Quasiclassical Trajectory Research Articles

Quasiclassical Trajectory Study of the Si + SH Reaction on an Accurate Double Many-Body Expansion Potential Energy Surface

An accurate potential energy surface (PES) for the HSiS system based on MRCI+Q calculations extrapolated to the complete basis set limit is presented. Modeled with the double many-body expansion (DMBE) method, the PES provides an accurate description of the long-range interactions, including electrostatic and dispersion terms decaying as R-4, R-5, R-6, R-8, R-10 that are predicted from dipole moments, quadrupole moments, and dipolar polarizabilities, which are also calculated at the MRCI+Q level. The novel PES is then used in quasiclassical trajectory calculations to predict the rate coefficients of the Si + SH → SiS + H reaction, which has been shown to be a major source of the SiS in certain regions of the interstellar medium. An account of the zero-point energy leakage based on various nonactive models is also given. It is shown that the reaction is dominated by long-range forces, with the mechanism Si + SH → SiSH → SSiH → SiS + H being the most important one for all temperatures studied. Although SSiH corresponds to the global minimum of the PES, the contribution from the direct reaction Si + SH → SSiH → SiS + H is less than 0.5% for temperatures higher than 500 K. The rovibrational distributions of the products are calculated using the momentum Gaussian binning method and show that as the temperature is increased the average vibrational quantum number decreases while the rotational distribution spreads up to larger values.

Permutation-Invariant-Polynomial Neural-Network-Based Δ-Machine Learning Approach: A Case for the HO2 Self-Reaction and Its Dynamics Study.

Δ-machine learning, or the hierarchical construction scheme, is a highly cost-effective method, as only a small number of high-level ab initio energies are required to improve a potential energy surface (PES) fit to a large number of low-level points. However, there is no efficient and systematic way to select as few points as possible from the low-level data set. We here propose a permutation-invariant-polynomial neural-network (PIP-NN)-based Δ-machine learning approach to construct full-dimensional accurate PESs of complicated reactions efficiently. Particularly, the high flexibility of the NN is exploited to efficiently sample points from the low-level data set. This approach is applied to the challenging case of a HO2 self-reaction with a large configuration space. Only 14% of the DFT data set is used to successfully bring a newly fitted DFT PES to the UCCSD(T)-F12a/AVTZ quality. Then, the quasiclassical trajectory (QCT) calculations are performed to study its dynamics, particularly the mode specificity.

Rovibrational-Specific QCT and Master Equation Study on N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) Systems in High-Energy Collisions.

This work presents a detailed investigation of the energy-transfer and dissociation mechanisms in N2(X1Σg+) + O(3P) and NO(X2Π) + N(4S) systems using rovibrational-specific quasiclassical trajectory (QCT) and master equation analyses. The complete set of state-to-state kinetic data, obtained via QCT, allows for an in-depth investigation of the Zel'dovich mechanism leading to the formation of NO molecules at microscopic and macroscopic scales. The master equation analysis demonstrates that the low-lying vibrational states of N2 and NO have dominant contributions to the NO formation and the corresponding extinction of N2 through the exchange process. For the considered temperature range, it is found that nearly 50% of the dissociation processes for N2 and NO molecules occur in the quasi-steady-state (QSS) regime, while for the Zel'dovich reaction, the distribution of the reactants does not reach the QSS conditions. Furthermore, using the QSS approximation to model the Zel'dovich mechanism leads to overestimating NO production by more than a factor of 4 in the high-temperature range. The breakdown of this well-known approximation has profound consequences for the approaches that heavily rely on the validity of QSS assumption in hypersonic applications. Finally, the investigation of the rovibrational state population dynamics reveals substantial similarities among different chemical systems for the energy-transfer and the dissociation processes, providing promising physical foundations for the use of reduced-order strategies in other chemical systems without significant loss of accuracy.

Unconventional SN2 retention pathways induced by complex formation: High-level dynamics investigation of the NH2 - + CH3I polyatomic reaction.

Investigations on the dynamics of chemical reactions have been a hot topic for experimental and theoretical studies over the last few decades. Here, we carry out the first high-level dynamical characterization for the polyatom-polyatom reaction between NH2 - and CH3I. A global analytical potential energy surface is developed to describe the possible pathways with the quasi-classical trajectory method at several collision energies. In addition to SN2 and proton abstraction, a significant iodine abstraction is identified, leading to the CH3 + [NH2⋯I]- products. For SN2, our computations reveal an indirect character as well, promoting the formation of [CH3⋯NH2] complexes. Two novel dominant SN2 retention pathways are uncovered induced by the rotation of the CH3 fragment in these latter [CH3⋯NH2] complexes. Moreover, these uncommon routes turn out to be the most dominant retention paths for the NH2 - + CH3I SN2 reaction.

