Ab initio and density function theory computational studies of the CH4 + H → CH3 + H2 reaction

The activation barrier for the CH₄ + H → CH₃ + H₂ reaction was evaluated with traditional ab initio and Density Functional Theory (DFT) methods. None of the applied ab initio and DFT methods was able to reproduce the experimental activation barrier of 11.0-12.0 kcal/mol. All ab initio methods (HF, MP2, MP3, MP4, QCISD, QCISD(T), G1, G2, and G2MP2) overestimated the activation energy. The best results were obtained with the G2 and G2MP2 ab initio computational approaches. The zero-point corrected energy was 14.4 kcal mol⁻¹. Some of the exchange DFT methods (HFB) computed energies which were similar to the highly accurate ab initio methods, while the B3LYP hybrid DFT methods underestimated the activation barrier by 3 kcal mol⁻¹. Gradient-corrected DFT methods underestimated the barrier even more. The gradient-corrected DFT method that incorporated the PW91 correlational functional even generated a negative reaction barrier. The suitability of some computational methods for accurately predicting the potential energy surface for this hydrogen radical abstraction reaction was discussed.     

A density functional study of chemical reactions

Density functional theory (DFT ) was used to study reactions involving small molecules. Relative energies of isomers and transition structures of diazene, formaldehyde, and methylenimine were determined using various DFT functionals and results were compared with MP 2 and MP 4 calculations. DFT reaction barriers were found to be consistently lower. For some reactions, such as OH + H₂→ H₂O + H, gradient-corrected functionals predict very low or nonexistent barriers. The hybrid Hartree–Fock–DFT adiabatic connection method (ACM ) often provides much better results in such cases. The performance of several density functionals, including ACM , was tested in calculations on over 100 atomization, hydrogenation, bond dissociation, and isodesmic reactions. The ACM functional provides consistently better geometries and reaction energetics than does any other functional studied. In cases where both HF and gradient-corrected DFT methods underestimate bond distances, the ACM geometries may be inferior to those predicted by gradient-corrected DFT methods. © 1995 John Wiley & Sons, Inc.     

The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

Gas phase study of the trans and gauche rotamers of 1,2-dicyanoethane, novel 1,2-dicyanodisilane and cyano(cyanomethyl)silane by ab initio and density functional methods

The gauche and trans rotamers of 1,2-dicyanoethane, novel 1,2-dicyanodisilane and cyano(cyanomethyl)silane have been studied theoretically in the gas phase. The methods used are second order M?ller-Plesset theory (MP2) and density functional theory (DFT). The basis set used is 6-311++G(d,p) for all atoms. B3LYP is the functional used for the DFT method and G2/MP2 calculation has also carried out using the MP2 optimised structure. All calculations have been done using Gaussian 03W. All structures have been fully optimised and the optimised geometries, dipole moments, moment of inertia and energies are reported. Energies of the optimised structures have been used to obtain the energy difference (DeltaE) between the trans and gauche rotamers. The optimised structures have been used for calculations of vibrational frequencies and these frequencies are reported with appropriate assignments. The computed parameters for 1,2-dicyanoethane compare satisfactorily with experimental literature values. However, the literature for 1,2-dicyanodisilane and cyano(cyanomethyl)silane, in terms of conformational studies, is limited and therefore the data of this work should also be appropriate for them. The results indicate that in general, the energy difference for these molecules is in the order 1,2-dicyanoethane>cyano(cyanomethyl)silane>1,2-dicyanodisilane.     

A comparative relativistic DFT and ab initio study on the structure and thermodynamics of the oxofluorides of uranium(IV), (V) and (VI)

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.     

