F2 dimer: Improved intermolecular potential energy surface using ab initio calculations

A computational study on the intermolecular potential energy of 44 different orientations of F₂ dimers is presented. Basis set superposition error (BSSE) corrected potential energy surface is calculated using the supermolecular approach at CCSD(T) and QCISD(T) levels of theory. The interaction energies obtained using the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets are extrapolated to the complete basis set limit using the latest extrapolation scheme. The basis set effect is checked and it is found that the extrapolated intermolecular energies provide the best compromise between the accuracy and computational cost. Among 1320 energy points of F₂–F₂ system covering more relative orientations, the most stable structure of the dimers was obtained with a well depth of ?146.62 cm^?1 that related to cross configuration, and the most unstable structure is related to linear orientation with a well depth of ?52.63 cm^?1. The calculated second virial coefficients are in good agreement with experimental data. The latest extrapolation scheme of the complete basis set limit at the CCSD(T) level of theory is used to determine the intermolecular potential energy surface of the F₂ dimer. Comparing the results obtained by the latest scheme with those by older schemes show that the new approach provides the best compromise between accuracy and computational cost.     

Computational models for proton transfer in biological systems

A computational scheme based on a “mixed basis set” approach is applied to the study of the structure and the energetics in proton transfer systems. Five hydrogen-bonded systems of the type (CH₃H_nA ‥ H ‥ BH_mCH₃)⁺, where A and B can be N, O, or S, have been investigated with various minimal and extended basis sets. Calculations with the extended basis set yield double-well potential energy curves, which the minimal basis set is unable to reproduce. Calculations with the mixed basis set, constructed from an extended basis set on the atoms engaged in the hydrogen transfer part and a minimal basis set on the rest of the molecule, give predictions of geometries, potential energy curves, and relative energies similar to the results from the extended basis set. Inclusion of polarization functions in the mixed basis set becomes essential in systems that contain third row atoms. This scheme should become useful in studies of large molecules in which different parts can be represented at different levels of computational complexity.     

AB initio calculations on intermolecular forces. The systems He…HF and He…H2O

The interaction energy between a He atom and a polar molecule (HF, H₂O) is calculated with a gaussian basis set both in the SCF approximation and with the inclusion of the intersystem correlation energy. The long range behaviour of the interaction energy is compared with results from perturbation theory.     

Rapidly calculated DFT relaxed iso-potential ϕ/ψ maps: β-cellobiose

New cellobiose ϕ_H/ψ_H maps are generated using a mixed basis set DFTr method, found to achieve a high level of confidence while reducing computer resources dramatically. Relaxed iso-potential maps are created for different conformational states of cellobiose, showing how glycosidic bond dihedral angles vary as different sets of hydroxymethyl rotamers and hydroxyl directions are examined. These maps are generated, fixing the dihedral ϕ_H and ψ_H values at ten degree intervals and energy optimizing the remaining geometry using the B3LYP/6-31+G* functional for all atoms except carbon atoms, where the functional B3LYP was used with the mixed basis set, 4-31G. Mapping results are compared between in vacuo structures using the mixed basis set, in vacuo using the full basis set, and those in which the implicit solvent method, COSMO, is included with the mixed basis set. Results show significant changes in position of energy minima with variation in hydroxyl rotamers and with application of solvent. Unique to this study is the mapping of the hydration energy at each ϕ_H/ψ_H point on the map using the energy derived at each point by applying COSMO. Using hydration gradients as a guide one observes directional solvent driven changes in the minimum energy positions. Interesting internal coordinate variances are described.     

Study of the hydrogen bond and of the proton transfer between two H2S molecules

The potential energy surface for the H₂S dimer is calculated as the sum of the SCF-MO-LCGO energy with a new, modified, basis set and the estimated dispersion energy. Proton affinities for SH^– and H₂S, and, as their difference, the energy of the proton transfer between two H₂S molecules, are also calculated. Despite the limited basis set used, the results are consistent with experimental data.This work was partly supported by the Polish Academy of Sciences within the project PAN-3.     

An improved calculation of the transition state for the F + H2 reaction

Using a large, balanced one-electron basis set, fully optimized reaction space (FORS) calculations to optimize the orbitals and to estimate the internal correlation energy, multi-reference configuration interaction calculations including all single and double excitations out of the FORS reference space to estimate a fraction of the external correlation energy, and the method of scaled external correlation (SEC), we calculate the interaction energy of F with H₂ in the vicinity of the saddle point for the reaction F + H₂ → HF + H. Our calculated barrier height, 1.6 kcal/mol, is considerably lower than values obtained in recent ab initio calculations, and the saddle point geometry is about 0.3 a₀ looser. This indicates that the part of the external correlation energy omitted from MR CISD calculations because of the incompleteness of the one-electron basis set and the truncation of the CI expansion, as estimated by the SEC method, has a significant effect on both the saddle point energy and its geometry.     

