Quantum dynamics of the O(3P)+CH4→OH+CH3 reaction: An application of the rotating bond umbrella model and spectral transform subspace iteration

The Dynamics of Reactions of O(3P) Atoms with Saturated Hydrocarbons and Related Compounds

We review the experimental and theoretical work which has been carried out on the dynamics of reactions of O(3P) with saturated hydrocarbons and related systems. We concentrate primarily on gas phase reactions, but also cover in less detail the more limited work on condensed phase and interfacial reactions. Although O(3P) + saturated alkane reactions are the primary focus, the dominant features of their dynamics are compared and contrasted with those of unsaturated alkanes, functionalised alkanes, and inorganic hydrides (including silanes, germanes, H2S, and hydrogen halides). The principal experimental techniques are reviewed. The experimentally determined quantities are identified, including excitation functions, OH rovibrational and fine-structure partitioning, the rather limited equivalent results for the organic radical co-product, and differential cross-sections. The dynamical conclusions that have been inferred are discussed and compared with the predictions of various levels of theory from semi-empirical models through to rigorous ab initio treatments. For many organic systems, most of the evidence points to OH being formed via a direct abstraction mechanism in which the O(3P) atom attacks along an isolated C–H bond. Outstanding problems with this basic interpretation and gaps in the current knowledge base are identified.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.

Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape

The rate constants and kinetic isotope effects for the O(³P) + CH₄ reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.

A QCT study of the role of the symmetric and antisymmetric stretch mode excitations of methane in the O(3P) + CH4 (νi = 0, 1; i = 1, 3) reaction

The CH stretching mode vibrational excitation opens up the reactive cone of acceptance, shifting the scattering angle from backward to sideways.

Energy efficiency in surmounting the central energy barrier: a quantum dynamics study of the OH + CH3 → O + CH4 reaction

A quantum dynamics study of the OH + CH₃ with a slightly early barrier shows that vibrational energy is more effective in promoting the reactivity than translational energy, which is just opposite to the Polanyi rules.

The hydrogen abstraction reaction O(3P) + CH4: a new analytical potential energy surface based on fit to ab initio calculations

Based exclusively on high-level ab initio calculations, a new full-dimensional analytical potential energy surface (PES-2014) for the gas-phase reaction of hydrogen abstraction from methane by an oxygen atom is developed. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath, taking especial caution respecting the location and characterization of the intermediate complexes in the entrance and exit channels. By comparing with the reference results we show that the resulting PES-2014 reproduces reasonably well the whole set of ab initio data used in the fitting, obtained at the CCSD(T) = FULL/aug-cc-pVQZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical surface we perform an extensive dynamics study using quasi-classical trajectory calculations, comparing the results with recent experimental and theoretical data. The excitation function increases with energy (concave-up) reproducing experimental and theoretical information, although our values are somewhat larger. The OH rotovibrational distribution is cold in agreement with experiment. Finally, our results reproduce experimental backward scattering distribution, associated to a rebound mechanism. These results lend confidence to the accuracy of the new surface, which substantially improves the results obtained with our previous surface (PES-2000) for the same system.

Communication: Imaging the effects of the antisymmetric-stretching excitation in the O(³P) + CH₄(v₃ = 1) reaction

Effects of one-quantum excitation of the antisymmetric-stretching mode of CH4(v3 = 1) on the O((3)P) + CH4 reaction were studied in a crossed-beam, ion-imaging experiment. In the post-threshold region, we found that (1) the product state distributions are dominated by the CH3(0₀) + OH(v' = 1) pair, (2) the product angular distributions extend toward sideways from the backward dominance of the ground-state reaction, and (3) vibrational excitation exerts a positive effect on reactivity, but translational energy is more efficient in promoting the rate of this central-barrier reaction. All major findings agree reasonably well with recent theoretical results. Some remaining questions are pointed out.

