Comparison of correlation effects on the inversion barriers in CF3 and NF3+ from perturbation theory and configuration interaction

The barriers to inversion in NF₃⁺ and CF₃ have been studied using fourth-order unrestricted Møller-Plesset perturbation theory and configuration interaction with all single and double excitations relative to UHF wavefunctions. The barriers calculated by the two methods are in agreement to within 1 kcal/mol. Correlation effects are found to increase the barrier in NF₃⁺ while in the isoelectronic CF₃ species correlation decreases the barrier.     

Ab Initio Study on the Potential Energy Surfaces of B4 Cluster

The singlet and triplet potential energy surfaces (PES) for the isomerization and dissociation reactions of B₄ isomers have been investigated using ab initio methods. Ten B4 isomers have been identified and of these 10 species, 4 have not been reported previously. The singlet rhombic structure ¹1 is found to be the most stable on the B₄ surface, in agreement with the results of previous reports. Several isomerization and dissociation pathways have been found. On the singlet PES, the linear ¹3b can rearrange to rhombus ¹1 directly, while ¹3c rearranges to ¹1 through two‐step reactions involving a cyclic intermediate. On the triplet PES, the capped triangle structure ³2 undergoes ring opening to the linear isomer ³3b with a barrier of 34.8 kcal/mol and 44.9 kcal/mol, and the latter undergoes ring closure to the square structure ³1 with a barrier of 30.4 kcal/mol and 33.0 kcal/mol at the MP4/6–311+G(3df)//MP2/6–311G(d) and CCSD/aug‐cc‐pVTZ//MP2/6–311G(d) levels of theory, respectively. The direct decomposition of singlet B₄ yielding to B₃+B is shown to have a large endothermicity of 87.3 kcal/mol (CCSD), and that producing 2B₂ to have activation energy of 133.4 kcal/mol (CCSD).     

A theoretical study of the inversion barrier in NF3+

The barrier to inversion in NF⁺₃ has been studied using ab initio molecular-orbital theory including geometry optimization at the correlation energy level. The barrier is predicted to be 12.6 kcal mol⁻¹. Comparison is made to previous theoretical and experimental results.     

Structures of gas-phase C2F 7 + ions

In an ion cyclotron resonance spectrometer, less than 96% of the C₇F ₇ ⁺ cation formed on electron ionization of perfluorotoluene reacts with hexamethyldisilazane. In contrast, the C₇F ₇ ⁺ from perfluoronorbornadiene or perfluorobicyclo[3.2.O]hepta-2,6-diene is nonreactive with hexamethyldisilazane. Collision-induced dissociation results support this dichotomy, although the evidence is not as clear-cut. The reactive ion is assigned the benzyl structure and the nonreactive ion the tropyl structure, on the basis of analogy with the protio cases. By AM1 calculations, the perfluorobenzyl ion is 25 kcal/mol more stable than the perfluorotropyl ion, the opposite of the situation for the protio analogs (? 12 kcal/mol). Ab initio calculations at the 3–21G level agree with the semiempirical energy difference to within 0.4 kcal/mol; at the more appropriate 6–31G*/MP2 level, the perfluorobenzyl cation is 9.7 kcal/mol more stable than the perfluorotropyl cation.     

Xenon-nitrogen chemistry: gas-phase generation and theoretical investigation of the xenon-difluoronitrenium ion F2N-Xe+

The xenon–difluoronitrenium ion F₂N? Xe⁺, a novel xenon–nitrogen species, was obtained in the gas phase by the nucleophilic displacement of HF from protonated NF₃ by Xe. According to Møller–Plesset (MP2) and CCSD(T) theoretical calculations, the enthalpy and Gibbs energy changes (ΔH and ΔG) of this process are predicted to be ?3 kcal mol^?1. The conceivable alternative formation of the inserted isomers FN? XeF⁺ is instead endothermic by approximately 40–60 kcal mol^?1 and is not attainable under the employed ion‐trap mass spectrometric conditions. F₂N? Xe⁺ is theoretically characterized as a weak electrostatic complex between NF₂⁺ and Xe, with a Xe? N bond length of 2.4–2.5 Å, and a dissociation enthalpy and free energy into its constituting fragments of 15 and 8 kcal mol^?1, respectively. F₂N? Xe⁺ is more fragile than the xenon–nitrenium ions (FO₂S)₂NXe⁺, F₅SN(H)Xe⁺, and F₅TeN(H)Xe⁺ observed in the condensed phase, but it is still stable enough to be observed in the gas phase. Other otherwise elusive xenon–nitrogen species could be obtained under these experimental conditions.     

