Can quasiclassical trajectory calculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of the H + H2 reaction?

Rate coefficients for the mass extreme isotopologues of the H + H(2) reaction, namely, Mu + H(2), where Mu is muonium, and Heμ + H(2), where Heμ is a He atom in which one of the electrons has been replaced by a negative muon, have been calculated in the 200-1000 K temperature range by means of accurate quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations and compared with the experimental and theoretical results recently reported by Fleming et al. [Science 331, 448 (2011)]. The QCT calculations can reproduce the experimental and QM rate coefficients and kinetic isotope effect (KIE), k(Mu)(T)/k(Heμ)(T), if the Gaussian binning procedure (QCT-GB)--weighting the trajectories according to their proximity to the right quantal vibrational action--is applied. The analysis of the results shows that the large zero point energy of the MuH product is the key factor for the large KIE observed.     

Kinetics of the hydrogen abstraction CHO + Alkane → HCHO + Alkyl reaction class: an application of the reaction class transition state theory

The kinetics of the hydrogen abstraction at alkanes by formyl radicals is investigated using the reaction class transition state theory (RC-TST) approach combined with the linear energy relationship (LER) or the barrier height grouping (BHG). The rate constants of a reaction in this class can be estimated through those of the reference reaction, CHO + C₂H₆, which are obtained from rate constants of the reaction that involves the smallest species, namely CHO + CH₄, using the explicit RC-TST scaling. The thermal rate constants of this smallest reaction are evaluated at the canonical variational transition state theory (CVT) with the corrections from the small-curvature tunneling (SCT) and hindered rotation (HR) treatments. Our analyses indicate that less than 40% systematic errors, on the average, exist in the predicted rate constants using both the LER approach, where only reaction energy is needed, and the BHG approach, where no additional information is needed; while comparing to explicit rate calculations the differences are less than 60%. Contribution to Mark S. Gordon 65th Birthday Festschrift Issue.     

Kinetics and dynamics of the NH3 + H → NH2 + H2 reaction using transition state methods, quasi-classical trajectories, and quantum-mechanical scattering

On a recent analytical potential energy surface developed by two of the authors, an exhaustive kinetics study, using variational transition state theory with multidimensional tunneling effect, and dynamics study, using both quasi-classical trajectory and full-dimensional quantum scattering methods, was carried out to understand the reactivity of the NH(3) + H → NH(2) + H(2) gas-phase reaction. Initial state-selected time-dependent wave packet calculations using a full-dimensional model were performed, where the total reaction probabilities were calculated for the initial ground vibrational state and for four excited vibrational states of ammonia. Thermal rate constants were calculated for the temperature range 200-2000 K using the three methods and compared with available experimental data. We found that (a) the total reaction probabilities are very small, (b) the symmetric and asymmetric N-H stretch excitations enhance the reactivity, (c) the quantum-mechanical calculated thermal rate constants are about one order of magnitude smaller than the transition state theory results, which reproduce the experimental evidence, and (d) quasi-classical trajectory calculations, which were performed with the main goal of analyzing the influence of the zero-point energy problem on the final dynamics results, reproduce the quantum scattering calculations on the same surface.     

Quantum instanton calculation of rate constants for the C2H6 + H → C2H5 + H2 reaction: anharmonicity and kinetic isotope effects

Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C(2)H(6) significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.     

Direct dynamics study on the reaction of N2H4 with F atom: a hydrogen abstraction reaction?

We present a systematic direct ab initio dynamics investigation of the reaction between N2H4 and F atom, which is predicted to have three possible reaction channels. The structures and frequencies at the stationary points and the points along the minimum energy paths (MEPs) of all reaction channels were calculated at the UB3LYP/6-31+G(d,p) level of theory. Energetic information of stationary points and the points along the MEPs was further refined by means of the CCSD(T)/aug-cc-pVTZ method. The calculated results revealed that the first two primary channels (N2H4+F-->N2H3+HF) are equivalent and occur synchronously via the formation of a pre-reaction complex with Cs symmetry rather than via the direct H abstraction. The pre-reaction complex then evolves into a hydrogen-bonding intermediate through a transition state with nearly no barrier and a high exothermicity, which finally makes the intermediate further decompose into N2H3 and HF. Another reaction channel of minor role (N2H4+F-->NH2F+NH2) was also found during the calculations, which has the same Cs pre-reaction complex but forms NH2F and NH2 via another transition state with high-energy barrier and low exothermicity. The rate constants of these channels were calculated using the improved canonical variational transition state theory with the small-curvature tunneling correction (ICVT/SCT) method. The three-parameter ICVT/SCT rate constant expressions of k(ICVT/SCT) at the CCSD(T)/aug-cc-pVTZ//UB3LYP/6-31+G(d,p) level of theory within 220-3000 K were fitted as (7.64x10(-9))T (-0.87) exp(1180/T) cm3 mole-1 s-1 for N2H4+F-->N2H3+HF and 1.45x10(-12)(T/298)(2.17) exp(-1710/T) cm3 mole-1 s-1 for N2H4+F-->NH2F+NH2.     

