Basis set effects on calculated geometries: 6-311++G** vs. aug-cc-pVDZ

The effect of basis sets on MP2 and CCSD calculated geometries has been investigated for a series of small organic molecules with two to four nonhydrogen atoms. Whereas 6-311++G** usually leads to satisfactory structures, this was not true with aug-cc-pVDZ, although it uses more basis functions than the former set. In addition, the smaller 6-311++G** invariably leads to lower calculated energies than aug-cc-pVDZ. With a given basis set, CCSD gives more satisfactory calculated geometries than MP2, but with a much greater computation time. For the compounds in this report, B3LYP/6-311++G** is quite effective in giving satisfactory calculated geometries at a relatively small computational cost.     

Structure of the boronic acid dimer and the relative stabilities of its conformers

Despite the widespread use of boronic acids in materials science and as pharmaceutical agents, many aspects of their structure and reactivity are not well understood. In this research the boronic acid dimer, [HB(OH)(2)](2), was studied by second-order M?ller-Plesset (MP2) perturbation theory and coupled cluster methodology with single and double excitations (CCSD). Pople split-valence 6-31+G*, 6-311G**, and 6-311++G** and Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the calculations. A doubly hydrogen-bonded conformer (1) of the dimer was consistently found to be lowest in energy; the structure of 1 was planar (C(2h)) at most computational levels employed but was significantly nonplanar (C(2)) at the MP2/6-311++G** and CCSD/6-311++G** levels, the result of an intrinsic problem with Pople-type sp-diffuse basis functions on heavy atoms. The dimerization energy, enthalpy, and free energy for the formation of (1) from the exo-endo conformer of the monomer were -10.8, -9.2, and +1.2 kcal/mol, respectively, at the MP2/aug-cc-pVTZ level. Several other hydrogen-bonded conformers of the dimer were local minima on the potential energy surface (PES) and ranged from 2 to 5 kcal/mol higher in energy than 1. Nine doubly OH-bridged conformers, in which the boron atoms were tetracoordinated, were also local minima on the PES, but they were all greater than 13 kcal/mol higher in energy than 1; doubly H-bridged structures proved to be transition states. MP2 and CCSD results were compared to those from the BLYP, B3LYP, OLYP, O3LYP, PBE1PBE, and TPSS functionals with the 6-311++G** and aug-cc-pVTZ basis sets; the PBE1PBE functional performed best relative to the MP2 and CCSD results. Self-consistent reaction field (SCRF) calculations predict that boronic acid dimerization is less favorable in solution than in vacuo.     

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.     

Basis set convergence of the coupled-cluster correction, δ(MP2)(CCSD(T)): best practices for benchmarking non-covalent interactions and the attendant revision of the S22, NBC10, HBC6, and HSG databases

In benchmark-quality studies of non-covalent interactions, it is common to estimate interaction energies at the complete basis set (CBS) coupled-cluster through perturbative triples [CCSD(T)] level of theory by adding to CBS second-order perturbation theory (MP2) a "coupled-cluster correction," δ(MP2)(CCSD(T)), evaluated in a modest basis set. This work illustrates that commonly used basis sets such as 6-31G*(0.25) can yield large, even wrongly signed, errors for δ(MP2)(CCSD(T)) that vary significantly by binding motif. Double-ζ basis sets show more reliable results when used with explicitly correlated methods to form a δ(MP2-F12)(CCSD(T(*))-F12) correction, yielding a mean absolute deviation of 0.11 kcal mol(-1) for the S22 test set. Examining the coupled-cluster correction for basis sets up to sextuple-ζ in quality reveals that δ(MP2)(CCSD(T)) converges monotonically only beyond a turning point at triple-ζ or quadruple-ζ quality. In consequence, CBS extrapolation of δ(MP2)(CCSD(T)) corrections before the turning point, generally CBS (aug-cc-pVDZ,aug-cc-pVTZ), are found to be unreliable and often inferior to aug-cc-pVTZ alone, especially for hydrogen-bonding systems. Using the findings of this paper, we revise some recent benchmarks for non-covalent interactions, namely the S22, NBC10, HBC6, and HSG test sets. The maximum differences in the revised benchmarks are 0.080, 0.060, 0.257, and 0.102 kcal mol(-1), respectively.     