Dynamics of the O(3P) + CH4 hydrogen abstraction reaction at hyperthermal collision energies

QCT calculations on a full-dimensional analytical potential energy surface (PES-2014) reproduce the experimental dynamics at 64.0 kcal mol⁻¹ for the O(³P) + CH₄ reaction.

Ring Polymer Molecular Dynamics Calculations of Thermal Rate Constants for the O((3)P) + CH4 → OH + CH3 Reaction: Contributions of Quantum Effects

The thermal rate constant of the O((3)P) + CH4 → OH + CH3 reaction is investigated with ring polymer molecular dynamics on a full-dimensional potential energy surface. Good agreement with experimental and full-dimensional quantum multiconfiguration time-dependent Hartree results between 300 and 1500 K was obtained. It is shown that quantum effects, for example, tunneling and zero-point energy, can be effectively and efficiently included in this path-integral based approach implemented with classical trajectories. Convergence with respect to the number of beads is rapid, suggesting wide applicability for other reactions involving polyatomic molecules.

Mode Selectivity for a "Central" Barrier Reaction: Eight-Dimensional Quantum Studies of the O((3)P) + CH4 → OH + CH3 Reaction on an Ab Initio Potential Energy Surface

The dynamics of a combustion reaction, namely, O((3)P) + CH4 → OH + CH3, is investigated with an eight-dimensional quantum model that includes representatives of all vibrational modes of CH4 and with a full-dimensional quasi-classical trajectory (QCT) method. The calculated excitation functions for the ground vibrational state CH4 agree well with experiment. Both quantum and QCT results suggest that excitation of the stretching modes of CH4 enhances the reaction, while the bending and umbrella modes have a smaller impact on reactivity, again consistent with experimental findings. However, none of the vibrational excitations has comparable efficiency in promoting the reaction as translational energy.

Dynamics of the O(3P) + CHD3(vCH = 0,1) reactions on an accurate ab initio potential energy surface

Recent experimental and theoretical studies on the dynamics of the reactions of methane with F and Cl atoms have modified our understanding of mode-selective chemical reactivity. The O + methane reaction is also an important candidate to extend our knowledge on the rules of reactivity. Here, we report a unique full-dimensional ab initio potential energy surface for the O((3)P) + methane reaction, which opens the door for accurate dynamics calculations using this surface. Quasiclassical trajectory calculations of the angular and vibrational distributions for the ground state and CH stretching excited O + CHD(3)(v(1) = 0,1) → OH + CD(3) reactions are in excellent agreement with the experiment. Our theory confirms what was proposed experimentally: The mechanistic origin of the vibrational enhancement is that the CH-stretching excitation enlarges the reactive cone of acceptance.

MIXED QUANTUM-CLASSICAL SEMI-RIGID VIBRATING ROTOR TARGET MODEL FOR ATOM-POLYATOM REACTION: O(3P) + CH4 → CH3 + OH

In this paper, a mixed quantum-classical semi-rigid vibrating rotor target (QC-SVRT) model has been applied to study the reaction O(3P) + CH4 → CH3 + OH based on H + CH4 potential surface of Jordan and Gilbert. In this approach, the relative translational motion between atom and polyatom molecules is treated classically while the others are treated quantum mechanically. The reaction probabilities and rate constants were carried out using the QC-SVRT approach. It was found that the QC-SVRT results are in good agreement with the quantum results and the reaction threshold is correctly produced in the present calculation. The application of this QC-SVRT approach makes it more practical to extend quantum reaction dynamics calculation to larger molecules and more complex systems without incurring significant loss of important quantum effects.

Thermal Rate Constants for Polyatomic Reactions: First Principles Quantum Theory

The truly accurate knowledge of molecular dynamics phenomena is generally achieved through a combination of detailed experiments and first principle theory. The complexity of such a level of description had until recently restricted accurate studies to rather small systems. However, the sophistication of theoretical methods and massive technological developments have provided remarkable progress in the detailed knowledge of reactive events during the past three decades. Moreover, significant progress towards the detailed understanding of polyatomic reaction has been made in recent years. Detailed experimental and accurate theoretical studies of reactions involving more than only three or four atoms are becoming increasingly available. In this work, aspects of the theoretical work aiming at the accurate description of polyatomic reactions are reviewed.