1,2,3-三氮杂苯－(水)3复合物多体相互作用

The interaction between 1,2,3-triazine and three water molecules was studied using density functional theory B3LYP method at 6-31-t＋＋G^＊＊ basis set. Various structures for 1,2,3-triazine-（water）n （n= 1, 2, 3） complex were investigated and the different lower energy structures were reported. Many-body analysis was also carded out to obtain relaxation energy and many-body interaction energy （two, three, and four-body）, and the most stable conformer has the basis set superposition error corrected interaction energy of -- 102.61 kJ/mol. The relaxation energy, two- and three-body interactions have significant contribution to the total interaction energy whereas four-body interaction was very small for 1,2,3-triazine-（water）3 complex.     

Nonadditivity of interaction in water trimers

The energy of (H₂O)₃ has been calculated for 29 geometrical configurations of the trimer using the SCF LCAO MO method and extended as well as minimal basis sets of Gaussian functions. For two configurations two intermediate basis sets have also been tested. The results show the nonadditive component of the interaction energy to be small. They also indicate that fairly reliable results for the trimer can be obtained using minimal basis sets and the counterpoise method to eliminate the basis set superposition error. The nonadditive contribution to the interaction energy is shown to be mainly due to the long-range induction interaction.     

First‐principle modelling of forsterite surface properties: Accuracy of methods and basis sets

The seven main crystal surfaces of forsterite (Mg₂SiO₄) were modeled using various Gaussian‐type basis sets, and several formulations for the exchange‐correlation functional within the density functional theory (DFT). The recently developed pob‐TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error‐corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C₆ coefficients that are more suitable than the standard ones to describe O? O interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface. © 2015 Wiley Periodicals, Inc.     

New global potential energy surface of the MgH2 system and dynamics studies of the reaction H + MgH → Mg + H2

A new global potential energy surface for the ground state of MgH₂ was constructed using the permutation invariant polynomial neural network method. About 70 000 ab initio energy points were calculated via the multi‐reference configuration interaction method method with aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets, and these points were used to construct the potential energy surface (PES). To avoid basis set superposition error, the basis set was extrapolated to the complete basis set limit using the two point energy extrapolation formula. The root mean square error of the present PES is only 8.85 meV. Initial state (v = 0, j = 0) dynamics studies were performed using the time‐dependent wave packet method with a second‐order split operator for the total angular momentum J up to a value of 50. Furthermore, the reaction probability, integral cross section, and thermal rate constant are reported and compared with available theoretical studies.     

Accurate ab intio determination of binding energies for rare-gas dimers by basis set extrapolation

To investigate the electron correlation effect on the binding energies of very weakly bound complexes at highly correlated levels, an extrapolation scheme exploiting the convergent behavior of the binding energy differences between two correlation levels with the correlation-consistent basis set aug-cc-pVXZ was explored. The scheme is based on extrapolating the binding energy differences between the lower and higher correlation levels (such as second-order Møller–Plesset perturbation theory and the single and double coupled-cluster method with perturbative triple correction level), CCSD(T), by X^–3 for relatively small basis set calculations to estimate the corresponding basis set limit, which is then added to the complete basis set(CBS) limit binding energy at the lower correlation level to derive the CBS limit binding energy at the higher level. Test results on rare-gas dimers Rg₂ (Rg is He, Ne, Ar) show that the CCSD(T) CBS limit binding energies estimated by this scheme with aug-cc-pVXZ and aug-cc-pV(X+1)Z basis sets are more accurate than the CBS limit estimated by direct extrapolation of correlation energies by X^–3 with aug-cc-pV(X+1)Z and aug-cc-pV(X+2)Z basis sets in most cases, which signifies the utility of the proposed extrapolation scheme as the level of electron correlation treatment increases. The nonnegligible discrepancy in the well depth near equilibrium between the experimental and the full connected single, double, and triple coupled-cluster method CBS limit estimate obtained by this procedure in the case of Ar₂ suggests that the previous semiempirical potential may be too attractive near equilibrium compared with the actual one.Acknowledgement The major portion of this work was carried out while the author was visiting the Quantum Theory Project (QTP) at the University of Florida. The author is thankful to Rodney Bartlett for hospitality and support during the visit. The author is also thankful to Ajith Perera for assistance in using the ACESII program package. Computational support from the QTP at the University of Florida and the Institute for Basic Science at Ajou University is gratefully acknowledged.     

Bond functions in molecular excited states: MRD CI calculations for the A3Σ+u,B3Πg and W3Δu states of N2

Using double-zeta plus polarization (DZP) basis sets systematically augmented with a variety of bond functions, the term dissociation energies are calculated for the A³Σ⁺_u, B³Π_g and W³Δ_u states of N₂. It is found that the best agreement with literature values is generally with a basis set composition of DZP augmented by a set of s, p and d orbitals at the bond midpoint. The excited state potential energy curves and spectroscopic constants for the B³Π_g state are calculated from this basis and compared with experimental values. Good agreement was obtained, considering the small basis set size, with the spectroscopic constants ω_e, ω_eχ_e, ω_ey_e, B_e and α_e and the dissociation energy D_e (e.g., D_e = 3.38 (3.681, exp.), 4.75 (4.897) and 4.77(4.873) eV for the A, B and W stages, respectively). Poorer agreement was obtained for the term energy T′₀ (7.92 versus 7.35 eV, exp., for the B state). The error in term energy arises largely from an error in the calculated ⁴S → ²D splitting (2.705 versus 2.383 eV, exp.), and shifting the potential curve for the B state by a constant amount leads to much improved agreement relative to the ground state. The counterpoise correction applied to the potential curve of the B state causes a drastic deterioration of the results and shows qualitatively incorrect behaviour, and is therefore not recommended for calculations of this type.     