Hydrogen peroxide clusters: the role of open book motif in cage and helical structures

Hartree-Fock (HF) calculations using 6-31G*, 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets show that hydrogen peroxide molecular clusters tend to form hydrogen-bonded cyclic and cage structures along the lines expected of a molecule which can act as a proton donor as well as an acceptor. These results are reiterated by density functional theoretic (DFT) calculations with B3LYP parametrization and also by second-order M?ller-Plesset perturbation (MP2) theory using 6-31G* and 6-311++G(d,p) basis sets. Trends in stabilization energies and geometrical parameters obtained at the HF level using 6-311++G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ basis sets are similar to those obtained from HF/6-31G* calculation. In addition, the HF calculations suggest the formation of stable helical structures for larger clusters, provided the neighbors form an open book structure.     

高级量子化学从头计算法研究N2和H2O分子间相互作用

在MP2/6-311++G(3d,3p)电子相关校正水平上,对N₂和H₂O分子间可能存在的氢键复合物进行全自由度能量梯度优化,发现了一个接近于直线的弱氢键总能量极小结构(1),进一步在高级电子相关校正的MP4SDTQ和CCSD(T)水平,用6-311++G(3d,3p)基组加上(3s3p2d1f)键函数,用MP4和CCSD(T)计算的结构1的结合能分别为-5.061kJ/mol和-4.715kJ/mol.     

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.     

HArF和HNO二聚体相互作用氢键的理论研究

The hydrogen bonding interaction of 1:1 dimer formed between HNO and HArF molecule has been completely investigated in the present study using Second-order M?ller-Plesset Perturbation (MP2) method in conjunction with 6-311+G**, 6-311++G** and 6-311++G(2d,2p) basis sets. The standard and CP-corrected calculations have been employed to determine the equilibrium structures, the vibrational frequencies and interaction energies. The interaction energies of the dimers were also calculated at G2MP2 level. Two stable structures are found as the minima. Dimer I(H···F)is a five-membered cyclic hydrogen bonded structure and is more stable than the Dimer II(H···O). The blue-shifted N-H···F hydrogen bond is confirmed with standard and CP-corrected calculations by the MP2 and DFT methods in conjunction with different basis sets. The results obtained at MP2 in conjunction with different basis sets show there is a red-shifted hydrogen bond (Ar-H···O) in the Dimer II(H···O). The topological and electronic properties, the origin of red- and blue-shifted hydrogen bonds were investigated at MP2/6-311++G(2d,2p) with CP corrected calculations. From the NBO analysis, the reasonable explanations for the red- and blue-shifted hydrogen bonds were proposed.     

A theoretical study of the H-abstraction reactions from HOI by moist air radiolytic products (H, OH, and O (3P)) and iodine atoms (2P(3/2))

The rate constants of the reactions of HOI molecules with H, OH, O ((3)P), and I ((2)P(3/2)) atoms have been estimated over the temperature range 300-2500 K using four different levels of theory. Geometry optimizations and vibrational frequency calculations are performed using MP2 methods combined with two basis sets (cc-pVTZ and 6-311G(d,p)). Single-point energy calculations are performed with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (pertubatively) electron excitations CCSD(T) using the cc-pVTZ, cc-pVQZ, 6-311+G(3df,2p), and 6-311++G(3df,3pd) basis sets. Reaction enthalpies at 0 K were calculated at the CCSD(T)/cc-pVnZ//MP2/cc-pVTZ (n = T and Q), CCSD(T)/6-311+G(3df,2p)//MP2/6-311G(d,p), and CCSD(T)/6-311++G(3df,3pd)//MP2/6-311G(d,p) levels of theory and compared to the experimental values taken from the literature. Canonical transition-state theory with an Eckart tunneling correction is used to predict the rate constants as a function of temperature. The computational procedure has been used to predict rate constants for H-abstraction elementary reactions because there are actually no literature data to which the calculated rate constants can be directly compared. The final objective is to implement kinetics of gaseous reactions in the ASTEC (accident source term evaluation code) program to improve speciation of fission products, which can be transported along the reactor coolant system (RCS) of a pressurized water reactor (PWR) in the case of a severe accident.     