Calculation of the inversion barriers of CF3 and NF3+

SCF and CI calculations of the inversion barriers in NF₃⁺ and CF₃ are reported. Our best calculations predict barrier heights of 17.1 and 39.1 kcal mol⁻¹ for NF₃⁺ and CF₃, respectively. The value for NF₃⁺ is in good agreement with experiment. Inclusion of electron correlation increases the barrier height for both species, in disagreement with previous calculations of Dixon (J. Chem. Phys. 83 (1985) 6055).     

Ab initio study of the reaction mechanism of water dissociation into the ionic species OH− and H3O+

A reaction mechanism of water dissociation is proposed where solvent effects are accounted for via a minimum stable model that considers the interaction of five water molecules. It is based on the fully self-consistent field (SCF) optimized structures of the reactant, product, and transition state, the calculations being at the Hartree–Fock and configuration interaction level [Møller–Plesset second-order perturbation (MP2) and coupled-cluster single and double excitations (CCSD)]. They were performed with four different basis sets that included polarized and diffuse orbitals. The dissociative mechanism leads to the ionic species OH⁻+H₃O⁺ as stable products and upon analysis of the energy hypersurface, a transition state is found which yields an activation barrier of 21.2 kcal/mol. This value is in good agreement with the experimentally determined enthalpy for the reaction. The contribution of the aggregation energy is emphasized. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 253–259, 1998     

Theoretical Study of Sticking Processes on Molecular Models of Silica Surfaces

The adsorption of small charged and neutral molecules on silica supports was modelled using perturbative post-Hartree–Fock quantum chemical methods (MP2 and MP4). The simplest spherosiloxane compound (H₄Si₄O₆) was used to mimic the surface while several molecules (namely CH₄, NH ₄ ⁺ , NH₃, OH ₃ ⁺ H ₃ ⁺ ) were considered as adsorbed species. Direct sticking of the molecules on one of the (Si–O)₃ ring leads to very different binding energies for cations (more than 11 kcal/mol) and neutral molecules (a few kcal/mol). These results indicate a dominant strong ion–multipole interaction for the first ones and a weak dispersion-type interaction for the latter. If the spherosiloxane cluster is screened by a mantle of accreted dust as it is the case in interstellar environment, the value of the binding energies, computed using the continuum dielectric theory, are predicted to be significantly reduced.     

Gas‐phase reactions of XH3+ (X = C,Si, Ge) with NF3: a comparative investigation on the detailed mechanistic aspects

The gas‐phase reaction of CH₃⁺ with NF₃ was investigated by ion trap mass spectrometry (ITMS). The observed products include NF₂⁺ and CH₂F⁺. Under the same experimental conditions, SiH₃⁺ reacts with NF₃ and forms up to six ionic products, namely (in order of decreasing efficiency) NF₂⁺, SiH₂F⁺, SiHF₂⁺, SiF⁺, SiHF⁺, and NHF⁺. The GeH₃⁺ cation is instead totally unreactive toward NF₃. The different reactivity of XH₃⁺ (X = C, Si, Ge) toward NF₃ has been rationalized by ab initio calculations performed at the MP2 and coupled cluster level of theory. In the reaction of both CH₃⁺ and SiH₃⁺, the kinetically relevant intermediate is the fluorine‐coordinated isomer H₃X‐F‐NF₂⁺ (X = C, Si). This species forms from the exoergic attack of XH₃⁺ to one of the F atoms of NF₃ and undergoes dissociation and isomerization processes which eventually result in the experimentally observed products. The nitrogen‐coordinated isomers H₃X‐NF₃⁺ (X = C, Si) were located as minimum‐energy structures but do not play an active role in the reaction mechanism. The inertness of GeH₃⁺ toward NF₃ is also explained by the endoergic character of the dissociation processes involving the H₃Ge‐F‐NF₂⁺ isomer. Copyright © 2009 John Wiley & Sons, Ltd.     

