的贡献:基于GEBF方法的密度泛函理论计算

采用密度泛函理论, 将基于能量的分子片方法(GEBF)应用于气相中优化B型脱氧核糖核酸(碱基对数目N=2, 5, 10)双螺旋构型的结构. 通过比较M06-2X泛函和其他方法(B3LYP、B3LYP-vdW和TPSS泛函)的结果, 发现不考虑碱基之间的π-π堆积作用将会导致碱基之间的纵向距离拉长. 随着体系双螺旋链长的增加, 没有考虑碱基堆积作用而导致的相邻碱基纵向距离拉长的程度快速衰减. 计算表明, 气相中B-DNA双螺旋结构的稳定性来源于其作用力(主要是氢键和π-π堆积作用)的协同性, 对不多于10组碱基对的体系而言, 其氢键的贡献明显大于碱基堆积作用.     

Performance of SM8 on a test to predict small-molecule solvation free energies

The SM8 quantum mechanical aqueous continuum solvation model is applied to a 17-molecule test set proposed by Nicholls et al. (J. Med. Chem. 2008, 51, 769) to predict free energies of solvation. With the M06-2X density functional, the 6-31G(d) basis set, and CM4M charge model, the root-mean-square error (RMSE) of SM8 is 1.08 kcal mol(-1) for aqueous geometries and 1.14 kcal mol(-1) for gas-phase geometries. These errors compare favorably with optimal explicit and continuum models reported by Nicholls et al., having RMSEs of 1.33 and 1.87 kcal mol(-1), respectively. Other models examined by these workers had RMSEs of 1.5-2.6 kcal mol(-1). We also explore the use of other density functionals and charge models with SM8 and the RMSE increases to 1.21 kcal mol(-1) for mPW1/CM4 with gas-phase geometries, to 1.50 kcal mol(-1) for M06-2X/CM4 with gas-phase geometries, and to 1.27-1.64 kcal mol(-1) with three different models at B3LYP gas-phase geometries.     

Photoexcitation of dinucleoside radical cations: a time-dependent density functional study

The excited states of dinucleoside phosphates (dGpdG, dApdA, dApdT, TpdA, and dGpdT) in their cationic radical states were studied with time-dependent density functional theory (TD-DFT). The ground-state geometries of all the dinucleoside phosphate cation radicals considered, in their base stacked conformation, were optimized with the B3LYP/6-31G(d) method. Further, to take into account the effect of the aqueous environment surrounding the dinucleoside phosphates, the polarized continuum model (PCM) was considered and the excitation energies were computed by using the TD-B3LYP/6-31G(d) method. From this study, we find that the first transition in all the dinucleoside molecules involves hole transfer from base to base. dG*+pdG and dApdA*+ were found to have substantially lower first transition energies than others with two different DNA bases. Higher energy transitions involve base to sugar as well as base to base hole transfer. The calculated TD-B3LYP/6-31G(d) transition energies are in good agreement with previous calculations with CASSCF/CAS-PT2 level of theory. This TD-DFT work supports the experimental findings that sugar radicals formed upon photoexcitation of G*+ in gamma-irradiated DNA and suggests an explanation for the wavelength dependence found.     

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.     

The charge-transfer states in a stacked nucleobase dimer complex: a benchmark study

Electronic singlet excitations of stacked adenine-thymine (AT) and guanine-cytosine (GC) complexes have been investigated with respect to local excitation and charge-transfer (CT) characters. Potential energy curves for rigid displacement of the nucleobases have been computed to establish the distance dependence of the CT states. The second-order algebraic diagrammatic construction [ADC(2)] method served as reference approach for comparison to a selected set of density functionals used within the time-dependent density functional theory (TD-DFT). Particular attention was dedicated to the performance of the recently developed family of M06 functionals. The calculations for the stacked complexes show that at the ADC(2) level, the lowest CT state is S(6) for the AT and as S(4) for the GC pair. At the reference geometry, the actual charge transferred is found to be 0.73 e for AT. In case of GC, this amount is much smaller (0.17 e). With increasing separation of the two nucleobases, the CT state is strongly destabilized. The M06-2X version provides a relatively good reproduction of the ADC(2) results. It avoids the serious overstabilization and overcrowding of the spectrum found with the B3LYP functional. On the other hand, M06-HF destabilizes the CT state too strongly. TD-DFT/M06-2X calculations in solution (heptane, isoquinoline, and water) using the polarizable continuum model show a stabilization of the CT state and an increase in CT character with increasing polarity of the solvent.     

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.     

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.     

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     

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.     

The structure characterization of dinucleoside and nucleoside glucopyranosides lipophilic phosphotriesters by fast-atom bombardment tandem mass spectrometry

Rules for the gas-phase fragmentation mechanism of the negative ions of lipophilic phosphotriester molecules of biological interest have been established by fast-atom bombardment mass spectrometry/mass spectrometry. The mass-analyzed ion kinetic energy spectra of the [M ? H]^? of dinucleoside (1–4) and nucleoside glucopyranoside (5–9) phosphotriesters show that in the absence of charges on the phosphate bridge, the availability of acidic protons on the 5′-end nucleobase drives a preferred reaction path which leads to 5′-O-nucleotide or 6-O-glucopyranoside monophosphate anions.     