Comparison of levels of electronic structure theory in direct dynamics simulations of C2H5F --> HF + C2H4 product energy partitioning

Direct dynamics simulations at the MP2/6-311++G** level of theory were performed to study C(2)H(5)F --> HF + C(2)H(4) product energy partitioning. The simulation results are compared with experiment and a previous MP2/6-31G* simulation. The current simulation with the larger basis set releases more energy to HF vibration and less to HF + C(2)H(4) relative translation as compared to the previous simulation with the 6-31G* basis set. The HF rotation and vibration energy distributions determined from the current simulation are in overall very good agreement with previous experimental studies of C(2)H(5)F dissociation by chemical activation and IRMPA. A comparison of the simulations with experiments suggests there may be important mass effects for energy partitioning in HX elimination from haloalkanes. The transition state (TS) structures and energies calculated with MP2 and the 6-31G* and 6-311++G** basis sets are compared with those calculated using CCD, CCSD, CCSD(T), and the 6-311++G** basis set.     

Dimers of boroglycine and methylamine boronic acid: a computational comparison of the relative importance of dative versus hydrogen bonding

Boronic acids are widely used in materials science, pharmacology, and the synthesis of biologically active compounds. In this Article, geometrical structures and relative energies of dimers of boroglycine, H2N-CH2-B(OH)2, and its constitutional isomer H3C-NH-B(OH)2, were computed using second-order M?ller-Plesset perturbation theory and density functional theory; Dunning-Woon correlation-consistent cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ basis sets were employed for the MP2 calculations, and the Pople 6-311++G(d,p) basis set was employed for a majority of the DFT calculations. Effects of an aqueous environment were incorporated into the results using PCM and COSMO-RS methodology. The lowest-energy conformer of the H2N-CH2-B(OH)2 dimer was a six-membered ring structure (chair conformation; Ci symmetry) with two intermolecular B:N dative-bonds; it was 14.0 kcal/mol lower in energy at the MP2/aug-cc-pVDZ computational level than a conformer with the classic eight-centered ring structure (Ci symmetry) in which the boroglycine monomers are linked by a pair of H-O...H bonds. Compared to the results of MP2 calculations with correlation-consistent basis sets, DFT calculations using the PBE1PBE and TPSS functionals with the 6-311++G(d,p) basis set were significantly better at predicting relative conformational energies of the H2N-CH2-B(OH)2 and H3C-NH-B(OH)2 dimers than corresponding calculations using the BLYP, B3LYP, OLYP, and O3LYP functionals, particularly with respect to dative-bonded structures.     

Mechanistic and kinetic study of the CH3CO + O2 reaction

Potential-energy surface of the CH3CO + O2 reaction has been calculated by ab initio quantum chemistry methods. The geometries were optimized using the second-order Moller-Plesset theory (MP2) with the 6-311G(d,p) basis set and the coupled-cluster theory with single and double excitations (CCSD) with the correlation consistent polarized valence double zeta (cc-pVDZ) basis set. The relative energies were calculated using the Gaussian-3 second-order Moller-Plesset theory with the CCSD/cc-pVDZ geometries. Multireference self-consistent-field and MP2 methods were also employed using the 6-311G(d,p) and 6-311++G(3df,2p) basis sets. Both addition/elimination and direct abstraction mechanisms have been investigated. It was revealed that acetylperoxy radical [CH3C(O)OO] is the initial adduct and the formation of OH and alpha-lactone [CH2CO2(1A')] is the only energetically accessible decomposition channel. The other channels, e.g., abstraction, HO2 + CH2CO, O + CH3CO2, CO + CH3O2, and CO2 + CH3O, are negligible. Multichannel Rice-Ramsperger-Kassel-Marcus theory and transition state theory (E-resolved) were employed to calculate the overall and individual rate coefficients and the temperature and pressure dependences. Fairly good agreement between theory and experiments has been obtained without any adjustable parameters. It was concluded that at pressures below 3 Torr, OH and CH2CO2(1A') are the major nascent products of the oxidation of acetyl radicals, although CH2CO2(1A') might either undergo unimolecular decomposition to form the final products of CH2O + CO or react with OH and Cl to generate H2O and HCl. The acetylperoxy radicals formed by collisional stabilization are the major products at the elevated pressures. In atmosphere, the yield of acetylperoxy is nearly unity and the contribution of OH is only marginal.     

