Quasi-classical Trajectory Method Research Articles

State-to-State Time-Dependent Quantum Dynamics Studies of the Si(3P) + OH(X 2Π) → OSi(X 1Σg+) + H(2S) Reaction Based on a New HOSi(X2A') Potential Energy Surface.

Quantum and quasi-classical dynamics calculations were conducted for the reaction of Si with OH on the latest potential energy surface (PES), which is obtained by fitting tens of thousands of ab initio energy points by using the many-body expansion formula. To obtain an accurate PES, all energy points calculated with aug-cc-pVQZ and aug-cc-pV5Z basis sets were extrapolated to the complete basis set limit. The accuracy of our new PES was verified by comparing the topographic characteristics and contour maps of potential energy with other works. In addition, the anharmonic vibrational frequencies of HOSi and HSiO based on the present ab initio and PES by means of quantum dynamics methods were calculated. Dynamics information such as reaction probability, integral cross sections (ICS), product distribution, and rate constants was obtained on the new HOSi(X2A') PES. The dynamic information calculated using the quasi-classical trajectory method and time-dependent wave packet method is generally in good agreement, except for the vibrational state-resolved ICSs of product. The calculated differential cross section and capture time reveal that the reaction is primarily governed by the complex formation mechanism.

Theoretical Investigation of Rate Coefficients and Dynamical Mechanisms for N + N + N Three-Body Recombination Based on Full-Dimensional Potential Energy Surfaces

Three-body recombination reactions, in which two particles form a bound state while a third one bounces off after the collision, play significant roles in many fields, such as cold and ultracold chemistry, astrochemistry, atmospheric physics, and plasma physics. In this work, the dynamics of the recombination reaction for the N3 system over a wide temperature range (5000–20,000 K) are investigated in detail using the quasi-classical trajectory (QCT) method based on recently developed full-dimensional potential energy surfaces. The recombination products are N2(X) + N(4S) in the 14A″ state, N2(A) + N(4S) in the 24A″ state, and N2(X) + N(2D) in both the 12A″ and 22A″ states. A three-body collision recombination model involving two sets of relative translational energies and collision parameters and a time-delay parameter is adopted in the QCT calculations. The recombination process occurs after forming an intermediate with a certain lifetime, which has a great influence on the recombination probability. Recombination processes occurring through a one-step three-body collision mechanism and two distinct two-step binary collision mechanisms are found in each state. And the two-step exchange mechanism is more dominant than the two-step transfer mechanism at higher temperatures. N2(X) formed in all three related states is always the major recombination product in the temperature range from 5000 K to 20,000 K, with the relative abundance of N2(A) increasing as temperature decreases. After hyperthermal collisions, the formed N2(X/A) molecules are distributed in highly excited rotational and vibrational states, with internal energies mainly distributed near the dissociation threshold. Additionally, the rate coefficients for this three-body recombination reaction in each state are determined and exhibit a negative correlation with temperature. The dynamic insights presented in this work might be very useful to further simulate non-equilibrium dynamic processes in plasma physics involving N3 systems.

Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N2-N2 Collisions using QCT Combined with Neural Network Models.

Using the quasi-classical trajectory method, we systematically studied the state-to-state vibrational relaxation process of N2(v1) + N2(v2) collisions over a wide temperature range (5000-30,000 K). Different temperature dependencies of the single- and multiquantum VV and VT events in various (v1,v2) collisions are captured, with the dominant channel being related to the initial vibrational energy levels (vmax = 50). At a specified relative translational energy, there is a monotonic relationship of the VT cross sections with the vibrational energy level, particularly in high-energy collisions. Additionally, we constructed well-trained neural network models (R-values reaching 0.99) using limited quasi-classical trajectory (QCT) data sets, which can be used to predict the state-to-state cross sections and rate coefficients of the VV processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2 + Δv) and VT processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2) (Δv = ±1, ±2, ±3) for collisions with arbitrary initial vibrational states. This work not only significantly reduces computational resources but also serves as a reference for the study of the state-to-state dynamics of all four-atom collision systems in hypersonic flows.

