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.     

Computational investigation of the weakly bound dimers HOX...SO(3) (X = F, Cl, Br)

The electronic structure and thermochemical stability of the HOX-SO(3) (X = F, Cl, Br) complexes is studied using second-order M?ller-Plesset perturbation theory (MP2). The calculated dissociation energies of the HOF-SO(3), HOCl-SO(3), and HOBr-SO(3) complexes are 5.43, 6.02, and 5.98 kcal mol(-1) at MP2/6-311++G(3df,3pd) level, respectively. Anharmonic OH stretching frequencies of the HOX (X = F, Cl, Br) moieties along with the frequency shifts upon complex formation are calculated at the MP2/6-311++G(2df,2p) level. AIM and NBO analyses were also performed. Theoretical data strongly encourage performing of matrix-isolation studies of the title complexes and their spectroscopic identification.     

Properties of the halogen-hydride interaction: an ab initio and "atoms in molecules" analysis

X-Cl...H-Y interactions are analyzed by applying ab initio methods as well as the Bader theory. All calculations were performed using Pople's basis sets (6-311++G(2df,2pd) and 6-311++G(3df,3pd)) as well as the Dunning-type bases (aug-cc-pVDZ and aug-cc-pVTZ) within the MP2 method. For the complexes analyzed here, X-Cl and H-Y may be treated as a Lewis acid and a Lewis base, respectively. The Cl...H interactions are rather weak or at most moderate since, for the strongest interaction of the F3...HLi complex, the binding energy calculated at the MP2/6-311++G(3df,3pd) level of approximation amounts to -3.4 kcal/mol, and the H...Cl distance is equal to 2.65 A, less than the corresponding sum of van der Waals radii. These interactions may be classified as halogen-hydride interactions. However, some of the complexes analyzed, especially F3SiCl...HBeF and F3SiCl...HBeF, are very weakly bound, probably by typical van der Waals interactions.     

Theoretical investigations on analytical potential energy function and spectroscopic parameters for the state b3Πu of dimer 7Li2

The SAC‐CI (symmetry‐adapted‐cluster configuration‐interaction) method presented in Gaussian 03 program package is applied to investigate the adiabatic potential energy curves (PECs) of ⁷Li₂(b³Π_u). These calculations are performed at numbers of basis sets, such as 6‐311++G(3df,3pd), 6‐311++G(2df,2pd), 6‐311++G(df,pd), D95V++, D95(3df,3pd), D95(d,p), cc‐PVTZ, 6‐311++G and 6‐311++G(d,p). All the ab initio calculated points are fitted to the analytic Murrell‐Sorbie functions and then used to compute the spectroscopic parameters. The analytic potential energy function (APEF) for this b³Π_u state is reported. By comparison, the spectroscopic parameters reproduced by the APEF attained at 6‐311++G(2df,2pd) are found to be very close to the latest experimental findings. With the APEF obtained at the SAC‐CI/6‐311++G(2df,2pd) level of theory, a total of 62 vibrational states is found when J = 0. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants for these vibrational states are also reported. The reasonable dissociation limit for this state is deduced using the calculated results at present. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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     

Inverse hydrogen bonds between SiH_4 and hydrides of Na,Mg and Be

The optimized geometries of the three complexes between MeHn (Me=Na,Mg,Be;n=1 or 2) and SiH4 have been calculated at the B3LYP/6-311++g**,MP2/6-311++g(3df,3pd) and MP2/aug-cc-pvtz levels,respectively.The red-shift inverse hydrogen bonds (IHBs) based on Si-H,an electron donor,were reported.The calculated binding energies with basis set super-position error (BSSE) correction of the three complexes are-5.98,-8.65 and-3.96 kJ mol-1 (MP2/6-311++g(3df,3pd)),respectively,which agree with the results obtained via M...     

