H + CD4 Abstraction Reaction Dynamics: Product Energy Partitioning

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.

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.

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.

Gaussian binning of the vibrational distributions for the Cl + CH4(v(4/2) = 0, 1) → H + CH3Cl(n(1)n(2)n(3)n(4)n(5)n(6)) reactions

We test several binning techniques to obtain mode-specific final-state distributions for polyatomic reactions. Normal mode analysis is done after an exact transformation to the Eckart frame. Standard histogram binning (HB) and three different variants of the energy-based Gaussian binning (1GB) are employed to obtain the probabilities of the vibrational states. We consider the two major issues of the polyatomic quasiclassical product analysis, i.e., (1) rounding the classical action to the nearest integer can result in unphysical states and (2) the normal-mode analysis can break down for highly distorted geometries. We show that 1GB can handle issue 1 when the total vibrational energy is evaluated in the normal mode space using the harmonic approximation and both issues 1 and 2 can be solved when the total vibrational energy is calculated exactly in the Cartesian space. We found that anharmonicity in the quantized energy levels does not have a significant effect on the final-state distributions. Quasiclassical trajectory calculations are performed for the reactant ground-state and bending-excited Cl((2)P(3/2)) + CH(4)(v(4/2) = 0, 1) → H + CH(3)Cl reactions using an ab initio potential energy surface. The product analysis techniques are successfully applied to the CH(3)Cl product molecules and some qualitative features of the results are discussed.

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.

Apparent failure of the Born-Oppenheimer static surface model for vibrational excitation of molecular hydrogen on copper

The accuracy of dynamical models for reactive scattering of molecular hydrogen, H(2), from metal surfaces is relevant to the validation of first principles electronic structure methods for molecules interacting with metal surfaces. The ability to validate such methods is important to progress in modeling heterogeneous catalysis. Here, we study vibrational excitation of H(2) on Cu(111) using the Born-Oppenheimer static surface model. The potential energy surface (PES) used was validated previously by calculations that reproduced experimental data on reaction and rotationally inelastic scattering in this system with chemical accuracy to within errors ≤ 1 kcal/mol ≈ 4.2 kJ/mol [Díaz C, et al. (2009) Science 326:832-834]. Using the same PES and model, our dynamics calculations underestimate the contribution of vibrational excitation to previously measured time-of-flight spectra of H(2) scattered from Cu(111) by a factor 3. Given the accuracy of the PES for the experiments for which the Born-Oppenheimer static surface model is expected to hold, we argue that modeling the effect of the surface degrees of freedom will be necessary to describe vibrational excitation with similar high accuracy.

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.

Quasiclassical trajectory study of the SiH(4)+H-->SiH(3)+H(2) reaction on a global ab initio potential energy surface

The SiH(4)+H-->SiH(3)+H(2) reaction has been investigated by the quasiclassical trajectory (QCT) method on a recent global ab initio potential energy surface [M. Wang et al., J. Chem. Phys. 124, 234311 (2006)]. The integral cross section as a function of collision energy and thermal rate coefficient for the temperature range of 300-1600 K have been obtained. At the collision energy of 9.41 kcalmol, product energy distributions and rovibrational populations are explored in detail, and H(2) rotational state distributions show a clear evidence of two reaction mechanisms. One is the conventional rebound mechanism and the other is the stripping mechanism similar to what has recently been found in the reaction of CD(4)+H [J. P. Camden et al., J. Am. Chem. Soc. 127, 11898 (2005)]. The computed rate coefficients with the zero-point energy correction are in good agreement with the available experimental data.

Quasiclassical trajectory study of the reaction H+CH4(nu3 = 0,1)-->CH3+H2 using a new ab initio potential energy surface

Detailed quasiclassical trajectory calculations of the reaction H+CH4(nu3 = 0,1)-->CH3 + H2 using a slightly updated version of a recent ab initio-based CH5 potential energy surface [X. Zhang et al., J. Chem. Phys. 124, 021104 (2006)] are reported. The reaction cross sections are calculated at initial relative translational energies of 1.52, 1.85, and 2.20 eV in order to make direct comparison with experiment. The relative reaction cross section enhancement ratio due to the excitation of the C-H antisymmetric stretch varies from 2.2 to 3.0 over this energy range, in good agreement with the experimental result of 3.0 +/- 1.5 [J. P. Camden et al., J. Chem. Phys. 123, 134301 (2005)]. The laboratory-frame speed and center-of-mass angular distributions of CH3 are calculated as are the vibrational and rotational distributions of H2 and CH3. We confirm that this reaction occurs with a combination of stripping and rebound mechanisms by presenting the impact parameter dependence of these distributions and also by direct examination of trajectories.

State-to-state reaction dynamics: A selective review

A selective review of state-to-state reaction dynamics experiments is presented. The review focuses on three classes of reactions that exemplify the rich history and illustrate the current state of the art in such work. These three reactions are (1) the hydrogen exchange reaction, H+H2-->H2+H and its isotopomers; (2) the H+RH-->H2+R reactions, where RH is an alkane, beginning with H+CH4-->H2+CH3 and extending to much larger alkanes; and (3) the Cl+RH-->HCl+R reactions, principally Cl+CH4-->HCl+CH3. We describe the experiments, discuss their results, present comparisons with theory, and introduce heuristic models.

Quasi-Classical Trajectory Calculations Analyzing the Reactivity and Dynamics of Asymmetric Stretch Mode Excitations of Methane in the H + CH4 Reaction

An exhaustive dynamics study was performed at two collision energies, 1.52 and 2.20 eV, analyzing the effects of the asymmetric (nu3) stretch mode excitation in the reactivity and dynamics of the gas-phase H + CH4 reaction. Quasi-classical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were performed on an analytical potential energy surface previously developed by our group. First, strong coupling between different vibrational modes in the entry channel was observed, indicating that energy can flow between these modes, and therefore that they do not preserve their adiabatic character along the reaction path; i.e., the reaction is nonadiabatic. Second, we found that the reactant vibrational excitation has a significant influence on the vibrational and rotational product distributions. With respect to the vibrational distribution, our results confirm the purely qualitative experimental evidence, although the theoretical results presented here are also quantitative. The rotational distributions are predictive, because no experimental data have been reported. Third, with respect to the reactivity, we found that the nu3 mode excitation by one quantum is more reactive than the ground state by a factor of about 2, independently of the collision energy, and in agreement with the experimental measurement of 3.0 +/- 1.5. Fourth, the state-to-state angular distributions of the products reproduce the experimental behavior at 1.52 eV, where the CH3 products scatter sideways and backward. At 2.20 eV this experimental information is not available, and therefore the results reported here are again predictive. The satisfactory reproduction of a great variety of experimental data by the present QCT study lends confidence to the potential energy surface constructed by our group and to those results whose accuracy cannot be checked by comparison with experiment.