Quantum dynamics of the P(2D) + H2 (X1[formula omitted]) → PH (X3Σ-) + H(2S) reaction

The title reaction is thought to be important for the astronomical PO formation, which may contribute to the generation of bioavailable H3PO3. Using quasi-classical trajectory (QCT) method, the state-specified (v = 0, j = 0) rate constant of this reaction was calculated. The comparison with previous temperature-averaged QCT rate constant shows that the effect of ro-vibrational excitation is relatively small below 2000 K. Then, the time-dependent wave packet (TDWP) method was applied to investigate the quantum reaction mechanisms, obtaining the state-specified (v = 0, j = 0) reaction probability, integral cross sections and rate constants. The number of partial waves and the integral interval of collision energy considered were rigorously tested to ensure the convergence of the TDWP rate constant below 2000 K. The TDWP rate constant agrees better to the latest experimental results at 291 to 685 K than those from the two QCT calculations. Also, the TDWP calculations can produce relatively reliable rate constants at 700 to 2000 K, where the Arrhenius formula fitted by experimental results ignores the temperature dependence of the activation energy. The calculated rate constants are helpful for modelling the phosphorus chemistry and determining the abundances of the P-bearing species in interstellar media (ISM).

Theoretical study of the O(3P) + CN(X2Σ+) → CO(X1Σ+) + N(2D)/N(4S) reactions.

The barrierless exothermic reactions between atomic oxygen and the cyano radical, O(3P) + CN(X2Σ+) → CO(X1Σ+) + N(2D)/N(4S), play a significant role in combustion, astrochemistry, and hypersonic environments. In this work, their dynamics and kinetics are investigated using both wave packet (WP) and quasi-classical trajectory (QCT) methods on recently developed potential energy surfaces of the 12A', 12A,″ and 14A″ states. The product state distributions in the doublet pathway obtained with the WP method for a few partial waves show extensive internal excitation in the CO product. This observation, combined with highly oscillatory reaction probabilities, signals a complex-forming mechanism. The statistical nature of the reaction is confirmed by comparing the WP results with those from phase space theory. The calculated rate coefficients using the WP (with a J-shifting approximation) and QCT methods exhibit agreement with each other near room temperature, 1.77 × 10-10 and 1.31 × 10-10cm3molecule-1s-1, but both are higher than the existing experimental results. The contribution of the quartet pathway is small at room temperature due to a small entrance channel bottleneck. The QCT rate coefficients are further compared with experimental results above 3000K, and the agreement is excellent.

First-principles mode-specific reaction dynamics.

Controlling the outcome of chemical reactions by exciting specific vibrational and/or rotational modes of the reactants is one of the major goals of modern reaction dynamics studies. In the present Perspective, we focus on first-principles vibrational and rotational mode-specific dynamics computations on reactions of neutral and anionic systems beyond six atoms such as X + C2H6 [X = F, Cl, OH], HX + C2H5 [X = Br, I], OH- + CH3I, and F- + CH3CH2Cl. The dynamics simulations utilize high-level ab initio analytical potential energy surfaces and the quasi-classical trajectory method. Besides initial state specificity and the validity of the Polanyi rules, mode-specific vibrational-state assignment for polyatomic product species using normal-mode analysis and Gaussian binning is also discussed and compared with experiment.

Theoretical dynamics studies of the CH3 + HBr → CH4 + Br reaction: effects of isotope substitution and vibrational excitation of CH3.

The rate coefficient for two deuterium substituted isotopologues of reaction CH3 + HBr → CH4 + Br has been determined using the quasiclassical trajectory (QCT) method. We used the analytical potential energy surface (PES) fitted to high-level ab initio points in earlier work. The PES exhibits a pre-reaction van der Waals complex and a submerged potential barrier. The rate coefficients of the deuterated isotopologue reactions, similarly to the pure-protium isotopologue, show significant deviation from the Arrhenius law, namely, the activation energy is negative below about 600 K and positive above it: k[CH3 + DBr] = 1.35 × 10-11 exp(- 2472/T) + 5.85 × 10-13 exp(335/T) and k[CD3 + HBr] = 2.73 × 10-11 exp(- 2739/T) + 1.46 × 10-12 exp(363/T). The CH3 + DBr reaction is slower by a factor of 1.8, whereas CD3 + HBr isotopologue is faster by a factor of 1.4 compared to the HBr + CH3 system across a wide temperature range. The isotope effects are interpreted in terms of the properties of various regions of the PES. Quantum state-resolved simulations revealed that the reaction of CH3 with HBr becomes slower when any of the vibrational modes of the methyl radical is excited. This contradicts the assumption that vibrational excitation of methyl radicals enhances its reactivity, which is of historical importance: this assumption was used as an argument against the existence of negative activation energy in a decade-long controversy in the 1980s and 1990s.