Projectile electron loss, excitation and de-excitation cross section database in a collision between two hydrogen atoms in the impact energy range between 50 keV–5.0 MeV, Part I: Target is in ground state

We present projectile electron loss, excitation, and de-excitation cross-sections database for H(nl)+H(1s) collision system. A four-body classical trajectory Monte Carlo (CTMC) and a quasi-classical trajectory Monte Carlo (QCTMC) methods were employed in the projectile energy range between 50 keV to 5.0 MeV.

Rotational Mode-Specificity in the Cl + C2H6 → HCl + C2H5 Reaction.

We perform rotational mode-specific quasi-classical trajectory simulations using a high-quality ab initio analytical potential energy surface for the Cl(2P3/2) + C2H6 → HCl + C2H5 reaction. As ethane, being a prolate-type symmetric top, can be characterized by the J and K rotational quantum numbers, the excitation of two rotational modes, the tumbling (J, K = 0) and spinning (J, K = J) rotations of the reactant is carried out with J = 10, 20, 30, and 40 at a wide range of collision energies. The impacts of rotational excitation on the reactivity, the mechanism, and the post-reaction distribution of energy are investigated: (1) exciting both rotational modes enhances the reactivity with the spinning rotation being more effective due to its coupling to the C–H stretching vibrational normal modes (C–H bond elongating effect) and larger rotational energies, (2) rotational excitation increases the dominance of direct rebound over the stripping mechanism, while collision energy favors the latter, (3) investing energy in tumbling rotation excites the translational motion of the products, while the excess spinning rotational energy readily flows into the internal degrees of freedom of the ethyl radical or, less significantly, into the HCl vibration, probably due to the pronounced rovibrational coupling in this case. We also study the relative efficiency of vibrational and rotational excitation on the reactivity of the barrierless and thus translationally hindered title reaction.

State-selective electron capture cross sections in collision between fully striped ions and ground state hydrogen atom—Classical treatment of the collision

We present a state-selective electron capture cross sections database from the ground state hydrogen atom. A standard three-body classical trajectory Monte Carlo (CTMC) and quasi-classical trajectory Monte Carlo (QCTMC) models were employed for impact energies between 10 and 200 keV/amu. The projectile ions are H+, He2+, Li3+, Be4+, B5+, C6+, N7+, and O8+. The cross sections are tabulated for each value of the final quantum numbers n, l, m, summed over m for the given n and l and over l and m for the given n. The maximum quantum number nmax is set to 4 for H+, He2+ and Li3+, as well as to 5 for Be4+, B5+, C6+, N7+ and O8+, respectively.

State-Specific Dynamic Study of the Exchange and Dissociation Reaction for O(3P) and O2($${}^{3}\Sigma _{g}^{ - }$$) Collision by Quasi-Classical Trajectory

State-Specific Dynamic Study of the Exchange and Dissociation Reaction for O(3P) and O2($${}^{3}\Sigma _{g}^{ - }$$) Collision by Quasi-Classical Trajectory

Roaming dynamics of H+C2D2 reaction on fundamental-invariant neural network potential energy surface

We performed extensive quasiclassical trajectory calculations for the H+C2D2→HD+C2D/D2+C2H reaction based on a recently developed, global and accurate potential energy surface by the fundamental-invariant neural network method. The direct abstraction pathway plays a minor role in the overall reactivity, which can be negligible as compared with the roaming pathways. The acetylene-facilitated roaming pathway dominates the reactivity, with very small contributions from the vinylidene-facilitated roaming. Although the roaming pathways proceed via the short-lived or long-lived complex forming process, the computed branching ratio of product HD to D2 is not far away from 2:1, implying roaming dynamics for this reaction is mainly contributed from the long-lived complex-forming process. The resulting angular distributions for the two product channels are also quite different. These computational results give valuable insights into the significance and isotope effects of roaming dynamics in the biomolecular reactions.

Fundamental invariant-neural network potential energy surface and dissociative chemisorption dynamics of N2 on rigid Ni(1 1 1)

We constructed a new full-dimensional potential energy surface (PES) for the dissociative chemisorption of N2 on rigid Ni(111). The PES was fitted using the fundamental invariant-neural network method based on DFT energy points. The resulting PES is accurately fitted with very small fitting error of about 4.5 meV, which reproduces well the minimum energy path and energies of stationary points. Based on the new PES, the effects of incidence energy, incidence angle as well as the vibrational excitations of impinging molecules on dissociation probability were investigated by quasi-classical trajectory calculations. The vibrational excitation enhances the reactivity more effectively than the same amount of translational energy, which is consistent with the very “product-like” transition state for this system. The dissociation occurs close to the bridge site, presumably due to the extremely tight and high-energy barriers of PES at top and hollow sites.