Density Functional Theory Studies on Intermolecular Interactions of 4‐Amino‐3,5‐dinitropyrazole with NH3 and H2O

Density functional theory (DFT) method with 6‐311++G** basis set was applied to study intermolecular interactions of 4‐amino‐3,5‐dinitropyrazole (LLM‐116)/NH₃ and LLM‐116/H₂O supermolecules. Four optimized stable supermolecules were found on the potential energy surface. The intermolecular interaction energy was calculated with basis set superposition error (BSSE) correction and zero point energy (ZPE) correction. The greatest corrected intermolecular interaction energies of LLM‐116/NH₃ and LLM‐116/H₂O supermolecules are –42.75 and –19.09 kJ×mol^‐1 respectively, indicating that the intensity of interaction between LLM‐116 and NH₃ is stronger than that of LLM‐116/H₂O. The intermolecular interaction is an exothermic process accompanied by a decrease in the probability of supermolecules formation, and the interactions become weak as temperature increase. Natural bond orbital (NBO) analysis was performed to reveal the origin of interaction. The IR spectra were obtained and assigned by vibrational analysis. Based on vibrational analysis, the changes of thermodynamic properties from LLM‐116 to supermolecules with temperature ranging from 200.0 to 400.0 K were obtained using statistical thermodynamic method.     

Investigation on the Mechanism for C–N Coupling of 3‐Iodopyridine and Pyrazole Catalyzed by Cu(I)

The reaction mechanism for C–N coupling of 3‐iodopyridine and pyrazole catalyzed by Cu(I) was studied by the density functional theory. All of the reactants, intermediates, transition states, and products were optimized with the B3LYP method at 6–31+G(d) basis set. The single‐point energy and zero‐point energy correction were calculated for the optimized configuration of each compound with the sane method at 6–311++G(d,p) basis set. Transition states have been confirmed by the corresponding vibration analysis and intrinsic reactions coordinate. In addition, nature bond orbital and atoms in molecules (AIM) theories have been used to analyze orbital interactions and bond natures. The results showed that the activation energy of the rate‐determining step in the absence of catalysts was 250.63 kJ·mol^?1, which were 74.01 and 131.68 kJ·mol^?1 via Cu₂O and CuI catalyzed, respectively. Results indicated that catalyst Cu₂O promotes reaction effectively. All calculations were consistent with experiments.     

Calculation of the interaction energy in a localized representation for a trimer (Ne3) system

We studied the transferability of the localized orbitals (LOs) of interacting Ne atoms using several basis sets. Both at SCF and at MP2 and MP3 levels, the contributions of the LOs have been calculated and discussed for the Ne₂ and Ne₃ systems. It was shown that for the LOs the transferability is satisfied to a good extent and due to the transferability the interaction energy at the correlated level can be calculated by using only the LOs of the supermolecule. The basis set superposition error (BSSE) is simply extracted from the intramolecular parts of the correlation energy. The two- and three-body interaction energies have been investigated for the studied systems. © John Wiley & Sons, Inc.     

Hydrogen bonding structure and many‐body interactions in 1,3,5‐triazine–(water)3 and 1,2,4‐triazine–(water)3 complexes

The hydrogen bonding structure and many‐body interactions between 1,3,5‐triazine (1,2,4‐triazine) and three water molecules are studied using the density functional theory (DFT) B3LYP method and 6‐31++G** basis set. Various structures of 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃ complexes are investigated, and the seven and eight stable structures are reported for 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃, respectively. Many‐body analysis is also carried out to obtain relaxation energy and many‐body interaction energy (two‐, three‐, and four‐body), and the most stable conformer has the basis set superposition error corrected interaction energy of ?92.09 and ?99.53 kJ/mol. The two‐ and three‐body interactions have significant contribution to the total interaction energy, whereas the relaxation energy, four‐body interactions are very small for 1,3,5‐triazine–(water)₃ and 1,2,4‐triazine–(water)₃ complexes. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The mechanism of carbonyl reduction by LiBH4: An ab initio investigation

The minimum energy path and the geometry of the transition state for the first stage of the reduction by LiBH₄ of R₂CO (RH, CH₃) to alcohol have been determined by ab initio SCF calculations using a small basis set and subsequently confirmed by further calculations using a larger basis set and CI methods. Attention has been focused on the changes of electron distribution during the reaction, the nature of the bonding, and the effect of chemical substituents. The results lend support to one of the proposed reaction mechanisms. Some supplementary data concerning the role of the solvent are also discussed.     

Study on the behavior of energy convergence in ab initio crystal orbital calculations

Summary This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N ₀). The energy convergence behavior with respect to N ₀ depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C₂H₄ unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N ₀ a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N ₀ = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N ₀ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.