Weakly bound complexes of N2O: an ab initio theoretical analysis toward the design of N2O receptors

Ab initio calculations at MP2/6-311++G(2d,2p) and MP2/6-311++G(3df,3pd) computational levels have been used to analyze the interactions between nitrous oxide and a series of small and large molecules that act simultaneously as hydrogen bond donors and electron donors. The basis set superposition error (BSSE) and zero point energy (ZPE) corrected binding energies of small N2O complexes (H2O, NH3, HOOH, HOO*, HONH2, HCO2H, H2CO, HCONH2, H2CNH, HC(NH)NH2, SH2, H2CS, HCSOH, HCSNH2) vary between -0.93 and -2.90 kcal/mol at MP2/6-311++G(3df,3pd) level, and for eight large complexes of N2O they vary between -2.98 and -3.37 kcal/mol at the MP2/6-311++G(2d,2p) level. The most strongly bound among small N2O complexes (HCSNH2-N2O) contains a NH..N bond, along with S-->N interactions, and the most unstable (H2S-N2O) contains just S-->N interactions. The electron density properties have been analyzed within the atoms in molecules (AIM) methodology. Results of the present study open a window into the nature of the interactions between N2O with other molecular moieties and open the possibility to design N2O abiotic receptors.     

Matrix isolation and ab initio study of the hydrogen-bonded H2O2-CO complex

The structure, energetics, and infrared spectrum of the H2O2-CO complex have been studied computationally with the use of ab initio calculations and experimentally by FTIR matrix isolation techniques. Computations predict two stable conformations for the H2O2-CO complex, both of which show almost linear hydrogen bonds between the subunits. The carbon-attached HOOH-CO complex is the lower-energy form, and it has an interaction energy of -9.0 kJmol(-1) at the CCSD(T)/6-311++G(3df,3pd)// MP2/6-311++G(3df,3pd) level. The higher-energy form, HOOH-OC, has an interaction energy of 4.7 kJmol(-1) at the same level of theory. Experimentally, only the lower-energy form, HOOH-CO, was observed in Ar, Kr, and Xe matrices, and the hydrogen bonding results in substantial perturbations of the observed vibrational modes of both complex subunits. UV photolysis of the complex species primarily produces a complex between water and carbon dioxide, but minor amounts of HCO and trans-HOCO were found as well.     

Microwave spectrum of 3-butyne-1-thiol: evidence for intramolecular S-H...pi hydrogen bonding

The microwave spectrum of 3-butyne-1-thiol has been studied by means of Stark-modulation microwave spectroscopy and quantum-chemical calculations employing the B3LYP/6-311++G(3df,2pd), MP2/aug-cc-pVTZ, MP2/6-311++G(3df,2pd), and G3 methods. Rotational transitions attributable to two conformers of this molecule were assigned. One of these conformers possesses an antiperiplanar arrangement of the atoms S-C1-C2-C3, while the other is synclinal and stabilized by the formation of an intramolecular hydrogen bond between the H-atom of the thiol group and the pi-electrons of the C[triple bond]C triple bond. The energy difference between these conformers was estimated to be 1.7(4) kJ mol(-1) by relative intensity measurements, with the hydrogen-bonded conformer being lower in energy. The spectra of five vibrationally excited states of the synclinal conformer were observed, and an assignment of these states to particular vibrational modes was made with the aid of a density functional theory (DFT) calculation of the vibrational frequencies at the B3LYP/6-311++G(3df,2pd) level of theory.     

FC(O)O自由基与NO2反应的量子化学研究

用量子化学DFT, MP2, G3和G3MP2方法对FC(O)O自由基与NO₂的反应机理进行了理论研究. 优化了反应势能面上各驻点的几何结构, 通过内禀反应坐标(IRC)计算和振动分析, 确认了反应中的过渡态, 并用过渡态理论(TST)计算了相关反应的速率常数.     

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).     