Ab initio calculations on the barrier height for the hydrogen addition to ethylene and formaldehyde. The importance of spin projection

Heats of reaction and barrier heights have been computed for H + CH₂CH₂ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH using unrestricted Hartree-Fock and Møller–Plesset perturbation theory up to fourth order (with and without spin annihilation), using single-reference configuration interaction, and using multiconfiguration self-consistent field methods with 3-21G, 6-31G(d), 6-31G(d,p), and 6-311G(d,p) basis sets. The barrier height in all three reactions appears to be relatively insensitive to the basis sets, but the heats of reaction are affected by p-type polarization functions on hydrogen. Computation of the harmonic vibrational frequencies and infrared intensities with two sets of polarization functions on heavy atoms [6-31G(2d)] improves the agreement with experiment. The experimental barrier height for H + C₂H₄ (2.04 ± 0.08 kcal/mol) is overestimated by 7?9 kcal/mol at the MP2, MP3, and MP4 levels. MCSCF and CISD calculations lower the barrier height by approximately 4 kcal/mol relative to the MP4 calculations but are still almost 4 kcal/mol too high compared to experiment. Annihilation of the largest spin contaminant lowers the MP4SDTQ computed barrier height by 8?9 kcal/mol. For the hydrogen addition to formaldehyde, the same trends are observed. The overestimation of the barrier height with Møller-Plesset perdicted barrier heights for H + C₂H₄ → C₂H₅, H + CH₂O → CH₃O, and H + CH₂O → CH₂OH at the MP4SDTQ /6-31G(d) after spin annihilation are respectively 1.8, 4.6, and 10.5 kcal/mol.     

Quantum-Chemical Study of Alkyl Carbenium Ions in 100% Sulfuric Acid

A quantum-chemical study of neutral and protonated monoalkyl sulfates RHSO₄and [RH₂SO₄]⁺(where R = CH₃, C₂H₅, iso-C₃H₇, and tert-C₄H₉) is carried out. Calculations are performed using the Hartree–Fock method in the 6-31G** and 6-31++G** basis sets taking into account electron correlation according to the Müller–Plesset perturbation theory MP2/6-31+G*//6-31+G*. Protonated tert-butyl sulfate was also calculated by the DFT B3LYP/6-31++G** method. It was found that monoalkyl sulfates are covalent compounds, and the complete abstraction of alkyl carbenium ions from them has substantial energy cost: 196.4, 161.7, 150.8 and 136.0 kcal/mol, respectively. Protonated methyl and ethyl sulfates are also covalent compounds according to the calculation. They have lower but still high energies of heterolytic dissociation (65.0 and 33.5 kcal/mol, respectively). The energy of R⁺abstraction from protonated isopropyl sulfate is much lower: 23.6 kcal/mol. The main covalent state and the ion–molecular pair, which is a carbenium ion [C(CH₃)₂H]⁺solvated by the H₂SO₄molecule, have about the same energy. The ground state of protonated tert-butyl sulfate corresponds to the ion–molecular complex [C(CH₃)⁺ ₃H₂SO₄] with still lower energy of carbenium ion [C(CH₃)₃]⁺abstraction, which is equal to 10.0 kcal/mol. Calculation according to the DFT B3LYP/6-31++G** method shows the absence of a minimum for the protonated tert-butyl sulfate with a covalent structure on the potential energy surface.     