Combined Quantum Mechanical and Quasi-Classical State-to-State Dynamical Study on the Isotopic Effect in H/D + LiH+/LiD+ → H2/HD/D2 + Li+ Reactions.

Coriolis-coupled quantum mechanical (QM-CC) and quasi-classical trajectory (QCT) calculations are carried out to investigate the dynamics of the H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ reactions on the ground electronic state potential energy surface reported by Martinazzo et al. (Martinazzo et al., J. Chem. Phys. 2003, 119, 11241). The QM-CC and QCT results at the initial state-selected and state-to-state levels are used to investigate the validity and accuracy of the QCT method for these exoergic barrierless reactions. Furthermore, the QCT method is used to understand the isotopic effects on reaction observables like total and state-to-state integral cross section, differential cross section, product energy disposal, and rate constants of H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ and H(D) + LiD+(v = 0, j = 0) → HD(D2) (v', j') + Li+ reactions. Attempts are also made to understand the impact of the isotopic substitution on the reaction mechanism. It is observed that QM-CC and QCT results closely follow each other at the initial state-selected and state-to-state levels. Noticeable kinematic effects of reagents on the reactivity and mechanism of the reactions are also observed.

Rotational Transitions in the N2 + Ion Induced by Collisions with Helium Atoms in Cold Helium Plasmas. A Quasiclassical Trajectory Study.

Cross-sections of state-to-state rotational transitions in electronically ground-state 14 (X2 ) ions induced by collisions with 4 He atoms have been calculated using a quasiclassical trajectory method and a set of artificial neural networks representing the /He potential energy surface. The training points for the neural networks have been calculated at a MCSCF (multi-configuration self-consistent field)/aug-cc-pVQZ level. A broad range of the /He collision energy has been considered ( eV) and the efficiency of vibrational transitions in the ion has also been analyzed. It has been found that vibrational transitions are negligible with respect to rotational transitions up to eV and that above this energy, both rotational and vibrational transitions in are marginal in the /He collisions.

State-Specific Dissociation and Inelastic Rate Constants for Collisions of H2 with H and He

Recent reports have called for planetary probe missions to the outer planets of the solar system. To support these missions, kinetic data for processes involving molecular hydrogen are required in order to conduct the necessary computational and experimental studies. The data available in the literature are currently incomplete owing to the broad range of temperatures required for these computational studies. In this work, the rate constants for the state-specific dissociation and inelastic scattering collisions between molecular hydrogen and H and He were calculated using the quasi-classical trajectory method in a range of translational energy between 0.1 and 15 eV. Comparisons with the state-specific cross sections reported in the literature are made for both systems. The full set of ro-vibrational state-specific cross sections is then used to compute the corresponding dissociation and inelastic reaction rate constants between 1000 and 30,000 K. Thermal and state-specific data are made available.

Dynamics studies of the Si+(2P) + D2 reaction by using quantum and quasi-classical methods

The dynamics calculations of the Si+ + D2 (v0 = 0, j0 = 0) → SiD+ + D reaction were carried out by using time-dependent quantum wave packet and quasi-classical trajectory methods. The integral cross sections were calculated and compared with the experimental data in the collision energy range from 1.0 to 10.0 eV. The results indicated that present values are in good agreement with the experimental data. In addition, reaction probabilities, the distribution of the SiD+ product and differential cross sections are also calculated. The differential cross section indicated that the “complex-forming” mechanism plays a dominant role in the low collision energy range and the abstraction mechanism dominates the reaction at high collision energies.

Polyatomic radiative association by quasiclassical trajectory calculations: Formation of HCN and HNC molecules in H + CN collisions.