Systematic study of the lowest energy states of Pd,Pd2, and Pd3

A systematic study has been carried out for the determination and characterization of the lowest states of Pd, Pd₂, and Pd₃ using some of the best ab initio tools available at present (conventional and DFT). Full electron ab initio calculations using the HF, MP2, MP3, MP4, and QCI methods were compared with DFT methods using several gradient-corrected functionals as well as the hybrid B3LYP functional that performed very well for the energetics studies of these small clusters. A suitable basis set has been found to perform considerably well with palladium atoms, another of double-ζ quality has been found insufficient to reproduce basic characteristics of the smallest palladium clusters. The results indicate that the ground state for Pd is a singlet. The dimer is a triplet; however, it is very difficult to ascertain due to the closeness between singlet and triplet states (0.9 kcal/mol). The trimer ground state was found to be a triplet with a separation from the lowest singlet of 3.2 kcal/mol. The lowest triplet and singlet of Pd₃ were practically equilateral triangles. © 1997 John Wiley & Sons, Inc.     

An assessment of density functional methods for studying molecular adsorption in cluster models of zeolites

The performance of six density functional theory (DFT) methods has been tested for a zeolite cluster containing three tetrahedral atoms (3T) and the complexes it forms with water and methanol molecules. The DFT methods (BLYP, BP86, BPW91, B3LYP, B3P86, B3PW91) give results in good agreement with second-order perturbation theory (MP2). The results in this paper provide evidence of the suitability of DFT methods for studying hydrogen-bonded adsorption complexes in zeolites. Generally, the hybrid DFT methods are in closer agreement with experiment and MP2 than the pure DFT methods for geometrical parameters. The only exception is the Z⁻ geometry, perhaps due to its anionic character. All DFT methods give results in good overall agreement with MP2 for intramolecular geometrical parameters of the adsorption complexes, intramolecular vibrational frequencies, and adsorption energies. The B3LYP method gives intermolecular geometries and intermolecular vibrational frequencies which are closest to those obtained from the MP2 method. Thus, the B3LYP method seems to be the best choice for a density functional treatment of molecular adsorption in zeolite systems.     

Quantum chemical study of solvent and substituent effects on the 1,5-hydride shift in 2,6-dimethyl-2-heptyl cations

The mechanism of the degenerate 1,5-hydride shift in 2,6-dimethyl-2-heptyl cations has been investigated using ab initio MP2 and density functional theory (DFT) hybrid (B3LYP) calculations. The potential-energy profile for the 1,5-hydride shift consists of three minima corresponding to two equivalent acyclic carbocations and one symmetrically mu-hydrido-bridged carbocation, while two equivalent unsymmetrically hydrido-bridged carbocations were located as transition-state structures. The calculated relative energy differences between acyclic carbocations and symmetrically mu-hydrido-bridged structure are significantly affected by introduction of alkyl and (CH2)n-substituents at the C4 position of the 2,6-dimethyl-2-heptyl cation structure. DFT self-consistent isodensity polarizable continuum method (SCI-PCM) and MP2 PCM continuum methods have been used to calculate the effect of solvation on geometries and relative energies of the species involved in the 1,5-hydride shift. It is found that relative energies of acyclic and mu-hydrido-bridged carbocation structures as well as the energy barriers for 1,5-hydride shifts are in accord with experimental data if solvation effects are taken into account.     

采用12种密度泛函理论方法表征三种三价铀复合物

比较了BP86、PBE、B3LYP、B3PW91、BHandHLYP、PBE0、X3LYP、CAM-B3LYP、TPSS、M06L、M06和M06-2X等12种采用了广义梯度近似(GGA、hybrid GGA、meta-GGA和hybrid meta-GGA)的密度泛函理论(DFT)方法在三个三价铀复合物表征中的应用. 研究模型采用铀复合物催化CO₂和CS₂官能团化反应中的三个中间体(Tp^*)₂U- η¹-CH₂Ph (Cpd2), (Tp^*)₂U- κ²-O₂CCH₂Ph (Cpd3) 和(Tp^*)₂U- κ²-S₂CCH₂Ph (Cpd4). 研究发现, B3LYP 和B3PW91 在几何结构和电子结构方面优于其它方法. 基于分子轨道理论的MP2 方法在Cpd2 和Cpd3 的表征中给出与DFT方法相近的结果, 而在Cpd4 的表征中表现出较大的差异. 这可能是由于同样是单参考态方法的MP2捕捉到了与DFT方法不同的电子结构. 同时, 通过对比分别采用小核赝势(5f-in-valence)和大核赝势(5f-in-core)基组处理铀原子的计算结果, 发现对测试的模型体系, 两种处理方法可获得相近的热力学能量. 与以往主要关注高价态锕系复合物的处理方法的评估工作不同, 本项工作适应逐渐增加的对低价态锕系分子体系的研究的需求, 对12 种常用的密度泛函理论方法在低价态锕系复合物研究中的应用进行了评估, 期望为处理类似体系的研究工作提供参考.     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

