Application of semirigid vibrating rotor target model to reaction of H+CH4→CH3+H2

The symmetric C-D stretching spectator mode in the H + CHD3 → H2 + CD3 reaction and its effect on dynamical modeling

The symmetric C-D stretching mode is a spectator mode in the H + CHD3 → H2 + CD3 reaction. Effects of multiple vibrational excitations of the CHD3 reactant are studied with the quantum transition-state (QTS) framework and an eight-dimensional (8D) model Hamiltonian developed by Palma and Clary. By including many thermal flux eigenstates, results have been obtained up to high energies, allowing the study of the symmetric C-D stretching spectator mode. A new concept of a state-specific thermal flux operator is proposed to analyze the C-D stretching spectator mode in detail, providing a new and insightful venue for studying transition-state control of chemical reactions. Furthermore, as a spectator mode, whether the C-D stretching motion can be excluded in a seven-dimensional (7D) model has not been fully interrogated, although the 7D model is a reasonable approximation and has provided accurate theoretical predictions. By comparing with available results of full-dimensional calculations, both the 7D and 8D models predict reasonably accurate results. However, the 7D model underestimates the mixing of two vibrational states that are in Fermi resonance. Despite its spectator nature, the C-D stretch is important in the dynamical modeling of chemical reaction systems affected by state mixing.

Full-dimensional quantum mechanical calculations of the reaction probability of the H + CH4 reaction based on a mixed Jacobi and Radau description

A full-dimensional time-dependent wave packet study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH₃ has been described using three Radau vectors, whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH₄. About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given. A comparison between the present approach and other methods, including reduced and full-dimensional ones, is also presented.

Testing the Palma-Clary Reduced Dimensionality Model Using Classical Mechanics on the CH4 + H → CH3 + H2 Reaction

Application of exact quantum scattering methods in theoretical reaction dynamics of bimolecular reactions is limited by the complexity of the equations of nuclear motion to be solved. Simplification is often achieved by reducing the number of degrees of freedom to be explicitly handled by freezing the less important spectator modes. The reaction cross sections obtained in reduced-dimensionality (RD) quantum scattering methods can be used in the calculation of rate coefficients, but their physical meaning is limited. The accurate test of the performance of a reduced-dimensionality method would be a comparison of the RD cross sections with those obtained in accurate full-dimensional (FD) calculations, which is not feasible because of the lack of complete full-dimensional results. However, classical mechanics allows one to perform reaction dynamics calculations using both the RD and the FD model. In this paper, an RD versus FD comparison is made for the 8-dimensional Palma-Clary model on the example of four isotopologs of the CH4 + H → CH3 + H2 reaction, which has 12 internal dimensions. In the Palma-Clary model, the only restriction is that the methyl group is confined to maintain C3v symmetry. Both RD and FD opacity and excitation functions as well as differential cross sections were calculated using the quasiclassical trajectory method. The initial reactant separation has been handled according to our one-period averaging method [ Nagy et al. J. Chem. Phys. 2016, 144, 014104 ]. The RD and FD excitation functions were found to be close to each other for some isotopologs, but in general, the RD reactivity parameters are lower than the FD reactivity parameters beyond statistical error, and for one of the isotopologs, the deviation is significant. This indicates that the goodness of RD cross sections cannot be taken for granted.

Theoretical Study of the Validity of the Polanyi Rules for the Late-Barrier Cl + CHD3 Reaction

The Polanyi rules, which state that vibrational energy is more efficient in promoting a late-barrier reaction than translational energy, were questioned recently by an experimental unexpected finding that the CH stretch excitation is no more effective in promoting the late-barrier Cl + CHD3 reaction than the translational energy. However, the present quantum dynamics study on the best-available potential energy surface for the title reaction reveals that the CH stretch excitation does promote the reaction significantly, except at low collision energies. Further studies should be carried out to solve the disagreements between theory and experiment on the reaction.

REACTION RATES: ACCURATE QUANTUM DYNAMICAL CALCULATIONS FOR POLYATOMIC SYSTEMS

Rate constants of chemical reactions can be computed directly: employing flux correlation functions, no scattering calculations are required. If the reaction is direct, the dynamical simulation can be restricted to the vicinity of the reaction barrier. Therefore accurate thermal rate constants and cumulative reaction probabilities can be calculated for rather large systems. Recent calculations have studied systems with up to six atoms, e.g., H + CH 4 → H 2 + CH 3. The calculations provide a full-dimensional quantum description of the reaction process.