Ab initio study on the dynamical properties of the hydrogen abstraction reaction NH2 + OH → NH + H2O

 The geometry of the transition state of the title reaction was optimized at the unrestricted Hartree–Fock, the spin-unrestricted second-order M?ller–Plesset, and the spin-unrestricted quadratic configuration interaction with all single and double substitutions levels of theory. The changes in the geometry, the bound vibrational modes, and the potential energy along the minimum energy path are discussed. Variational transition-state theory rate constants calculated with the tunneling and curvature effect correction agree very well with the experimental values. Received: 23 April 1999 / Accepted: 9 June 1999 / Published online: 15 December 1999     

MRD CI calculations of excited states of the SiH3 radical,including potential curves for the inversion mode and the dissociation SiH3 → SiH2 + H

Using the MRD CI method and large basis sets the vertical spectrum of silyl radical (SiH₃) has been calculated. The lowest excited state is the 4s Rydberg state, 41000 cm⁻¹ (5.2 eV) above the ground state. Only one excited valence state (2²E) was encountered, all other states are of Rydberg type. From potential curves for the inversion mode (symmetric bending motion) it was inferred that all Rydberg states are planar, whereas the valence excited state is highly pyramidalized. The investigation of the dissociation reaction SiH₃ → SiH₂ + H leads to the conclusion that the first excited state is dissociative.     

Kinetics and dynamics study of the H + CCl4?��?HCl(v��, j��)?+?CCl3 reaction

Based on a previous potential energy surface describing the H?+?CCl₄ reaction, a new analytical surface named PES-2010 was developed modifying both the functional form to give it more flexibility, and the calibration process in which exclusively theoretical information was used. Thus, the surface is completely symmetric with respect to the permutation of the four methane chlorine atoms, and no experimental information is used in the process. For the kinetics, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 300?C2,500?K. The theoretical results reproduce the experimental variation with temperature. The influence of the tunneling factor is small, since the abstraction reaction involves the motion of a heavy particle (a chlorine atom) that cannot easily tunnel through the reaction barrier. The coupling between the reaction coordinate and the vibrational modes shows qualitatively that the HCl stretching mode in the products appears vibrationally excited. The dynamics study was performed using quasi-classical trajectory calculations, including corrections to avoid the zero-point energy problem. First, we found that the HCl(????, j??) product mostly appears with small rotational energy and vibrational population inversion. Second, the state-specific scattering distributions show backward scattering, which becomes more noticeable as the HCl(????) vibrational state increases. Unfortunately, no experimental dynamics data are available for the title reaction, but the comparison with the kinematically similar and well-studied H?+?Cl₂ reaction shows good agreement, indicative of similar mechanisms. These kinetics and dynamics results seem to indicate that the potential energy surface is adequate to describe this reaction, and the reasonable agreement with experiment lends further confidence to this new surface.     

Infrared spectra of Rh atom reaction products with C2H2: the HRhCCH, RhCCH, RhCCH2, and Rh-η2-C2H2 molecules

Laser-ablated Rh atoms react with C(2)H(2) upon co-condensation in excess argon and neon to form the insertion product HRhCCH, the alkyne RhCCH, the vinylidene RhCCH(2), and the metallacycle complex Rh-η(2)-(C(2)H(2)). These species are identified through (13)C(2)H(2), C(2)D(2), and mixed C(2)HD isotopic substitutions and density functional theory isotopic frequency calculations. The HRhCCH molecule is characterized by the CH stretching mode at 3306.2 cm(-1) (Ar) and 3310.9 cm(-1) (Ne), the Rh-H stretching mode at 2090.8 cm(-1) (Ar) and 2111.0 cm(-1) (Ne), and two CCH deformation modes at 584.3 and 573.3 cm(-1) (Ar) and 587.1 and 580.3 cm(-1) (Ne). The absorptions for the vinylidene RhCCH(2) complex are observed at 3150.9 (Ar), 3147.2 (Ne) (CH stretching), 1690.1 (Ar), 1694.3 (Ne) (CC stretching), and 804.9 (Ar), 810.5 cm(-1) (Ne) (CCH deformation). The metallacycle Rh-η(2)-(C(2)H(2)) complex is also identified through CC stretching and CCH deformation modes. The insertion reaction of ground Rh atom to the C-H bond is spontaneous on the basis of the growth of HRhCCH absorptions upon annealing in both solid neon and argon. Here, we show that atomic Rh can convert acetylene to the simple Rh vinylidene complex, analogous to that found for ligand-supported Rh complexes.     