Theoretical study of light-metal tetrahydroaluminates

Ab initio calculations of the structural, energetic, vibrational, and magnetic characteristics of the lowest-lying structures for isolated molecules and ions of light-metal tetrahydroaluminates (Li, Na, Be, Mg, and Al) have been performed by the perturbation theory (MP2), quadratic configuration interaction (QCISD(T)), coupled cluster (CCSD(T)), and density functional theory (B3LYP) methods using the 6-31G*, 6-31G**, 6-311+G**, and 6-311++G** basis sets. The trends in the behavior of the molecular characteristics have been analyzed in various related series of these compounds. The results are compared with the data on analogous light-metal tetrahydroborates calculated at the same levels of theory. The differences in structure and stability between analogous hydroborate and alanate complexes are examined. The economical approximation B3LYP/6-311++G**//B3LYP/6-311+G** has been shown to adequately reproduce the results obtained at the higher level of theory CCSD(T)/6-311++G**//MP2/6-31G* even though it requires considerably shorter CPU times and smaller amounts of memory.     

A Theoretical Study of the Kinetics of the Hydrogen Atom Abstraction Reactions from Cyclopropane by H,O (3P), and Cl (2P3/2) Atoms and OH Radicals

The rate constants of the H‐abstraction reactions from cyclopropane by H, O (³P), Cl (²P_3/2), and OH radicals have been calculated over the temperature range of 250?2500 K using two different levels of theory. Calculations of optimized geometrical parameters and vibrational frequencies are performed using the MP2 method combined with the cc‐pVTZ basis set and the 6–311++G(d,p) basis set. Single‐point energy calculations have been carried out with the highly correlated ab initio coupled cluster method in the space of single, double, and triple (perturbatively) electron excitations CCSD(T) using either the cc‐pVTZ, aug‐cc‐pVTZ, and aug‐cc‐pVQZ basis sets or the 6–311++G(3df,3pd) basis set. The CCSD(T) calculated potential energies have been extrapolated to the complete basis limit (CBS) limit. The Full Configuration Interaction (FCI) energies have been also estimated using the continued‐fraction approximation as proposed by Goodson (J. Chem. Phys., 2002, 116, 6948–6956). Canonical transition‐state theory combined with an Eckart tunneling correction has been used to predict the rate constants as a function of temperature using two kinetic models (direct abstraction or complex mechanism) at two levels of theory (CCSD(T)‐cf/CBS//MP2/cc‐pVTZ and CCSD(T)‐cf/6–311++G(3df,3pd)//MP2/6–311++G(d,p)). The calculated kinetic parameters are in reasonable agreement with their literature counterparts for all reactions. In the light of these trends, the use of the Pople‐style basis sets for studying the reactivity of other systems such as larger cycloalkanes or halogenated cycloalkanes is recommended because the 6–311++G(3df,3pd) basis set is less time consuming than the aug‐cc‐pVQZ basis set. Based on our calculations performed at the CCSD(T)‐cf/CBS//MP2/cc‐pVTZ level of theory, the standard enthalpy of formation at 298 K for the cyclopropyl radical has been reassessed and its value is (290.5 ± 1.6) kJ mol^?1.     

Methyl radical also reacts by the frontside mechanism: an ab initio study of some homolytic substitution reactions of methyl radical at silicon,germanium and tin

Ab initio calculations using 6-311G**, cc-pVDZ, aug-cc-pVDZ, and a (valence) double-zeta pseudopotential (DZP) basis sets, with (MP2, QCISD, CCSD(T)) and without (UHF) the inclusion of electron correlation, and density functional (B3LYO) calculations predict that homolytic substitution reactions of the methyl radical at the silicon atom in disilane can proceed via both backside and frontside attack mechanisms. At the highest level of theory (CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ), energy barriers (delta E) of 47.4 and 48.6 kJ mol-1 are calculated for the backside and frontside reactions respectively. Similar results are obtained for reactions involving germanium and tin with energy barriers (delta E) of between 46.5 and 67.3, and 41.0 and 73.3 kJ mol-1 for the backside and frontside mechanisms, respectively. These data suggest that homolytic substitution reactions of methyl radical at silicon, germanium, and tin can proceed via either homolytic substitution mechanism.     