Aminolysis of a model nerve agent: a computational reaction mechanism study of o,s-dimethyl methylphosphonothiolate

The mechanism for the aminolysis of a model nerve agent, O,S-dimethyl methylphosphonothiolate, is investigated both at density functional level using M062X method with 6-311++G(d,p) basis set and at ab initio level using the second-order M?ller-Plesset perturbation theory (MP2) with the 6-311+G(d,p) basis set. The catalytic role of an additional NH(3) and H(2)O molecule is also examined. The solvent effects of acetonitrile, ethanol, and water are taken into account employing the conductor-like screening model (COSMO) at the single-point M062X/6-311++G(d,p) level of theory. Two possible dissociation pathways, methanethiol and methyl alcohol dissociations, along with two different neutral mechanisms, a concerted one and a stepwise route through two neutral intermediates, for each pathway are investigated. Hyperconjugation stabilization that has an effect on the stability of generated transition states are investigated by natural bond order (NBO) approach. Additionally, quantum theory of atoms in molecules analysis is performed to evaluate the bond critical (BCP) properties and to quantify strength of different types of interactions. The calculated results predict that the reaction of O,S-dimethyl methylphosphonothiolate with NH(3) gives rise to parallel P-S and P-O bond cleavages, and in each cleavage the neutral stepwise route is always favorable than the concerted one. The mechanism of NH(3) and H(2)O as catalyst is nearly similar, and they facilitate the shuttle of proton to accelerate the reaction. The steps involving the H(2)O-mediated proton transfer are the most suitable ones. The first steps for the stepwise process, the formation of neutral intermediate, are the rate-determining step. It is observed that in the presence of catalyst the reaction in the stepwise path possesses almost half the activation energy of the uncatalyzed one. A bond-order analysis using Wiberg bond indexes obtained by NBO calculation predicts that usually all individual steps of the reactions occur in a concerted fashion showing equal progress along different reaction coordinates.     

An ab initio correlated study of the potential energy surface for the HOBr.H2O complex

The potential energy surface (PES) for the HOBr.H(2)O complex has been investigated using second- and fourth-order M?ller-Plesset perturbation theory (MP2, MP4) and coupled cluster theory with single and doubles excitations (CCSD), and a perturbative approximation of triple excitations (CCSD-T), correlated ab initio levels of theory employing basis sets of triple zeta quality with polarization and diffuse functions up to the 6-311++G(3dp,3df ) standard Pople's basis set. Six stationary points being three minima, two first-order transition state (TS) structures and one second-order TS were located on the PES. The global minimum syn and the anti equilibrium structure are virtually degenerated [DeltaE(ele-nuc) approximately 0.3 kcal mol(-1), CCSD-T/6-311++G(3df,3pd) value], with the third minima being approximately 4 kcal mol(-1) away. IRC analysis was performed to confirm the correct connectivity of the two first-order TS structures. The CCSD-T/6-311++G(3df,3pd)//MP2/6-311G(d,p) barrier for the syn<-->anti interconversion is 0.3 kcal mol(-1), indicating that a mixture of the syn and anti forms of the HOBr.H(2)O complex is likely to exist.     

Theoretical Comparison of the Linear and Bent Structures for the Weakly Bound CO2—HF Complex

Density‐functional theory method (DFT) B3LYP/6–311++G(3df,2pd) and Moller‐Plesset perturbation method (MP2) MP2/6–311++G(3df,2pd) of Gaussian 03 were selected for the theoretical study of weakly bound CO₂—HF complex. In addition to the well‐known linear structure, the various bent structure complexes were also found in this work. The self‐consistent energy differences were only around 0.02 kJ/mol between the bent structure and linear structure by comparison. From the results of H‐bonding distance, dHF elongation and red shift of VHF vibration frequency, all the evidence shows that the H‐bonding effect in the bent structure is stronger than the linear structure. However, if one compares the Gibbs energy of the complex formation by temperature variation, it is very easily found that the linear form is favored under the thermal conditions of most temperatures whenever T ≥ 40 K. Such a fact is consistent with the former spectroscopic observed result of Klemperer et al.     