Reaction Pathway Control via Reactant Vibrational Excitation and Impact on Product Vibrational Distributions: The O + HO2 → OH + O2 Atmospheric Reaction.

Chemical reactions often have multiple pathways, the control of which is of fundamental and practical importance. In this Letter, we examine the dynamics of the O + HO2 → OH + O2 reaction, which plays an important role in atmospheric chemistry, using quasi-classical trajectories on a recently developed full-dimensional potential energy surface (PES). This reaction has two pathways leading to the same products: the H abstraction pathway (Oa + HObOc → OaH + ObOc) and the O abstraction pathway (Oa + HObOc → ObH + OaOc). Under thermal conditions, the reaction is dominated by the latter channel, which is barrierless, leading to vibrational excitation of the O2 product. However, we demonstrate that excitation of the HO2 reactant in its O-H (v1) vibrational mode results in dramatic switching of the reaction pathway to the activated H abstraction channel, which leads to a highly excited OH product vibrational state distribution. The implications of such dynamical effects in the atmospheric chemistry are discussed.

Initial state-selected scattering for the reactions H + CH4/CHD3 and F + CHD3 employing ring polymer molecular dynamics.

The inclusion of nuclear quantum effects (NQEs) in molecular dynamics simulations is one of the major obstacles for an accurate modeling of molecular scattering processes involving more than a couple of atoms. An efficient method to incorporate these effects is ring polymer molecular dynamics (RPMD). Here, we extend the scope of our recently developed method based on non-equilibrium RPMD (NE-RPMD) from triatomic chemical reactions to reactions involving more atoms. We test the robustness and accuracy of the method by computing the integral cross sections for the H/F + CH4/CHD3 reactions where the methane molecule is either initially in its vibrational ground or excited state (C-H stretch). Furthermore, we analyze the extent to which NQEs are described by NE-RPMD. The method shows significant improvement over the quasiclassical trajectory approach while remaining computationally efficient.

Dissection of the Multichannel Reaction O(3P) + C2H2: Differential Cross-Sections and Product Energy Distributions.

The O(3P) + C2H2 reaction plays an important role in hydrocarbon combustion. It has two primary competing channels: H + HCCO (ketenyl) and CO + CH2 (triplet methylene). To further understand the microscopic dynamic mechanism of this reaction, we report here a detailed quasi-classical trajectory study of the O(3P) + C2H2 reaction on the recently developed full-dimensional potential energy surface (PES). The entrance barrier TS1 is the rate-limiting barrier in the reaction. The translation of reactants can greatly promote reactivity, due to strong coupling with the reaction coordinate at TS1. The O(3P) + C2H2 reaction progress through a complex-forming mechanism, in which the intermediate HCCHO lives at least through the duration of a rotational period. The energy redistribution takes place during the creation of the long-lived high vibrationally (and rotationally) excited HCCHO in the reaction. The product energy partitioning of the two channels and CO vibrational distributions agree with experimental data, and the vibrational state distributions of all modes of products present a Boltzmann-like distribution.

The effect of zero‐point energy in simulating organic reactions with post‐transition state bifurcation

AbstractAmbimodal reactions involve a single transition state leading to multiple products. To assess the ratio of the bifurcation products, quasiclassical trajectories (QCTs) are initiated from transition state geometries that are randomly sampled using the zero‐point energy (ZPE) plus thermal energy of a molecule's vibrational modes. However, in the QCTs, the influence of ZPE percentage in the resulting bifurcation ratio and time gap between formation of bonds is not well understood. To benchmark the effect of varying the percentage of the molecules' inherent ZPE used in the simulation, three organic reactions with distinct mechanisms that all display post‐transition state bifurcation were selected. The three reactions studied include an intramolecular [6 + 4]/[4 + 2] cycloaddition, an asynchronous nitrene insertion, and an SN2/addition to a carbonyl on an α‐bromoketone. These reactions encompass various modes of bond formation and cleavage, offering a broad view of the influence of ZPE scaling in evaluating the product ratio resulted from post‐transition state bifurcation. Exploring means of tuning selectivity in simulation enables development of more accurate organic reaction modeling for synthetic prediction. This work will establish a basis for future QCT studies of organic reactions.

Machine learning product state distributions from initial reactant states for a reactive atom-diatom collision system.

