Reactions dynamics for X + H2 insertion reactions (X = C(1D), N(2D), O(1D), S(1D)) with Cayley propagator ring-polymer molecular dynamics

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions.

Universal behavior in complex-mediated reactions: Dynamics of S(1D) + o-D2 → D + SD at low collision energies

Reactive and elastic cross sections and rate coefficients have been calculated for the S(1D) + D2(v = 0, j = 0) reaction using a modified hyperspherical quantum reactive scattering method. The considered collision energy ranges from the ultracold regime, where only one partial wave is open, up to the Langevin regime, where many of them contribute. This work presents the extension of the quantum calculations, which in a previous study were compared with the experimental results, down to energies in the cold and ultracold domains. Results are analyzed and compared with the universal case of the quantum defect theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)]. State-to-state integral and differential cross sections are also shown covering the ranges of low-thermal, cold, and ultracold collision energy regimes. It is found that at E/kB < 1 K, there are substantial departures from the expected statistical behavior and that dynamical features become increasingly important with decreasing collision energy, leading to vibrational excitation.

Quantum and quasi-classical dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state

The dynamics of the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations. For the moderate collision energies considered (E_c = 0.001 to 0.4 eV, corresponding to a range from 10 K to 4600 K) the total reaction probabilities from the two different treatments of the nuclear dynamics agree very favourably. The undulations present in P(E) from the quantum mechanical treatment can be related to stabilization of the intermediate CO₂ complex with lifetimes on the 0.05 ps time scale. This is also confirmed from direct analysis of the TDWP simulations and QCT trajectories. Product diatom vibrational and rotational level resolved state-to-state reaction probabilities from TDWP and QCT simulations agree well except for the highest product vibrational states (v′ ≥ 15) and for the lowest product rotational states (j′ ≤ 10). Opening of the product vibrational level CO(v′ = 17) requires ∼0.2 eV from QCT and TDWP simulations with O₂(j = 0) and decreases to 0.04 eV if all initial rotational states are included in the QCT analysis, compared with E_c > 0.04 eV obtained from experiments. It is thus concluded that QCT simulations are suitable for investigating and realistically describe the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction down to low collision energies when compared with results from a quantum mechanical treatment using TDWPs.

The dynamics of the C(³P) + O₂(³Σ⁻_g) → CO(¹Σ⁺) + O(¹D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations.

Signature of shape resonances on the differential cross sections of the S(1D)+H2 reaction

Shape resonances appear when the system is trapped in an internuclear potential well after tunneling through a barrier. They manifest as peaks in the collision energy dependence of the cross section (excitation function), and in many cases, their presence can be observed experimentally. High-resolution crossed-beam experiments on the S(¹D) + H₂(j = 0) reaction in the 0.81-8.5 meV collision energy range reaction revealed non-monotonic behavior and the presence of oscillations in the reaction cross section as a function of the collision energy, as predicted by quantum mechanical (QM) calculations. In this work, we have analyzed the effect of shape resonances on the differential cross sections for this insertion reaction by performing additional QM calculations. We have found that, in some cases, the resonance gives rise to a large enhancement of extreme backward scattering for specific final states. Our results also show that, in order to yield a significant change in the state-resolved differential cross section, the resonance has to be associated with constructive interference between groups of partial waves, which requires not getting blurred by the participation of many product helicity states.

An Empirical Dynamical Barrier for Statistical Theory of Low-Energy Reactive S(1D) + HD(j = 0), H2(j = 0) Collisions

A simple model potential is proposed to describe the dynamical barrier in the mean interaction potential at small distances between the reactants in S(¹D) + HD(¹Σ, v = 0, j = 0) reaction. The statistical theory of collision complex formation and complex decay is applied to calculate the total reaction cross sections and the cross sections for SH and SD productions in the range of low collision energies E_c = (0.4-60) meV. The results are compared with measured cross sections and results of hyperspherical close coupling calculations. As a check of consistency the same comparisons are presented for the case of S(¹D) + H₂(¹Σ, v = 0, j = 0) reaction.