The gas-phase and solution mechanism of the isotope exchange reaction OH- + D2 = OD- + HD: Beam study of the solvated-ion reaction OH-. H2O + D2 in the collision energy range 0–2 eV

In a tandem mass spectrometer we have measured the excitation functions (reaction cross section as a function of collision energy) for the following solvated-ion reactant pairs: OH^-.(H₂O) + H₂; OD^-.(D₂O) + D₂; and OH^-.(H₂O) + D₂—in the collision energy range 0–2 eV. Product channels include H₃O^--type production, collision-induced dissociation of reactants and products (OH^- and H^- types) and isotopic mixing. These solvated-ion reactions are used to correlate the reactivity of the isotope exchange reaction OH^- + D₂→OD^- + HD occuring in the gas phase and solution, identifying a proton-transfer mechanism occuring within an H₃O^- intermediate.     

The reaction Ne+H 2 + (v=0, 1, 2, 3, 4)→NeH++H: 3D potential energy surface and quasiclassical trajectory calculations

A three-dimensional potential energy surface for the endoergic reaction Ne+H ₂ ⁺ →NeH⁺+H in the² A′ ground state of the system NeH ₂ ⁺ has been calculated by quantum chemical ab initio methods (CEPA approximation). The calculated points on this surface were fitted to an analytic ansatz in terms of an extended LEPS functional form augmented by a correction function. The latter was expanded in polynomials in inverse powers of the internuclear distances. This analytic form was used for quasiclassical trajectory calculations of reactive cross sections. In agreement with experimental investigations a strong vibrational enhancement is observed, i.e. the reaction is markedly favored if the necessary reaction energy is supplied as vibrational energy of H ₂ ⁺ rather than as relative translational energy. Other properties of the reaction dynamics such as the backward to forward scattering ratio, the lifetime of the collision complex NeH ₂ ⁺ , and final rotational and vibrational state distributions are also discussed on the basis of the quasiclassical trajectory calculations.     

Time-dependent wave packet quantum and quasi-classical trajectory study of He + H₂⁺, D₂⁺ → HeH⁺ + H, HeD⁺ + D reaction on an accurate FCI potential energy surface

The quantum scattering dynamics and quasi-classical trajectory (QCT) calculations have been carried out for the title reaction on an accurate potential energy surface (PES) computed using the full configuration interaction (FCI). On the basis of the PES, the integral cross-sections of He + H?? (v = 0-3, j = 1) → HeH? + H reaction have been calculated, and the results are generally agreed with the experimental cross-sections obtained by Tang et al. [J. Chem. Phys. 2005, 122, 164301] after taking into account the experimental uncertainties, which proves the reliability of implementing dynamics calculations on the FCI PES. The reaction probability of He + D?? (v = 0-2, j = 0) → HeD? + D reactions for total angular momentum J = 0 and the integral cross-section (ICS) have been calculated. The significant quantum effect has been explored by the comparison between the QCT reaction probabilities (or ICS) and the quantum mechanical (QM) reaction probabilities (or ICS), which may be attributed to the deep well in the PES of this light atoms system. Furthermore, the role of Coriolis coupling (CC) effects has also been found not important by the comparison between the CC calculation and the centrifugal sudden (CS) approximation calculation, except that the CC total cross-sections for the v = 1 and 2 states show the collision energy-dependent behaviors in the low-energy area, which are different from those based on the CS calculation.     

On the fine-structure dependence of the Cs(7p, 2P12,320)+H2→ CsH+H reaction cross section

The experimentally observed effect of the Cs¹ fine-structure level on the title reaction is reproduced by a rough (collinear, one dimensional) dynamical treatment using accurate long-distance entrance channel potentials, as obtained from an effective Hamiltonian method, and hemiquantal dynamics in the collision energy range 0.03 to 0.13 eV. The system is shown to behave adiabatically at large distances, to undergo a transition from adiabatic to diabatic behaviour with respect to spin-orbit coupling in the 11–8.5 au Cs-H distance range, and to transfer adiabatically the whole ²Σ⁺ weight of the electronic wavefunction into theionic channel in the harpooning region.     

Comparative study of the photoassociation reaction of He + X+→ HeX+ (X = H,D): Including multiphoton transitions and dissociations

Using the time-dependent quantum wave packet method, the photoassociation (PA) processes of He + H ⁺→ HeH⁺ and He + D ⁺→ HeD⁺, driven by the sin²-shaped femtosecond laser pulse in the electronic ground state, including multiphoton transitions and dissociations, are investigated for a wide range of initial collision momenta spanning from 1 to 4 a.u. (or for the collision energy roughly in the ranges of 0.009∼0.148 eV and 0.006∼0.089 eV for HeH⁺ and HeD⁺ systems, respectively). It is found that, at some collision momenta, multiphoton transitions to deeply bound states are inevitable to occur and can greatly decrease the PA probability of the target state that selected is the vibrational state v = 6. For the dissociation process, the higher-order (two- and three-photon) dissociations, measured from the target state, tend to be significant at relative high collision energies, which implies that above-threshold dissociations may also be an important loss mechanism in the PA process. In addition, it is also shown that the higher-order dissociation is much stronger for HeH⁺ systems than that for HeD⁺ systems at a given collision momentum, and could be enhanced by the strong transitions among deeply bound states.     