A machine-learned model for predicting product state distributions from specific initial states (state-to-distribution or STD) for reactive atom-diatom collisions is presented and quantitatively tested for the N(4S) + O2(X3Σg -) → NO(X2Π) + O(3P) reaction. The reference dataset for training the neural network consists of final state distributions determined from quasi-classical trajectory (QCT) simulations for ∼2000 initial conditions. Overall, the prediction accuracy as quantified by the root-mean-squared difference (∼0.003) and the R2 (∼0.99) between the reference QCT and predictions of the STD model is high for the test set, for off-grid state-specific initial conditions, and for initial conditions drawn from reactant state distributions characterized by translational, rotational, and vibrational temperatures. Compared with a more coarse grained distribution-to-distribution (DTD) model evaluated on the same initial state distributions, the STD model shows comparable performance with the additional benefit of the state resolution in the reactant preparation. Starting from specific initial states also leads to a more diverse range of final state distributions, which requires a more expressive neural network compared with DTD. A direct comparison between QCT simulations, the STD model, and the widely used Larsen-Borgnakke (LB) model shows that the STD model is quantitative, whereas the LB model is qualitative at best for rotational distributions P(j') and fails for vibrational distributions P(v'). As such, the STD model can be well-suited for simulating nonequilibrium high-speed flows, e.g., using the direct simulation Monte Carlo method.

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 (Ec = 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 Ec > 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.

An accurate full-dimensional H4O potential energy surface and dynamics of an exchange reaction.

H2O and H2 are ubiquitous in the universe and their collisions play a crucial role in astrophysical processes. The reaction between the two also provides a prototype for understanding dynamics through four-center transition states. In this work, we adopted a strategy of combing two ab initio methods, CCSD(T)-F12a/AVTZ and MRCI-F12 + Qrot/AVTZ, to provide a balanced description for all regions of the configuration space, including one hydrogen exchange channel and two dissociation channels, namely H2 + H2O, H + H + H2O, and H + OH + H2. About 40 500 points were sampled to cover all dynamically relevant space, and the permutation invariant polynomial-neural network (PIP-NN) method was employed to develop a high-precision full-dimensional potential energy surface (PES), with a total fitting error of 0.055 kcal mol-1. Using a quasi-classical trajectory (QCT) method, the reaction dynamics and mode specificity of the hydrogen exchange channel were studied on the PES. It has been found that the stretching mode of H2, the bending, the symmetric stretching, the asymmetric stretching mode of H2O, and the translational mode can all promote reactivity. The strongest promotion effect comes from the H-H stretching mode. The Sudden Vector Projection (SVP) model was applied to predict mode specificity effects and rationalize the product energy partitioning. In both cases, the QCT and SVP results are generally consistent with each other. Furthermore, the hydrogen exchange channel was found to be dominated by sideways scattering.

Validating experiments for the reaction H2 + NH2- by dynamical calculations on an accurate full-dimensional potential energy surface.

Ion-molecule reactions play key roles in the field of ion related chemistry. As a prototypical multi-channel ion-molecule reaction, the reaction H2 + NH2- → NH3 + H- has been studied for decades. In this work, we develop a new globally accurate potential energy surface (PES) for the title system based on hundreds of thousands of sampled points over a wide dynamically relevant region that covers long-range interacting configuration space. The permutational invariant polynomial-neural network (PIP-NN) method is used for fitting and the resulting total root mean squared error (RMSE) is extremely small, 0.026 kcal mol-1. Extensive dynamical and kinetic calculations are carried out on this PIP-NN PES. Impressively, a unique phenomenon of significant reactivity suppression by exciting the rotational mode of H2 is reported, supported by both the quasi-classical trajectory (QCT) and quantum dynamics (QD) calculations. Further analysis uncovers that exciting the H2 rotational mode would prevent the formation of the reactant complex and thus suppress the reactivity. The calculated rate coefficients for H2/D2 + NH2- agree well with the experimental results, which show an inverse temperature dependence from 50 to 300 K, consistent with the capture nature of this barrierless reaction. The significant kinetic isotope effect observed by experiments is well reproduced by the QCT computations as well.

Capturing quantum effects with quasi-classical trajectories in the D + H+3 → H2D+ + H reaction.

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H+3 → H2D+ + H reaction. Using the same H+4 potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H2D+ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H+3, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.

Effect of Reactant's Rotational Excitation on Stereodynamic Properties of C+Sh(V=0, J=0-40)→Cs+H Reaction Investigated with Quasi Classical Trajectory Method

Effect of Reactant's Rotational Excitation on Stereodynamic Properties of C+Sh(V=0, J=0-40)→Cs+H Reaction Investigated with Quasi Classical Trajectory Method