Energetics and structure of glycine and alanine based model peptides: Approximate SCC-DFTB,AM1 and PM3 methods in comparison with DFT,HF and MP2 calculations

We calculate relative energies and geometries of important secondary structural elements for small glycine and alanine based polypeptides containing up to eight residues. We compare the performance of the approximate methods AM1, PM3 and self-consistent charge, density-functional tight-binding (SCC-DFTB) to density-functional theory (DFT), Hartree–Fock (HF) and MP2. The SCC-DFTB is able to reproduce structures and relative energies of various peptide models reliably compared to DFT results. The AM1 and PM3 methods show deficiencies in describing important secondary structure elements like extended, helical or turn structures. The discrepancies between different ab initio (HF, MP2) and DFT (B3LYP) methods for medium sized basis sets (6-31G*) also show the need for higher level calculations, since systematic errors found for small molecules may add up when investigating longer polypeptides.     

An investigation of the quantum chemical description of the ethylenic double bond in reactions: II. Insertion of ethylene into a titanium–carbon bond

Insertion of ethylene into the Ti–methyl bond in TiH₂CH⁺₃ is chosen as a model reaction for investigating the performance of a range of contemporary quantum chemical models in polymerization studies. Basis set effects are investigated at the self-consistent-field level, covering Hartree–Fock, pure DFT, and hybrid DFT. In agreement with findings in part I of this study, the basis set sensitivity of ethylene is shown to introduce a bias in computed energetics, amounting to 2–3 kcal/mol when DZP bases are used to compute the overall heat of monomer insertion. The geometry of stationary points relevant to the insertion reaction is determined using hybrid density functional theory. Based on these structures, the energy profile of the insertion reaction is computed using a range of popular quantum chemical approximations. The methods include Hartree–Fock and Møller–Plesset (MP) perturbation theory up through the fourth order in spin-restricted, spin-unrestricted, and spin-projected formalisms. Furthermore, configuration-interaction-based methods are included, of which the top level method is singly and doubly excited coupled clusters with a perturbative estimate of the contribution from triply excited configurations added [CCSD(T)]. The performance of the methods just mentioned, as well as three pure density functional and three hybrid density functional methods, are compared with respect to “best” relative energies, defined through extrapolation of CCSD(T) correlation energies according to the PCI scheme of Siegbahn and coworkers. Even though the MP series show poor convergence, spin-projected MP2, as well as two pure DFT methods (BPW91, BP86) and PCI-78 based on the MCPF method, show similar and very good agreement with best relative energies for the insertion reaction. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 947–960, 1998     

The determination of the equilibrium structures of oxygen,ozone, and hydrogen peroxide using the ab initio and density functional theory methods

The geometries and energies of small oxygen containing molecules are studied by both the ab initio and density functional theory (DFT) methods. The RHF, MP2, and QCISD(T) ab initio methods, BHandH, BHandHLYP, BeckeSLYP, Becke3P86 DFT hybrid methods, BLYP, and the BP86 non-local DFT methods with the 3-21G¹, 6-31G(d,p), 6-311 + G(2d,2p) and 6-311 + + G(3df,3pd) basis sets were used for the computational study. The obtained results from the different methods were compared to the experimental values. The suitability of the DFT methods for reproducing experimental data were discussed.     