Kinetics of the thermal dehydration of potassium titanium oxalate, K2TiO(C2O4)2·2H2O

The thermal dehydration reaction of potassium titanium oxalate, K₂TiO(C₂O₄)₂·2H₂O, has been studied by means of thermogravimetry (TG), differential thermal analysis (DTA), and differential scanning calorimetry (DSC) in nitrogen atmosphere at different heating rates. K₂TiO(C₂O₄)₂·2H₂O dehydrates in a single step through a practically irreversible process. The activation energy involved and its dependence on the conversion degree were estimated by evaluating the thermogravimetric data according to model-free methods, and values of activation energy were determined for the dehydration reaction. Activation energy values were also evaluated from DSC data using isoconversional methods. The complexity of the dehydration of K₂TiO(C₂O₄)₂·2H₂O is illustrated by the dependence of E on the extent of conversion, ?? (0.05??????????0.95).     

The entrance complex, transition state, and exit complex for the F + H2O → HF + OH reaction. Definitive predictions. Comparison with popular density functional methods

Following the H + H(2) and F + H(2) reactions, the fluorine atom - water system has the potential to become one of the best understood chemical reactions. Stationary points for the F + H(2)O potential energy surface have been located with the "Gold Standard" CCSD(T) method using the Dunning correlation consistent basis sets through quintuple zeta. The CCSD(T)/cc-pV5Z barrier height is prediced to be 2.5 kcal mol(-1), less than previous estimates of 4-7 kcal mol(-1). From higher level theoretical studies of the prototypical F + H(2) reaction, this barrier should be less than 0.5 kcal mol(-1) above the exact, nonrelativistic classical barrier height. 41 of the 49 DFT methods applied to F + H(2)O predict no barrier at all. The eight DFT methods that do predict a barrier show exothermicities that are somewhat too small. The CCSD(T)/cc-pV5Z entrance complex is bound by 3.4 kcal mol(-1) relative to separated F + H(2)O. The analogous exit complex is bound by 5.9 kcal mol(-1) relative to separated HF + OH.     

Equation of state calculations for CO2, C2H4 and N2 using perturbation theory. Effect of damping the quadrupole—quadrupole and induced-quadrupole series at small intermolecular separations

Mohan, R., Prahlada Rao, D. and Babu, S.V., 1986. Equation of state calculations for CO₂, C₂H₄ and N₂ using perturbation theory. Effect of damping the quadrupole—quadrupole and induced-quadrupole series at small intermolecular separations. Fluid Phase Equilibria, 25: 171-193.Pure component equation of state (EOS) and thermodynamic property calculations are made for three quadrupolar molecues CO₂, C₂H₄ and N₂. A simple ‘spherical + quadrupole—quadrupole (Q—Q) + induced-quadrupole (ind-Q)' potential model is assumed to represent the molecular interaction. However, the usual Q—Q and ind-Q interaction energy series expansion expressions are retained only beyond a chosen intermolecular separation, r_cut-off, close to the molecular size. For smaller separations, the diverging nature of the series is damped in an extreme manner by putting these interaction energies to zero. Perturbation theory and an optimisation procedure are used to calculate the reduced thermodynamic quantities, the optimal values of the parameters, σ, ε, and finally the saturation loci, pressure, entropy, internal energy at high densities for the real systems. A comparison with experimental data indicates the usefulness of considering damped multipole—multipole, induced-multipole interactions in high pressure studies.     

Ab initio calculations for the N(2D) + CH4 reaction: Does the N(2D) atom really insert into CH bonds of alkane molecules?

The geometry of the transition state for the N(²D) + CH₄ reaction has been reoptimized at the complete‐active‐space self‐consistent field theory with a large active space and we have confirmed that the N(²D) atom initially inserts into a CH bond to form adiabatically an intermediate radical, CH₃NH(²A″). Extensive single‐point calculations at the multireference configuration interaction level of theory have also been carried out to understand the feature of the potential energy surface for the C–H insertion reaction. In addition, we have found that the N(²D)+CH₄ reaction dynamics on the second lowest doublet state (²A′) is dominated by C–H insertion although the barrier height is somewhat larger in energy than the corresponding insertion barrier associated with the lowest doublet state. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 190–197, 2000