The present article focuses on the development of the first principle theory of reaction rates. It reviews theoretical developments and benchmark applications to reactions as CH4 + H → CH3 + H2 and CH4 + O → CH3 + OH. The importance of quantum effects for the thermal rate constants in different temperature regimes is discussed in detail. The accuracy of the classical transition state theory and of different approximate quantum theories is investigated in detail. A quantum transition state concept which facilitates accurate reaction rate calculations for polyatomic reaction is described. Benchmark results for the CH4 + H → CH3 + H2 reaction are shown which demonstrate that the accuracy of thermal rate constants calculated by first principle theory can rival the accuracy of available experimental data. The perspectives offered by these developments are discussed.

Quantum dynamics study of H+NH3→H2+NH2 reaction

We report in this paper a quantum dynamics study for the reaction H+NH3-->NH2+H2 on the potential energy surface of Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The quantum dynamics calculation employs the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] and time-dependent wave packet method to propagate the wave function. Initial state-specific reaction probabilities are obtained, and an energy correction scheme is employed to account for zero point energy changes for the neglected degrees of freedom in the dynamics treatment. Tunneling effect is observed in the energy dependency of reaction probability, similar to those found in H+CH4 reaction. The influence of rovibrational excitation on reaction probability and stereodynamical effect are investigated. Reaction rate constants from the initial ground state are calculated and are compared to those from the transition state theory and experimental measurement.

Seven-dimensional quantum dynamics study of the H+NH3-->H2+NH2 reaction

Initial state-selected time-dependent wave packet dynamics calculations have been performed for the H+NH3-->H2+NH2 reaction using a seven-dimensional model and an analytical potential energy surface based on the one developed by Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The model assumes that the two spectator NH bonds are fixed at their equilibrium values. The total reaction probabilities are calculated for the initial ground and seven excited states of NH3 with total angular momentum J=0. The converged cross sections for the reaction are also reported for these initial states. Thermal rate constants are calculated for the temperature range 200-2000 K and compared with transition state theory results and the available experimental data. The study shows that (a) the total reaction probabilities are overall very small, (b) the symmetric and asymmetric NH stretch excitations enhance the reaction significantly and almost all of the excited energy deposited was used to reduce the reaction threshold, (c) the excitation of the umbrella and bending motion have a smaller contribution to the enhancement of reactivity, (d) the main contribution to the thermal rate constants is thought to come from the ground state at low temperatures and from the stretch excited states at high temperatures, and (e) the calculated thermal rate constants are three to ten times smaller than the experimental data and transition state theory results.

Seven-dimensional quantum dynamics study of the O(P3)+CH4 reaction

The initial state selected time-dependent wave packet calculations have been carried out to study the title reaction with seven degrees of freedom included by restricting the nonreacting CH(3) group under C(3V) symmetry and the CH bond length in the group. Total reaction probabilities as well as integral cross sections were calculated for the ground and four vibrationally excited reagent states. Our calculation shows that the reactivity is very small for the reaction for collision energy up to 1.0 eV for all the initial states. Initial vibration excitation of CH(4), in particular, the CH stretch excitation, enhances the reactivity, but only part of the excitation energy deposited can be used to reduce the reaction threshold. The rate constant for the ground initial state agrees rather well with that from a recent quasiclassical trajectory study and is larger than that from the semirigid vibrating rotor target calculations, in particular, in the low temperature region. On the other hand, the thermal rate constant calculated from the integral cross sections for these five vibrational states is about a factor of 20 smaller than that from the multiconfiguration time-dependent Hartree study.