Theoretical study of light-metal tetrahydroborates

Ab initio calculations of the structural, energetic, vibrational, and magnetic characteristics of the lowest-lying structures for isolated molecules and ions of light-metal tetrahydroborates (Li, Na, Be, Mg, and Al) have been performed by the perturbation theory (MP2), quadratic configuration interaction (QCISD(T)), coupled cluster (CCSD(T)), and density functional theory (B3LYP) methods using the 6-31G*, 6-31G**, 6-311+G**, and 6-311++G** basis sets. The trends in the behavior of the structural parameters, the energies of different decomposition pathways, barriers to internal rotation of BH₄ groups, normal mode frequencies, magnetic shielding constants, and spin density distribution (in radicals) have been analyzed in various related series of these compounds. The results obtained by ab initio methods and at the DFT level are compared. The economical approximation B3LYP/6-311++G**//B3LYP/6-311+G** adequately reproduces the results obtained at the higher level of theory CCSD(T)/6-311++G*s*//MP2/6-31G* even though it requires considerably shorter CPU times and smaller amounts of memory.     

Transition state structure and energetics of the N(2)O + X (X = Cl,Br) reactions

The structural and vibrational properties of the transition state of the N(2)O + X (X = Cl,Br) reactions have been characterized by ab initio methods using density functional theory. We have employed Becke's hybrid functional (B3LYP), and transition state optimizations were performed with 6-31G(d), 6-311G(2d,2p), 6-311+G(3d,2p), and 6-311+G(3df,2p) basis sets. For the chlorine atom reaction the coupled-cluster method (CCSD(T)) with 6-31G(d) basis set was also used. All calculations resulted in transition state structures with a planar cis arrangement of atoms for both reactions. The geometrical parameters of transition states at B3LYP are very similar, and the reaction coordinates involve mainly the breaking of the N-O bond. At CCSD(T)/6-31G(d) level a contribution of the O-Cl forming bond is also observed in the reaction coordinate. In addition, several highly accurate ab initio composite methods of Gaussian-n (G1, G2, G3), their variations (G2(MP2), G3//B3LYP), and complete basis set (CBS-Q, CBS-Q//B3LYP) series of models were applied to compute reaction energetics. All model chemistries predict exothermic reactions. The G3 and G2 methods result in the smallest deviations from experiment, 1.8 and 0 kcal mol(-1), for the enthalpies of reaction for N(2)O reaction with chlorine and bromine, respectively. The G3//B3LYP and G1 methods perform best among the composite methods in predicting energies of the transition state, with a deviation of 1.9 and 3.0 kcal mol(-1), respectively, in the activation energies for the above processes. However, the B3LYP/6-311+G(3df,2p) method gives smaller deviations of 0.4 and -1.0 kcal mol(-1), respectively. The performance of the methodologies applied in predicting transition state energies was analyzed.     

Theoretical study of the regioselectivity of the cycloaddition reaction between cyclopentadiene and methyleneketene

Three possible reaction schemes for the cycloaddition reaction between methyleneketene and cyclopentadiene were studied by DFT (density functional theory) and ab initio calculations. All of these cycloaddition reactions are exothermic, concerted but nonsynchronous processes. The computed activation energies indicate that the norbornene product yielded from a 1,2-addition of methyleneketene with cyclopentadiene (reaction (1)) is the primary product. The performance of various computational methodologies, MP2, MP4, and CCSD(T), in conjunction with a wide array of basis sets, 6-31G(d), 6-311+G(d,p), aug-cc-pVDZ, and aug-cc-pVTZ, in obtaining reliable activation and reaction energies of the reactions under investigation has been critically analyzed.