We have developed the polyatomic extension of the established [M. Gustafsson, J. Chem. Phys. 138, 074308 (2013)] classical theory of radiative association in the absence of electronic transitions. The cross section and the emission spectrum of the process is calculated by a quasiclassical trajectory method combined with the classical Larmor formula which can provide the radiated power in collisions. We have also proposed a Monte Carlo scheme for efficient computation of ro-vibrationally quantum state resolved cross sections for radiative association. Besides the method development, the global potential energy and dipole surfaces for H + CN collisions have been calculated and fitted to test our polyatomic semiclassical method.

Effects of the third body (O and N) on the recombination of molecular nitrogen using quasi-classical trajectory methods

The investigation of the recombination reactions poses significant challenges due to the complexities involved in three-body collisions including simultaneous interaction of three bodies and multiple time scales. This work aims to investigate the complex dynamics involved in the recombination of atomic nitrogen to form molecular nitrogen using the quasi-classical trajectory method for the N3 and the N2O systems. The recombination pathways considered include a single-step direct reaction and a two-step mechanism that involves the formation of an intermediate with a finite lifetime which is stabilized through a subsequent collision with a third body. The latter is further classified as Lindemann or Chaperon mechanism based on the role played by the third body. The model uses a time-lag parameter to allow for a consistent treatment of all the reaction pathways. It is observed that the recombination probability is greatest for collisions involving low translational energies and low time lags. Recombination rate coefficients are evaluated using a novel rate coefficient expression developed for three-body collisions. Low temperature recombination rate coefficients, which can be computationally prohibitive to evaluate using traditional detailed balance methods, can be evaluated at a low computational cost. The recombination pathways are determined algorithmically by identifying the various interaction time scales. The direct mechanism is found to have a larger recombination probability, but a lower rate coefficient. The effect of the third body (oxygen and nitrogen atoms) on the recombination dynamics is explored in detail. It is observed that the recombination in excess of O atom leads to a larger population of the low internal energy states, as opposed to recombination in the excess of N atoms. The dominance of the Chaperon mechanism is seen in both systems.

Reaction dynamics of P(4S) + O2(X3Σ−g) → O(3P) + PO(X2Π) on a global CHIPR potential energy surface of PO2(X2A1): implications for atmospheric modelling

Abstract. The reaction dynamics of P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are thought to be important in atmospheric and interstellar chemistry. Based on the state-of-the-art ab initio energy points, we analytically constructed a global potential energy surface (PES) for the ground-state PO2(X2A1) using the combined-hyperbolic-inverse-power-representation (CHIPR) method. A total of 6471 energy points were computed by the multireference configuration interaction method with the Davidson correction and aug-cc-pV5Z basis set. The analytical CHIPR PES reproduces ab initio energies accurately with a root-mean-square deviation of 91.5 cm−1 (or 0.262 kcal mol−1). The strongly bound valence region of the PES has complicated topographical features with multiple potential wells and barriers. The attributes of the important intermediates are carefully validated with our geometry optimization results, as well as previous experimental and computational results. Finally, the reaction probability, integral cross sections, and rate constants for P(4S) + O2(X3Σg-) → O(3P) + PO(X2Π) are calculated using the quasi-classical trajectory and time-dependent wave packet methods. The trends of probability and integral cross section versus the collision energy can be divided into three stages, which are governed by the entrance barriers or exothermicity of the reaction. The rate constant demonstrates strong Arrhenius linear behaviour at relatively low temperatures but deviates from this pattern at high temperatures. The calculated cross sections and rate constants are helpful for modelling the phosphorus chemistry in atmospheric and interstellar media.

Alternating Stereospecificity upon Central-Atom Change: Dynamics of the F- +PH2 Cl SN 2 Reaction Compared to its C- and N-Centered Analogues.