Matrix-isolation FT-IR study and theoretical calculations of the vibrational, tautomeric and H-bonding properties of hypoxanthine

The neutral compound hypoxanthine is investigated using the technique of matrix-isolation FT-IR spectroscopy combined with density functional theory (DFT) and ab initio methods. Two theoretical methods (RHF and DFT/B3-LYP) are compared for vibrational frequency prediction, and four methods (RHF//RHF, MP2//RHF, DFT//DFT and MP2//DFT) for prediction of the relative energies of the tautomers and the interaction energies of the complexes. All the possible tautomeric forms have been considered theoretically, and the results indicate that two oxo forms (O17 and O19) and one hydroxy form (H9-r1) are the three most stable forms. The experimental FT-IR spectra are consistent with this prediction, and nearly all the characteristic spectral features of these forms have been identified in the spectrum. A theoretical study of the H-bonded complexes of these three tautomers with water is also performed. Several structures have been found for each form and the results demonstrate that the closed complexes with two H-bonds are the most stable systems due to the H-bond cooperative effect.     

Highlevel ab initio and hybrid density functional theory study of the energy profile for the CO+CO reaction

Two complete basis set and three hybrid density functional computational studies were applied in the exploration of the ¹CO+²CO⁺ reaction potential energy surface. One molecular carbon monoxide–carbon monoxide cation molecular associate was elucidated as the structure with the lowest energy on the potential energy surface. Ionization energies, bond dissociation energies, and enthalpies of formation for every di and tri-atomic molecule on the potential energy surface were estimated with the two complete basis sets and the three hybrid density functional theory methods. Six different endothermic channels for the ¹CO+²CO⁺ reaction were evaluated with ab initio and DFT methods. The computed energies and structural parameters are compared with experimental values where available. Some new energies for this reaction system were suggested.     

Comparison of some representative density functional theory and wave function theory methods for the studies of amino acids

Energies of different conformers of 22 amino acid molecules and their protonated and deprotonated species were calculated by some density functional theory (DFT; SVWN, B3LYP, B3PW91, MPWB1K, BHandHLYP) and wave function theory (WFT; HF, MP2) methods with the 6-311++G(d,p) basis set to obtain the relative conformer energies, vertical electron detachment energies, deprotonation energies, and proton affinities. Taking the CCSD/6-311++G(d,p) results as the references, the performances of the tested DFT and WFT methods for amino acids with various intramolecular hydrogen bonds were determined. The BHandHLYP method was the best overall performer among the tested DFT methods, and its accuracy was even better than that of the more expensive MP2 method. The computational dependencies of the five DFT methods and the HF and MP2 methods on the basis sets were further examined with the 6-31G(d,p), 6-311++G(d,p), aug-cc-pVDZ, 6-311++G(2df,p), and aug-cc-pVTZ basis sets. The differences between the small and large basis set results have decreased quickly for the hybrid generalized gradient approximation (GGA) methods. The basis set convergence of the MP2 results has been, however, very slow. Considering both the cost and the accuracy, the BHandHLYP functional with the 6-311++G(d,p) basis set is the best choice for the amino acid systems that are rich in hydrogen bonds.     

Ab initio and DFT computer studies of complexes of trimethylphosphine and products of substituted phosphonium cations with hydroxide, chloride and fluoride anions: Phosphorus analogues of choline and acetylcholine

