Accurate potential energy surface and quantum reaction rate calculations for the H+CH4→H2+CH3 reaction

Accurate Quantum Dynamics Calculations for the Cl + CH4/CHD3/CD4 Reaction Rates

Full-dimensional quantum dynamics simulations of the reaction of Cl with methane and its isotopomers are reported. Thermal rate constants are computed for the Cl + CH4 → HCl + CH3, Cl + CHD3 → HCl + CD3, and Cl + CD4 → DCl + CD3 reactions. Temperatures between 200 and 500 K are considered. In this temperature range, excellent agreement with the experiment is obtained. A detailed analysis of the kinetic isotope effect reveals the crucial importance of the CH3/CD3 umbrella motion. Comparison with approximate ring-polymer molecular dynamics simulations shows significant differences depending on the isotope studied.

Current Status of the X + C2H6 [X ≡ H, F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C₂H₆ → HX + C₂H₅; X ≡ H, F(²P), Cl(²P), O(³P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(³P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.

Perceptions on the Treatment of Apparent Isotope Effects during the Analyses of Reaction Rate and Mechanism

Isotope substitution, a compelling tool of physical chemistry, has been broadly applied in the research field of heterogeneous catalysis. In general, upon the differences in mass-related atomic vibrational frequencies and...

Full-dimensional quantum dynamics study of isotope effects for the H2 + NH2/ND2/NHD and H2/D2/HD + NH2 reactions

A full-dimensional quantum dynamical study for the bimolecular reactions of hydrogen molecules with amino radicals for different isotopologues is reported. The nonreactive amino radical is described by two Radau vectors that are very close to the valence bond coordinates. Potential-optimized discrete variable representation basis is used for the vibrational coordinates of the amino radical. Starting from the reaction H₂ + NH₂, we study the isotope effects for the two reagents separately, i.e., H₂ + NH₂/ND₂/NHD and H₂/D₂/HD + NH₂. The effects of different vibrational mode excitations of the reagents on the reactivities are studied. Physical explanations about the isotope effects are also provided thoroughly including the influence of vibrational energy differences between the different isotopologues and the impact of the tunneling effect.

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.

Kinetic isotope effects in the water forming reaction H2/D2 + OH from rigorous close-coupling quantum dynamics simulations

Rigorous quantum dynamics simulations of thermal rate constants and kinetic isotope effects for the water-forming H₂/D₂ + OH reaction are presented, which show increased tunneling below 300 K and can serve as benchmarks for approximate methods.

Natural reaction channels in H + CHD3 → H2 + CD3

Natural reaction channels control the mode-specific chemistry of methane and its isotopomeres.

Kinetic isotope effects and how to describe them

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

Wavepacket dynamics and the multi-configurational time-dependent Hartree approach

Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.

Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations

The instanton method obtains approximate tunneling rates from the minimum-action path (known as the instanton) linking reactants to the products at a given temperature. An efficient way to find the instanton is to search for saddle-points on the ring-polymer potential surface, which is obtained by expressing the quantum Boltzmann operator as a discrete path-integral. Here we report a practical implementation of this ring-polymer form of instanton theory into the Molpro electronic-structure package, which allows the rates to be computed on-the-fly, without the need for a fitted analytic potential-energy surface. As a test case, we compute tunneling rates for the benchmark H + CH₄ reaction, showing how the efficiency of the instanton method allows the user systematically to converge the tunneling rate with respect to the level of electronic-structure theory.

Control of chemical reactivity by transition-state and beyond

It has been long established that the transition state for an activated reaction controls the overall reactivity, serving as the bottleneck for reaction flux. However, the role of the transition state in regulating quantum state resolved reactivity has only been addressed more recently, thanks to advances in both experimental and theoretical techniques. In this perspective, we discuss some recent advances in understanding mode-specific reaction dynamics in bimolecular reactions, mainly focusing on the X + H2O/CH4 (X = H, F, Cl, and O(3P)) systems, extensively studied in our groups. These advances shed valuable light on the importance of the transition state in mode-specific and steric dynamics of these prototypical reactions. It is shown that many mode-specific phenomena can be understood in terms of a transition-state based model, which assumes in the sudden limit that the ability of a reactant mode for promoting the reaction stems from its coupling with the reaction coordinate at the transition state. Yet, in some cases the long-range anisotropic interactions in the entrance (or exit) valley, which govern how the trajectories reach (or leave) the transition state, also come into play, thus modifying the reactive outcomes.

Vibrational excitation influence on the H + BrO → HBr + O reaction: a quasi-classical trajectory investigation

Quasi-classical trajectory calculations are employed to investigate the vibrational excitation effect on the scalar and vector properties of the H + BrO → HBr + O reaction using a X1A′ state ab initio potential energy surface (J. Chem. Phys. 2000, 113, 4598). The reaction probability, cross section, and rate constant are carried out with the effect of the collision energy (Ecol = 0.1–6 kcal/mol) and vibrational levels (v = 0–3). A significant vibrational dependency has been observed in the reaction probability and cross section at a relatively low collision energy area and has also been found in a low-temperature (T < 150 K) region of the rate constant. In addition, two product angular distributions, P(θr) and P(ϕr), and two generalized polarization-dependent differential cross sections, PDDCS00 and PDDCS20, are calculated as well. All of these scalar and vector properties have shown sensitive behaviors to the vibrational levels.

Constructing Potential Energy Surfaces for Polyatomic Systems: Recent Progress and New Problems

Different methods of constructing potential energy surfaces in polyatomic systems are reviewed, with the emphasis put on fitting, interpolation, and analytical (defined by functional forms) approaches, based on quantum chemistry electronic structure calculations. The different approaches are reviewed first, followed by a comparison using the benchmark H + CH4 and the H + NH3 gas-phase hydrogen abstraction reactions. Different kinetics and dynamics properties are analyzed for these reactions and compared with the available experimental data, which permits one to estimate the advantages and disadvantages of each method. Finally, we analyze different problems with increasing difficulty in the potential energy construction: spin-orbit coupling, molecular size, and more complicated reactions with several maxima and minima, which test the soundness and general applicability of each method. We conclude that, although the field of small systems, typically atom-diatom, is mature, there still remains much work to be done in the field of polyatomic systems.