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     

Dispersion corrected double high-hybrid and gradient-corrected density functional theory study of light cation–dihydrogen (M+–H2, where M = Li, Na, B and Al) van der Waals complexes

Structure, frequencies, H–H stretching frequency shifts, interaction energy, depth of the potential well and dissociation energy of the light cation–dihydrogen (M⁺–H₂, where M = Li, Na, B, and Al) van der Waals complexes have been studied in detail using dispersion corrected double-hybrid and gradient-corrected density functional methods in conjunction with correlation consistent valence triple-ζ basis set. Equilibrium bond distance and dissociation energy agree very well with the experimental and theoretical values wherever available. The dissociation energies of Li⁺–H₂, B⁺–H₂, Na⁺–H₂, and Al⁺–H₂ van der Waals complexes calculated from the potential energy curves at mPW2PLYP-D/cc-pVTZ level are 4.83, 3.68, 2.42, and 1.25 kcal/mol, respectively, at a distances of 1.95, 2.25, 2.40, and 2.95 Å. Among all these complexes, Al⁺–H₂ complex is comparatively less stable, as their dissociation energy as well as depth of the potential well are smaller compared to others complexes. The symmetry-adapted perturbation theory (SAPT) has been applied to quantify the nature of interactions. The SAPT results show that the contribution of dispersion and induction are significant, although electrostatic dominates.     

Energetics of proton transfer between carbon atoms (H3CH ? CH3)−

Ab initio calculations were carried out to study the potential energy surface of (H₃C? H? CH₃)^?. The 6–31G* basis set is supplemented by a set of diffuse p functions on both C and H (with a range of exponents for the latter). The binding energy of CH₄ and CH₃^? to form the (H₃CH? CH₃)^? complex is about 2 kcal/mol, much smaller than for comparable ionic H-bonded systems involving O or N atoms. Nearly half of this interaction energy is due to correlation effects, computed at second and third orders of Møller-Plesset perturbation theory. Correlation is also responsible for substantial reductions in the energy barrier to proton transfer within the complex. This barrier is computed to be 13?15 kcal/mol at the MP3 level, depending upon the exponent used for the H p functions.     

Gas‐phase reactions of SiHn+ (n = 1,2) with NF3: A computational investigation on the detailed mechanistic aspects

The mechanism of the gas‐phase reactions of SiH_n⁺ (n = 1,2) with NF₃ were investigated by ab initio calculations at the MP2 and CAS‐MCSCF level of theory. In the reaction of SiH⁺, the kinetically relevant intermediates are the two isomeric forms of fluorine‐coordinated intermediate HSi‐F‐NF₂⁺. These species arise from the exoergic attack of SiH⁺ to one of the F atoms of NF₃ and undergo two competitive processes, namely an isomerization and subsequent dissociation into SiF⁺ + HNF₂, and a singlet‐triplet crossing so to form the spin‐forbidden products HSiF⁺ + NF₂. The reaction of SiH₂⁺ with NF₃ involves instead the concomitant formation of the nitrogen‐coordinated complex H₂Si‐NF₃⁺ and of the fluorine‐coordinated complex H₂Si‐F‐NF₂⁺. The latter isomer directly dissociates into NF₂⁺ + H₂SiF, whereas the former species preferably undergoes the passage through a conical intersection point so to form a H₂SiF‐NF₂⁺ isomer, which eventually dissociates into H₂SiF⁺ and NF₂. © 2012 Wiley Periodicals, Inc.     

Ab initio study of hydrogen bonding in the phenol–water system

Three hydrogen-bonded minima on the phenol-water, C₆H₅OH—H₂O, potential energy surface were located with 3–21G and 6–31G** basis sets at both Hartree–Fock and MP2 levels of theory. MP2 binding energies were computed using large “correlation consistent” basis sets that included extra diffuse functions on all atoms. An estimate of the effect of expanding the basis set to the triple-zeta level (multiple f functions on carbon and oxygen and multiple d functions on hydrogen) was derived from calculations on a related prototype system. The best estimates of the electronic binding energies for the three minima are –7.8, –5.0, and –2.0 kcal/mol. The consequences of uncertainties in the geometries and limitations in the level of correlation recovery are analyzed. It is suggested that our best estimates will likely underestimate the complete basis set, full CI values by 0.1–0.3 kcal/mol. Vibrational normal modes were determined for all three minima, including an MP2/6–31G** analysis for the most strongly bound complex. Computational strategies for larger phenol–water complexes are discussed. © John Wiley & Sons, Inc.     