pi-H...O hydrogen bonds: multicenter covalent pi-H interaction acts as the proton-donating system

The MP2 method and the Pople-style basis sets 6-311++G(d,p), 6-311++G(2df,2pd), and 6-311++G(3df,3pd) were used to perform calculations on H3O+...C2H2 and C2H3+...C2H2 complexes and related species. Hydrogen bonds existing for the analyzed complexes were investigated as well as related pi-H...O --> pi...H-O and pi-H...pi --> pi...H-pi proton-transfer processes. For some of the complexes analyzed the multicenter pi-H interaction possessing the properties of a covalent bond acts as a proton donor; more generally it is classified as the Lewis acid. The quantum theory of "atoms in molecules" (QTAIM) was also applied to deepen the nature of these interactions in terms of characteristics of bond critical points. The pi-H...O, O-H...pi, and pi-H...pi interactions analyzed here may be classified as hydrogen bonds since their characteristics are the same as or at least similar to those of typical hydrogen bonds. H...pi interactions are common in crystal structures of organic and organometallic compounds. The analyses performed here show a continuum of such interactions since there are H...pi contacts possessing the characteristics of weak intermolecular interactions on the one hand and pi-H multicenter covalent bonds on the other. Ab initio and QTAIM results support the latter statements.     

The molecular structure of fluoromalononitrile as determined by gas-phase electron diffraction and ab initio calculations

The molecular structure of fluoromalononitrile was studied by means of gas-phase electron diffraction and quantum mechanical methods using HF/6-31G(d), MP2/6-311++G(2df,2pd) and DFT/B3LYP/6-31G(d), B3PW91/6-31G(d), B3LYP/6-311++G(2df,2pd) and B3PW91/6-311++G(2df,2pd). The r(g) and angle(alpha) structural parameters we obtained from the present analysis are: CC=1.487(5) A, CN=1.157(3) A, CF=1.386(5) A, CH=1.096 A (ass.), angleCCC=106.7(1.0) degrees , angleCCF=108.0(0.7) degrees , angleCCN=177.6(2.0) degrees . Uncertainties in parenthesis are 3sigma.     

Insights into N‐Heterocyclic Carbene (NHC)‐Catalyzed Asymmetric Addition of 2H‐Azirine with Aldehyde

The possible mechanisms and origin of the enantioselectivity of the reaction between 2H‐azirine and an aldehyde catalyzed by an N‐heterocyclic carbene (NHC) were theoretically studied and predicted at the M06‐2X/6‐31G(d,p)/IEF‐PCM_MTBE//M06‐2X‐GD3/6‐311++G(2df, 2pd)/IEF‐PCM_MTBE level. The most favorable reaction pathway consists of four steps, i.e., complexation of the NHC and the aldehyde, stepwise [1,2]‐proton transfer, C?C bond formation coupled with another proton transfer, and recycling of the NHC. The computational results indicate that the stereoselectivity‐determining step is also the rate‐determining step, which is the third step (i.e., intermolecular addition). The calculated 99 % ee is very close to the experimentally observed value of 96 % ee, demonstrating that the calculations are reliable. Two important roles of the NHC were identified by global reaction index (GRI) analysis and natural population analysis (NPA), that is, realizing the umpolung reactivity of the aldehyde and facilitating the deprotonation of aldehyde. Moreover, the efficiency of different NHC catalysts can be mainly predicted by computing the nucleophilic index of the corresponding Breslow intermediates. Furthermore, distortion/interaction and noncovalent interaction (NCI) analyses revealed that the π???π interactions between the NHC and substrates were the key factor in the reaction enantioselectivity.     