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.     

Substituents destabilize the molecule by increasing biradicaloid character and stabilize by intramolecular charge transfer in the derivatives of benzobis(thiadiazole) and thiadiazolothienopyrazine: a computational study

Keeping in view the possible applications of singlet open-shell molecules as semiconductors, non-classical derivatives of the heterocyclic rings benzobis(thiadiazole) (BBT) and its positional isomer thiadiazolothienopyrazine (TTP) are characterized using DFT methodologies. M06-2X, B3LYP and BHandHLYP functionals were used to optimize the geometries and estimate the vertical transition energies. It is observed that unlike the BHandHLYP functional (50% exchange), which gives rise to spin-contaminated solutions for all molecules in the series, M06-2X (54% exchange) affords a wavefunction either with no instability or negligible instability for most of the molecules. The results are compared with the earlier reported experimental data and those obtained herein using the spin-flip (SF)-5050 method. It is found that B3LYP does not fare well while on the other hand the M06-2X and SF-50-50 are in good agreement with the experimental results. It is seen that M06-2X TD-DFT for the molecules can be carried out without major spin contamination and also that the more time-consuming CI can be avoided for the calculation of transition energies. The biradical nature of the molecules is estimated by the singlet-triplet gap. Intramolecular charge transfer is calculated. It is found that the ring substituents donate charge in the ground state, creating a zwitterionic structure. Thus the substituents play an interesting dual role, decreasing the stability of the molecule by increasing the biradical character (small HOMO-LUMO gap), and stabilization of this ground state by intramolecular charge transfer.     

Computational methods to calculate accurate activation and reaction energies of 1,3-dipolar cycloadditions of 24 1,3-dipoles

Theoretical calculations were performed on the 1,3-dipolar cycloaddition reactions of 24 1,3-dipoles with ethylene and acetylene. The 24 1,3-dipoles are of the formula X≡Y(+)-Z(-) (where X is HC or N, Y is N, and Z is CH(2), NH, or O) or X═Y(+)-Z(-) (where X and Z are CH(2), NH, or O and Y is NH, O, or S). The high-accuracy G3B3 method was employed as the reference. CBS-QB3, CCSD(T)//B3LYP, SCS-MP2//B3LYP, B3LYP, M06-2X, and B97-D methods were benchmarked to assess their accuracies and to determine an accurate method that is practical for large systems. Several basis sets were also evaluated. Compared to the G3B3 method, CBS-QB3 and CCSD(T)/maug-cc-pV(T+d)Z//B3LYP methods give similar results for both activation and reaction enthalpies (mean average deviation, MAD, < 1.5 kcal/mol). SCS-MP2//B3LYP and M06-2X give small errors for the activation enthalpies (MAD < 1.5 kcal/mol), while B3LYP has MAD = 2.3 kcal/mol. SCS-MP2//B3LYP and B3LYP give the reasonable reaction enthalpies (MAD < 5.0 kcal/mol). The B3LYP functional also gives good results for most 1,3-dipoles (MAD = 1.9 kcal/mol for 17 common 1,3-dipoles), but the activation and reaction enthalpies for ozone and sulfur dioxide are difficult to calculate by any of the density functional methods.     

A quantitative study of intrinsic non-covalent interactions within complexes of α-cyclodextrin and benzoate derivatives

A novel deconvolution method for energy-resolved reaction cross sections is applied to determine intrinsic gas-phase dissociation energies for non-covalent α-cyclodextrin host-guest complexes. M06-2X//M06-L/6-31+G(d,p) calculations reproduce the experimental results and enable us to quantify the contribution of intermolecular hydrogen bonding.     

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.     

Density functional theory study of the oxidation reaction in the gas and aqueous phase of allyl methyl disulfide with hydroxyl radical

Structural Chemistry - An in silico analysis of the oxidation mechanism of allyl methyl disulfide (AMDS) by hydroxyl radical was achieved at DFT level using B3LYP, CAM-B3LYP, M06-2X, and BMK...     

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.     

Nucleosides and Nucleotides. Part 13. Synthesis and spectral properties of 1- (3′-O-Phosphoryl-2′-deoxy-β -D-ribofuranosyl)-2(1H)-pyridone-(3′-5′)-1-(2′-deoxy-β-D-ribofuranosyl)-2 (1H)-pyridone

The dinucleoside phosphate Π_dpΠ_d ( 4 ) was synthesized from the monomers 1-(5′-O-monomethoxytrityl - 2′ - deoxy - β - D - ribofuranosyl) - 2 (1 H) - pyridone ((MeOTr) Π_d, 2 ) and 1-(5′-O-phosphoryl-3′-O-acetyl-2′-deoxy-β-D -ribofuranosyl)-(1H)-pyridone (pΠ_d(Ac), 3 ). Its 6.4% hyperchromicity and an analysis of the ¹H-NMR. spectra indicate that the conformation and the base-base interactions in 4 are similar to those in natural pyrimidine dinucleoside phosphates.