Theoretical calculations (DFT, MP2) are reported for up to four sets of reaction products of trimethylphosphine, (CH₃)₃P, each with H₂O, HCl and HF together with DFT calculations on up to three sets of reaction products of substituted phosphonium cations, (CH₃)₃P–R⁺. These products comprise (a) P(III) normal complexes (CH₃)₃PHY, (b) P(IV) ‘reverse’ complexes Y(H–CH₂)₃P–R, (c) P(IV) ylidic complexes YHCH₂(CH₃)₂P–R and (d) P(V) covalent compounds Y–P(CH₃)₃–R for Y=HO, Cl and F and R=H, CH₃, C₂H₅, C₂H₄OH and C₂H₄OC:OCH₃. Calculations are carried out at the B3LYP/6-31+G(d,p) level in all cases and also at the MP2/6-31+G(d,p) level for systems in which R=H. Minimum energy structures are determined for predicted complexes or structures and geometrical properties, harmonic vibrations and BSSE corrected binding energies are reported and compared with the limited experimental information available. Potential energy scans predict equilibria between covalent trigonal bipyramidal P(V) forms and reverse complexes comprising hydrogen bonded or ion pair, tetrahedral P(IV) forms separated by low potential energy barriers. Similar scans are also reported for equilibria between reverse complexes and ylidic complexes for Y=OH and R=CH₃, C₂H₅, C₂H₄OH and C₂H₄OC:OCH₃. Corrected binding energies, structures and values of harmonic modes are discussed in relation to bonding The names ‘pholine’ and ‘acetylpholine’ are suggested for phosphorus analogues to choline and acetylcholine.     

Calculation of bond dissociation energies for oxygen containing molecules by ab initio and density functional theory methods

Two ab initio (ROHF and MP2), one local (SVWN), four hybrid (BHandH, BHandHLYP, Becke3LYP, and Becke3P86), and two nonlocal (BLYP and BP86) density functional theory (DFT) methods are used for calculating the dissociation energies of molecules that contain H(SINGLE BOND)O, O(SINGLE BOND)O and O(SINGLE BOND)C bonds. The sensitivity to the basis set of the prediction of bond dissociation energies with DFT methods was tested with Becke3LYP on the H(SINGLE BOND)O dissociation energy of water. The 6–31 + G(d) methods are chosen as the smallest basis set which produces reasonable results. The calculated values for all other ab initio and DFT methods were performed with these basis sets and then compared with the experimental data. The suitability of DFT methods for computing reliable bond dissociation energies of oxygen containing molecules is discussed. © 1996 John Wiley & Sons, Inc.     

High level ab initio and density functional theory study of bond selective dissociation of CH3SH and CH3CH2SH radical cations

Selective bond dissociation energies for CH₃SH and CH₃CH₂SH radical cations were evaluated with G1, G2, G2MP2, B3LYP, BLYP, and SVWN computational methods. It was determined that both G2 and CBSQ evaluate very accurate bond dissociation energies for thiol radical cations, while gradient-corrected BLYP computes the best energies of three employed DFT methods. For the CH₃CH₂SH radical cation, new, higher than previously estimated selective bond dissociation energies were suggested. Received: 10 September 1997 / Accepted: 9 September 1998 / Published online: 11 November 1998     

Ab initio and equilibrium bond angles. Structures of HNO and H2O2

The possibility of calculating accurate ab initio bond angles is examined using a sample of 29 molecules (35 independent angles) containing only first row atoms and whose equilibrium structures are known. Three different correlated methods are compared: MP2, CCSD(T), and DFT, using the hybrid functional B3LYP. The convergence of Dunning's correlation consistent polarized valence basis sets, cc-pVnZ is also studied. It is found that the CCSD(T) method is consistently the most accurate; the DFT/B3LYP being slightly less reliable than MP2. It is shown that when convergence of the basis set is achieved (which is dependent on the kind of bonding) and when the effect of diffuse functions on electronegative atoms is taken into account, a high accuracy may be obtained: 0.03° for the median of absolute deviations or 0.07° for the mean absolute deviation. It does not exclude the possibility that the ab initio method may fail in some particular case, for instance when a large amplitude motion is involved. The MP2/cc-pVQZ method gives a mean absolute deviation of 0.22° to be compared with the 0.07° of the CCSD(T) method. To obtain these results, it was necessary to reanalyze the structure of a few molecules, particularly, a new and more accurate structure is proposed for nitroxyl, HNO and hydrogen peroxide, H₂O₂.