Electron correlation effects in ionic hydrogen clusters

We employ density functional, post‐Hartree–Fock, and quantum Monte Carlo methods to study the electronic structure, geometries, and behavior of positively charged H_m⁺ clusters with m=3,5,…,17. Their structure consists of a tightly bound H₃⁺ core ion surrounded by successive solvation shells of H₂ molecules. For the largest clusters, we propose new geometries. We find that correlated methods yield the stepwise decrease of enthalpies for dissociation of H₂ from the clusters observed in experiments. Our best results are obtained by the diffusion Monte Carlo method, and by including finite temperature entropic effects, we are able to reproduce the experimental dissociation enthalpies with an unprecedented accuracy of less than 0.5 kcal/mol. These benchmark results contrast with erroneous predictions discovered in the density functional approaches. Finally, our analysis of the cluster energy surfaces indicates that under quantum and thermal fluctuations, the outer solvation shells will exhibit pronounced fluctional behavior. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 83: 86–95, 2001     

Theoretical study of thermal decomposition of azomethane

Summary.  Thermal one- and two-bond dissociation processes of cis- and trans-azomethane were studied by ab initio computation with DZP and TZ2P basis sets, using the d(N–C) bond lengths as the reaction coordinates. The geometries were optimized at the MP2 level, and the dissociation energies obtained exploiting a single-point, fourth-order M?ller–Plesset calculations [MP4SDTQ/TZ2P]. At this level of theory including zero-point energies, the trans-isomer is by 9.3 kcal/mol more stable than the cis-isomer. The results show that the energetically more favourable one-bond cleavage proceeds without transition state with the predicted bond dissociation energy D ₀ of 47.8 kcal/mol for trans-azomethane and 38.5 kcal/mol for cis-azomethane. With calculated barrier heights the unimolecular dissociation rate constants have been determined by means of the RRKM theory. The second-order saddle points localized for synchronous decomposition pathways lie 13 (trans)-23(cis) kcal/mol above the one-bond dissociation energies [MP2/DZP]. Received May 28, 1996/Final version received November 1, 1996 / Accepted November 1, 1996     

Protonation enthalpies in fluorosulfonic acid using ab initio self-consistent reaction field theory

Electrostatic solvation free energies were computed for several small neutral bases and their conjugate acids using a continuum solvation model called the self-consistent isodensity polarizable continuum model (SCIPCM). The solvation energies were computed at the restricted Hartree–Fock (RHF) and second-order Møller–Plesset (MP2) levels of theory, as well as with the Becke3–Lee–Yang–Parr (B3LYP) density functional theory, using the standard 6–31G** Gaussian basis set. The RHF solvation energies are similar to those computed at the correlated MP2 and B3LYP theoretical levels. A model for computing protonation enthalpies for neutral bases in fluorosulfonic acid solvent leads to the equation ΔH(B)=−PA(B)+ΔE_t(BH⁺)−ΔE_t(B)+β, where PA(B) is the gas phase proton affinity for base B, ΔE_t(BH⁺) is the SCIPCM solvation energy for the conjugate acid, and ΔE_t(B) is the solvation energy for the base. A fit to experimental values of ΔH(B) for 10 neutral bases (H₂O, MeOH, Me₂O, H₂S, MeSH, Me₂S, NH₃, MeNH₂, Me₂NH, and PH₃) gives β=238.4±2.9 kcal/mol when ΔΔE_t is computed using the 0.0004 e⋅bohr⁻³ isodensity surface for defining the solute cavity at the RHF/6–31G** level. The model predicts that for carbon monoxide ΔH(CO)=10 kcal/mol. Thus, protonation of CO is endothermic, and the conjugate acid HCO⁺ (formyl cation) behaves as a strong acid in fluorosulfonic acid. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 250–257, 1998     

Ab initio calculation of the electronic structure and the barrier to pyramidal inversion for H3S+

The electronic structure of H₃S⁺ is examined by ab initio MO calculations (STO 3G) and is compared with those of other XH₃ type molecules. The barrier to pyramidal inversion and the proton affinity of H₂S are calculated to be 34.8 and 225.05 kcal/mol respectively. Computations are made with respect to a model A₃S⁺ which is employed to discuss the barrier to pyramidal inversion of H₃S⁺, where A corresponds to an electromagnetive substituent or an electron donating one.