Dynamics of X+CH4 (X=H,O,Cl) reactions: How reliable is transition state theory for fine-tuning potential energy surfaces?

Trajectory calculations run on global potential energy surfaces have shown that the topology of the entrance channel has strong implications on the dynamics of the title reactions. This may explain why huge differences are observed between the rate constants calculated from global dynamical methods and those obtained from local methods that employ the same potential energy surfaces but ignore such topological details. Local dynamics approaches such as transition state-based theories should then be used with caution for fine-tuning potential energy surfaces, especially for fast reactions with polyatomic species since the key statistical assumptions of the theory may not be valid for all degrees of freedom.

How Active Is the Bend Excitation of Methane in the Reaction with O(3P)?

The role of bending excitation of methane in the reaction with O(3P) is investigated in a crossed-beam experiment. Previous theories predicted that either stretch or bend excitation of the reactant promotes chemical reactivity and that initial bending excitation of CH4 preferentially yields umbrella-excited CH3 products. Experimentally, both predictions for bend-excited reagent were not borne out in this investigation. We found instead that compared to the ground-state reagent, bend-excited methane yields more vibrational excitation of the hydroxyl coproduct. The first reported product angular distributions show predominant backward scatterings for both ground-state and bend-excited methanes, which corroborate well with a direct rebound reaction mechanism.

Quasiclassical Trajectory Study of the O(3P) + CH4→ OH + CH3Reaction with a Specific Reaction Parameters Semiempirical Hamiltonian

We present a theoretical study of the O(3P) + CH4 --> OH + CH3 reaction using electronic structure, kinetics, and dynamics calculations. We calculate a grid of ab initio points at the PMP2/AUG-cc-pVDZ level to characterize the potential energy surface in regions of up to 1.3 eV above reagents. This grid of ab initio points is used to derive a set of specific reaction parameters (SRP) for the MSINDO semiempirical Hamiltonian. The resulting SRP-MSINDO Hamiltonian improves the quality of the standard Hamiltonian, particularly in regions of the potential energy surface beyond the minimum-energy reaction path. Quasiclassical-trajectory calculations are used to study the reaction dynamics with the original and the improved MSINDO semiempirical Hamiltonians, and a prior surface. The SRP-MSINDO semiempirical Hamiltonian yields OH rotational distributions in agreement with experimental results, improving over the results of the other surfaces. Thermal rate constants estimated with Variational Transition State Theory using the SRP-MSINDO Hamiltonian are also in agreement with experiments. Our results indicate that reparametrized semiempirical Hamiltonians are a good alternative to generating potential energy surfaces for accurate dynamics studies of polyatomic reactions.

The effects of surface temperature on the gas-liquid interfacial reaction dynamics of O(3P)+squalane

OH/OD product state distributions arising from the reaction of gas-phase O(3P) atoms at the surface of the liquid hydrocarbon squalane C30H62/C30D62 have been measured. The O(3P) atoms were generated by 355 nm laser photolysis of NO2 at a low pressure above the continually refreshed liquid. It has been shown unambiguously that the hydroxyl radicals detected by laser-induced fluorescence originate from the squalane surface. The gas-phase OH/OD rotational populations are found to be partially sensitive to the liquid temperature, but do not adapt to it completely. In addition, rotational temperatures for OH/OD(v'=1) are consistently colder (by 34+/-5 K) than those for OH/OD(v'=0). This is reminiscent of, but less pronounced than, a similar effect in the well-studied homogeneous gas-phase reaction of O(3P) with smaller hydrocarbons. We conclude that the rotational distributions are composed of two different components. One originates from a direct abstraction mechanism with product characteristics similar to those in the gas phase. The other is a trapping-desorption process yielding a thermal, Boltzmann-like distribution close to the surface temperature. This conclusion is consistent with that reached previously from independent measurements of OH product velocity distributions in complementary molecular-beam scattering experiments. It is further supported by the temporal profiles of OH/OD laser-induced fluorescence signals as a function of distance from the surface observed in the current experiments. The vibrational branching ratios for (v'=1)/(v'=0) for OH and OD have been found to be (0.07+/-0.02) and (0.30+/-0.10), respectively. The detection of vibrationally excited hydroxyl radicals suggests that secondary and/or tertiary hydrogen atoms may be accessible to the attacking oxygen atoms.