A new potential energy surface for the H2S system and dynamics study on the S((1)D) + H2(X(1)Σg(+)) reaction

We constructed a new global potential energy surface (PES) for the electronic ground state ((1)A') of H2S based on 21,300 accurate ab initio energy points over a large configuration space. The ab initio energies are obtained from multireference configuration interaction calculations with a Davidson correction using basis sets of quadruple zeta quality. The neural network method is applied to fit the PES, and the root mean square error of fitting is small (1.68 meV). Time-dependent wave packet studies for the S((1)D) + H2(X(1)Σg(+)) → H((2)S) + SH(X(2)Π) reaction on the new PES are conducted to study the reaction dynamics. The calculated integral cross sections decrease with increasing collision energy and remain fairly constant within the high collision energy range. Both forward and backward scatterings can be observed as expected for a barrierless reaction with a deep well on the PES. The calculated integral cross sections and differential cross sections are in good agreement with the experimental results.

INVESTIGATION OF THE EXCHANGE REACTION H + H′S → HS + H′ ON THE 1A′ STATE POTENTIAL ENERGY SURFACE

The quantum time dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the exchange reaction H(2S) + H′S(2Π) → HS(2Π) + H′(2S) on the 1A′ potential energy surface (PES). The integral cross sections of the H + H′S (v = j = 0) → HS + H′ reaction calculated by the two methods were presented. The results reveal that the integral cross sections (ICS) decrease with the collision energy increasing. The result of the QCT calculations is reasonably consistent with the time-dependent wave packet. Moreover, the differential cross sections (DCS) were calculated by the QCT method at the four different collision energies, which display a forward–backward symmetry. A long-lifetime H2S intermediate complex of the exchange reaction was found according to the trajectories. In the stereodynamics investigation, the polar and dihedral angle distribution functions were calculated, which have the distinct oscillations. The oscillations could be attributed to the deep well on the 1A′ PES. However, based on the polar-angle and dihedral angle distribution functions, it could be predicted that the main product rotational angular momentum preferentially point to the positive or negative direction of y-axes.

Rate coefficients from quantum and quasi-classical cumulative reaction probabilities for the S(1D) + H2 reaction

Cumulative reaction probabilities (CRPs) at various total angular momenta have been calculated for the barrierless reaction S((1)D) + H(2) → SH + H at total energies up to 1.2 eV using three different theoretical approaches: time-independent quantum mechanics (QM), quasiclassical trajectories (QCT), and statistical quasiclassical trajectories (SQCT). The calculations have been carried out on the widely used potential energy surface (PES) by Ho et al. [J. Chem. Phys. 116, 4124 (2002)] as well as on the recent PES developed by Song et al. [J. Phys. Chem. A 113, 9213 (2009)]. The results show that the differences between these two PES are relatively minor and mostly related to the different topologies of the well. In addition, the agreement between the three theoretical methodologies is good, even for the highest total angular momenta and energies. In particular, the good accordance between the CRPs obtained with dynamical methods (QM and QCT) and the statistical model (SQCT) indicates that the reaction can be considered statistical in the whole range of energies in contrast with the findings for other prototypical barrierless reactions. In addition, total CRPs and rate coefficients in the range of 20-1000 K have been calculated using the QCT and SQCT methods and have been found somewhat smaller than the experimental total removal rates of S((1)D).

Dynamics of the S(1D2)+HD(j=0) reaction at collision energies approaching the cold regime: a stringent test for theory

We report integral cross sections for the S(1D2)+HD(j=0)→DS+H and HS+D reaction channels obtained through crossed-beam experiments reaching collision energies as low as 0.46 meV and from adiabatic time-independent quantum-mechanical calculations. While good overall agreement with experiment at energies above 10 meV is observed, neither the product channel branching ratio nor the low-energy resonancelike features in the HS+D channel can be theoretically reproduced. A nonadiabatic treatment employing highly accurate singlet and triplet potential energy surfaces is clearly needed to resolve the complex nature of the reaction dynamics.