Coupling Interactions between Sulfurous Acid and the Hydroperoxyl Radical

Radical–molecule complexes associated with the hydroperoxyl radical (HOO) play an important role in atmospheric chemistry. Herein, the nature of the coupling interactions between sulfurous acid (H₂SO₃) and the HOO radical is systematically investigated at the B3LYP/6‐311++G(3df,3pd) level of theory in combination with the atoms in molecules (AIM) theory, the natural bond orbital (NBO) method, and energy decomposition analyses (EDA). Eight stable stationary points possessing double H‐bonding features were located on the H₂SO₃???HOO potential energy surface. The largest binding energies of ?12.27 and ?11.72 kcal mol^?1 are observed for the two most stable complexes, where both of them possess strong double intermolecular H‐bonds of partially covalence. Moreover, the characteristics of the IR spectra for the two most stable complexes are discussed to provide some help for their possible experimental identification.     

Theoretical Study on Gas Phase Reactions of OH Hydrogen-Abstraction from Formyl Fluoride with Di erent Catalysts

The mechanisms and kinetics of the gas phase reactions that the hydrogen atom in formyl uoride (FCHO) abstracted by OH in the presence of water, formic acid (FA), or sulfuric acid (SA) are theoretically investigated at the CCSD(T)/6-311++G(3df, 3pd)//M06-2X/6-311++G(3df, 3pd) level of theory. The calculated results show that the barriers of the transition states involving catalysts are lowered to -2.89, -6.25, and -7.76 kcal/mol from 3.64 kcal/mol with respect to the separate reactants, respectively, which re ects that those catalysts play an important role in reducing the barrier of the hydrogen abstraction reaction of FCHO with OH. Additionally, using conventional transition state theory with Eckart tun-neling correction, the kinetic data demonstrate that the entrance channel X FCHO+OH (X=H₂O, FA, or SA) is signi cantly more favorable than the pathway X OH+FCHO. More-over, the rate constants of the reactions of FCHO with OH radical with H₂O, FA, or SA introduced are computed to be smaller than that of the naked OH+FCHO reaction because the concentration of the formed X FCHO or X OH complex is quite low in the atmosphere.     

The importance of lone pair delocalizations: theoretical investigations on the stability of cis and trans isomers in 1,2-halodiazenes

The relative and thermodynamic stabilities of cis and trans isomers of 1,2-dihalodiazenes (XN=NX; X = F, Cl, or Br) were examined using high level ab initio and density functional theory (DFT) calculations. For 1,2-dihalodiazenes, it was found that the cis isomers were more stable than the corresponding trans isomers, despite the existence of several cis destabilizing mechanisms, such as steric exchange between halogen lone pairs and dipole-dipole electrostatic repulsions (Delta(trans-cis) = 3.15, 7.04, and 8.19 kcal mol(-1), respectively, at BP86/6-311++G(3df,3pd)//B3LYP /6-311++G(3df,3pd) level). Their origin of the cis-preferred difference in energy was investigated with natural bond orbital (NBO) analysis to show that the "cis effect" came mainly from antiperiplanar interactions (AP effect) between the nitrogen lone pair and the neighboring antibonding orbital of the N-X bond (n(N) --> sigma(N'X'*)). The delocalization of halogen lone-pair into the antibonding orbital of the N=N bonds (the LP effects) was also found to enhance the cis preference by 1.20 to 6.58 kcal mol(-1), depending on the substituted halogen atom. The total amount of the AP effect increased as the halogen atom became larger, and the increased AP effect promoted the triple-bond-like nature of the N=N bond (shorter N=N bond length and wider NNX angle). The greater AP effect also made the N'-X' bond easier to cleave (longer N-X bond length), and a higher energy level than that of the nitrogen lone pair was found in the N-Br bonding orbital in 1,2-dibromodiazenes, thus indicating the significant instability of this molecule. The degradability of the N-Cl bond in 1,2-dichlorodiazenes and the fair stability of the N-F bond in 1,2-fluorodiazenes were also confirmed theoretically, and were found to be consistent with the previous experimental and theoretical reports. These results clearly indicate the dominance of lone-pair-related hyperconjugations on the basic electronic structure and energetic natures of 1,2-dihalodiazene systems.