State-selected dynamics of the complex-forming bimolecular reaction Cl[sup −]+CH[sub 3]Cl[sup ʹ]→ClCH[sub 3]+Cl[sup ʹ−]: A four-dimensional quantum scattering study

Time-independent quantum scattering calculations have been carried out on the Walden inversion S(N)2 reaction Cl(-)+CH(3)Cl(')(v(1),v(2),v(3))-->ClCH(3)(v(1) ('),v(2) ('),v(3) ('))+Cl('-). The two C-Cl stretching modes (quantum numbers v(3) and v(3) (')) and the totally symmetric internal modes of the methyl group (C-H stretching vibration, v(1) and v(1) ('), and inversion bending vibration, v(2) and v(2) (')) are treated explicitly. A four-dimensional coupled cluster potential energy surface is employed. The scattering problem is formulated in hyperspherical coordinates using the exact Hamiltonian and exploiting the full symmetry of the problem. Converged state-selected reaction probabilities and product distributions have been calculated up to 6100 cm(-1) above the vibrational ground state of CH(3)Cl, i.e., up to initial vibrational excitation (2,0,0). In order to extract all scattering resonances, the energetic grid was chosen to be very fine, partly down to a resolution of 10(-12) cm(-1). Up to 2500 cm(-1) translational energy, initial excitation of the umbrella bending vibration, (0,1,0), is more efficient for reaction than exciting the C-Cl stretching mode, (0,0,1). The combined excitation of both vibrations results in a synergic effect, i.e., a considerably higher reaction probability than expected from the sum of both independent excitations, even higher than (0,0,2) up to 1500 cm(-1) translational energy. Product distributions show that the umbrella mode is strongly coupled to the C-Cl stretching mode and cannot be treated as a spectator mode. The reaction probability rises almost linearly with increasing initial excitation of the umbrella bending mode. The effect with respect to the C-Cl stretch is five times larger for more than two quanta in this mode, and in agreement with previous work saturation is found. Exciting the high-frequency C-H stretching mode, (1,0,0), yields a large increase for small energies [more than two orders of magnitude larger than (0,0,0)], while for translational energies higher than 2000 cm(-1), it becomes a pure spectator mode. For combined initial excitations including the symmetric C-H stretch, the spectator character of the latter is even more pronounced. However, up to more than 1500 cm(-1) translational energy, the C-H vibration does not behave adiabatically during the course of reaction, because only 20% of the initial energy is found in the same mode of the product molecule. The distribution of resonance widths and peak heights is discussed, and it is found that individual resonances pertinent to intermediate complexes Cl(-)...CH(3)Cl show product distributions independent of the initial vibrational state of the reactant molecule. The relatively high reactivity, of resonance states with respect to excitation of any mode, found in previous work is confirmed in the present calculations. However, reactivity of intermediate states and reactivity with respect to initial vibrational excitation have to be distinguished. There is a strong mixing between the vibrational states reflected in numerous avoided crossings of the hyperspherical adiabatic curves.

Quantum scattering calculations on chemical reactions

This review discusses recent quantum scattering calculations on bimolecular chemical reactions in the gas phase. This theory provides detailed and accurate predictions on the dynamics and kinetics of reactions containing three atoms. In addition, the method can now be applied to reactions involving polyatomic molecules. Results obtained with both time-independent and time-dependent quantum dynamical methods are described. The review emphasises the recent development in time-dependent wave packet theories and the applications of reduced dimensionality approaches for treating polyatomic reactions. Calculations on over 40 different reactions are described.