In the article, an introduction to the theory of flux correlation functions is given. Methods for the efficient computation of accurate thermal rate constants and cumulative reaction probabilities are reviewed. Connections to transition state ideas are highlighted. The multi-configurational time-dependent Hartree (MCTDH) approach, which facilitates efficient multi-dimensional wave packet propagation, is described and its use in reaction rate calculation is discussed. As examples, recent results for the prototypical polyatomic reaction H + CH 4 → H 2 + CH 3 are presented and rotational effects on the reaction rates of H 2 + OH → H + H 2 O , O + HCl → OH + Cl , and H 2 + Cl → H + HCl are discussed.

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.

Depression of reactivity by the collision energy in the single barrier H + CD4 -> HD + CD3 reaction

Crossed molecular beam experiments and accurate quantum scattering calculations have been carried out for the polyatomic H + CD(4) --> HD + CD(3) reaction. Unprecedented agreement has been achieved between theory and experiments on the energy dependence of the integral cross section in a wide collision energy region that first rises and then falls considerably as the collision energy increases far over the reaction barrier for this simple hydrogen abstraction reaction. Detailed theoretical analysis shows that at collision energies far above the barrier the incoming H-atom moves so quickly that the heavier D-atom on CD(4) cannot concertedly follow it to form the HD product, resulting in the decline of reactivity with the increase of collision energy. We propose that this is also the very mechanism, operating in many abstraction reactions, which causes the differential cross section in the backward direction to decrease substantially or even vanish at collision energies far above the barrier height.

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.

Thermochemistry and Accurate Quantum Reaction Rate Calculations for H2/HD/D2 + CH3

Accurate quantum-mechanical results for thermodynamic data, cumulative reaction probabilities (for J = 0), thermal rate constants, and kinetic isotope effects for the three isotopic reactions H2 + CH3 --> CH4 + H, HD + CH3 --> CH4 + D, and D2 + CH3 --> CH(3)D + D are presented. The calculations are performed using flux correlation functions and the multiconfigurational time-dependent Hartree (MCTDH) method to propagate wave packets employing a Shephard interpolated potential energy surface based on high-level ab initio calculations. The calculated exothermicity for the H2 + CH3 --> CH4 + H reaction agrees to within 0.2 kcal/mol with experimentally deduced values. For the H2 + CH3 --> CH4 + H and D2 + CH3 --> CH(3)D + D reactions, experimental rate constants from several groups are available. In comparing to these, we typically find agreement to within a factor of 2 or better. The kinetic isotope effect for the rate of the H2 + CH3 --> CH4 + H reaction compared to those for the HD + CH3 --> CH4 + D and D2 + CH3 --> CH(3)D + D reactions agree with experimental results to within 25% for all data points. Transition state theory is found to predict the kinetic isotope effect accurately when the mass of the transferred atom is unchanged. On the other hand, if the mass of the transferred atom differs between the isotopic reactions, transition state theory fails in the low-temperature regime (T < 400 K), due to the neglect of the tunneling effect.

Accurate quantum calculations of the reaction rates for H∕D+CH4

In previous work [T. Wu, H. J. Werner, and U. Manthe, Science 306, 2227 (2004)], accurate quantum reaction rate calculations of the rate constant for the H+CH4-->CH3+H2 reaction have been presented. Both the electronic structure calculations and the nuclear dynamics calculations are converged with respect to the basis sets employed. In this paper, the authors apply the same methodology to an isotopic variant of this reaction: D+CH4-->CH3+HD. Accurate rate constants are presented for temperatures between 250 and 400 K. For temperatures between 400 and 800 K, they use a harmonic extrapolation to obtain approximate rate constants for H/D+CH4. The calculations suggest that the experimentally reported rate constants for D+CH4 are about a factor of 10-20 too high. For H+CH4, more accurate experiments are available and agreement is much better: the difference is less than a factor of 2.6. The kinetic isotope effect for the H/D+CH4 reactions is studied and compared with experiment and transition state theory (TST) calculations. Harmonic TST was found to provide a good description of the kinetic isotope effect.

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.

A full dimensional, nine-degree-of-freedom, time-dependent quantum dynamics study for the H2+C2H reaction

A full dimensional, nine-degree-of-freedom (9DOF), time-dependent quantum dynamics wave packet approach is presented for the study of the H2+C2H-->H+C2H2 reaction system. This is the first full dimensional quantum dynamics study for a diatom-triatom reaction system. The effects of the initial vibrational and rotational excitations of the reactants on the reactivity of this reaction are investigated. This study shows that vibrational excitations of H2 enhance the reactivity; whereas, the vibrational excitations of C2H only have a small effect on the reaction probability. In addition, the bending excitations of C2H, compared to the ground state reaction probability, hinder the reactivity. Comparison of the ground state reaction probabilities of the 9DOF and 8DOF shows the reaction probability from the full dimensional calculation is larger, with more prominent resonance features.