Kinetics and dynamics of the S(1D2) + H2 → SH + H reaction at very low temperatures and collision energies

We report combined studies on the prototypical S(1D2) + H2 insertion reaction. Kinetics and crossed-beam experiments are performed in experimental conditions approaching the cold energy regime, yielding absolute rate coefficients down to 5.8 K and relative integral cross sections to collision energies as low as 0.68 meV. They are supported by quantum calculations on a potential energy surface treating long-range interactions accurately. All results are consistent and the excitation function behavior is explained in terms of the cumulative contribution of various partial waves.

Effect of collision energy on cross sections and product alignments for the C(1D) + H2 (v = 0, j = 0) insertion reactions

Quasi-classical trajectory (QCT) calculations of total reaction probabilities and vibrationally state-resolved reaction probabilities at total angular momentum J = 0 as a function of collision energy for the C(1D) + H2 (v = 0, j = 0) reactions have been performed on an ab initio potential-energy surface [ J. Chem. Phys. 2001, 115, 10701]. In addition, the integral cross sections as a function of collision energy have been carried out for the same reaction. The product rotational alignments have also been calculated, which are almost invariant with respect to collision energies.

Mean potential phase space theory of chemical reactions

A nonconventional application of phase space theory to the insertion reactions A+H(2), with A=C((1)D) and S((1)D), is presented. Instead of approximating the potential energies of interaction between separated fragments by their isotropic long-range contributions, as in the original theory, the latter are replaced by the accurate potential energies averaged with respect to Jacobi angles. The integral and differential cross sections obtained from this mean potential phase space theory (MPPST) turn out to be in very satisfying agreement with the benchmark predictions of the time-independent and time-dependent statistical quantum methods. The formal and numerical simplicity of MPPST with respect to any approach combining statistical assumptions and dynamical calculations makes it a promising tool for studying indirect polyatomic reactions.

Significant Nonadiabatic Effects in the S(1D) + HD Reaction

A nonadiabatic quantum dynamics calculation involving four coupled potential energy surfaces (two degenerate 3A' ', one 3A', and one 1A') and the spin-orbit coupling matrix for these states is reported for the title reaction. The results show that the important discrepancy between theoretically calculated and experimentally measured intramolecular isotope effects can at least in part be attributed to significant nonadiabatic effects.

Dynamics of insertion reactions of H2 molecules with excited atoms

Recent progress in the study of insertion reactions of hydrogen molecules with excited atoms is reviewed in this article. In particular, the dynamics of the reaction of O(1D), N(2D), C(1D), and S(1D) with H2 and its isotopomers, which have received a great deal of attention over the past decade, are examined in detail. All of these systems have in common the existence of several potential energy surfaces (PES) correlating with the reagents' states, and consequently, they can give rise to reaction following different adiabatic and nonadiabatic pathways. The main contribution, however, arises from their ground singlet PESs which feature the existence of deep wells with small or null barriers for insertion. Accordingly, these reactions proceed mainly via formation of relatively long-lived collision complexes and display an overall nearly statistical behavior. In spite of their similarities, the various reactions have peculiar characteristics caused by important differences of their respective PESs. The contribution of excited PES to the global reactivity, which has also become an important issue and a challenge both for theory and experiment, is also examined. The different theoretical approaches are discussed in the text, along with the experimental results obtained by a variety of techniques. The recent exact quantum treatments of these reactive systems together with the development of a rigorous statistical model have contributed to a very accurate description which in many cases matches very well the detailed measurements. The quasi-classical trajectory (QCT) method has also provided a fairly accurate description of the reaction dynamics for these systems. In particular, the analysis in terms of collision times has yielded interesting clues about the reaction mechanisms.

Quantum Dynamics of the H + O2 → O + OH Reaction on an Accurate ab Initio Potential Energy Surface

We report exact time-dependent and time-independent quantum mechanical studies of the title reaction on an accurate ab initio potential energy surface of Xu et al. (J. Chem. Phys. 2005, 122, 24305). The J = 0 reaction probabilities for several reactant states show sharp resonance structures superimposed on relatively low backgrounds, and they are remarkably different from existing quantum results on an earlier potential energy surface (DMBE-IV). The new findings reported here suggest that our current understanding of this important reaction might require significant revision.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.