Central-atom effects on bimolecular nucleophilic substitution (SN 2) reactions are well-known in chemistry, however, the atomic-level SN 2 dynamics at phosphorous (P) centers has never been studied. We investigate the dynamics of the F- +PH2 Cl reaction with the quasi-classical trajectory method on a novel full-dimensional analytical potential energy surface fitted on high-level ab initio data. Our computations reveal intermediate dynamics compared to the F- +CH3 Cl and the F- +NH2 Cl SN 2 reactions: phosphorus as central atom leads to a more indirect SN 2 reaction with extensive complex-formation with respect to the carbon-centered one, however, the title reaction is more direct than its N-centered pair. Stereospecificity, characteristic at C-center, does not appear here either, due to the submerged front-side-attack retention path and the repeated entrance-channel inversional motion, whereas the multi-inversion mechanism discovered at nitrogen center is also undermined by the deep Walden-well. At low collision energies, 6 % of the PH2 F products form with retained configuration, mostly through complex-mediated mechanisms, while this ratio reaches 24 % at the highest energy due to the increasing dominance of the direct front-side mechanism and the smaller chance for hitting the deep Walden-inversion minimum. Our results suggest pronounced central-atom effects in SN 2 reactions, which can fundamentally change their (stereo)dynamics.

SiS formation in the interstellar medium via SiH + S collisions

ABSTRACT One of the most important Si-bearing species in the intersellar medium is the SiS molecule. Thermal rate coefficients and other collisional properties are calculated for its formation via the title reaction using the quasi-classical trajectory method. An accurate representation of the HSiS potential energy surface is employed, which has been modelled from high-level ab initio calculations and a reliable description of long-range interactions as implied by the underlying double many-body expansion method. The calculated rate coefficients for the $\rm SiH + S \rightarrow SiS + H$ reaction can be modelled with k(T) = α(T/300)βe−γ/T where $\alpha =0.63\times 10^{-10}\, \rm cm^3\, s^{-1}$, β = -0.11, and $\gamma = 11.6\, \rm K$. This result is only slightly lower than that for SiS formation via Si + SH collisions. The contribution of each reaction mechanism and the rovibrational energy distributions of the nascent SiS molecule are also calculated. The title collision can also yield SH ($\rm SiH + S \rightarrow SH + Si$), but the corresponding rate coefficient is 20 to 27 times smaller than for SiS formation ($\alpha =0.025\times 10^{-10}\rm cm^3\, s^{-1}$, β =-0.13, and $\gamma = 9.38\, \rm K$). The role of intersections between excited electronic states is also discussed, based on novel calculations including eight electronic states.

High-Energy Quantum Dynamics of the 15N + o-14N14N Rovibrational Activation and Isotope Exchange Processes.

We report full quantum reaction probabilities, computed within the framework of time-independent quantum mechanics using hyperspherical coordinates, for the 15N + 14N14N inelastic and reactive collision processes, restricted to total angular momentum J = 0, for kinetic energies up to 4.5 eV. We take advantage of the nonzero (i = 1) nuclear spin of 14N, leading to the existence of two nuclear spin isomers of 14N14N, namely, ortho- and para-14N14N, to restrict the study to the ortho molecular nitrogen species, with even rotational quantum number j = 0, 2, ... states. Specifically, we start with diatomic reagents ortho-14N14N in the initial rotational state j = 0. A comparison with similar works previously published by other groups using time-dependent wave packet and quasi-classical trajectory methods for the 14N + 14N14N fully symmetric collision is given. We find that reactive processes 15N + 14N14N involving atom exchange do not happen for collision energies less than 2.2 eV. Collisions at energies of around 2.0 eV are most effective for populating reactants' rovibrational states, that is, for inelastic scattering, whereas those at energies close to 5.0 eV yield a newly formed 14N15N isotopologue in a wide variety of excited vibrational levels.

Vibrational Mode-Specific Dynamics of the OH + C2H6 Reaction.

We investigate the effects of the initial vibrational excitations on the dynamics of the OH + C2H6 → H2O + C2H5 reaction using the quasi-classical trajectory method and a full-dimensional analytical ab initio potential energy surface. Excitation of the initial CH, CC, and OH stretching modes enhances, slightly inhibits, and does not affect the reactivity, respectively. Translational energy activates the early-barrier title reaction more efficiently than OH and CC stretching excitations, in accord with the Polanyi rules whereas CH stretching modes have similar or higher efficacy than translation, showing that these rules are not always valid in polyatomic processes. Scattering angle, initial attack angle, and product translational energy distributions show the dominance of direct stripping with increasing collision energy, side-on OH and isotropic C2H6 attack preferences, and substantial reactant-product translational energy transfer without any significant mode specificity. The reactant vibrational excitation energy of OH and C2H6 flows into the H2O and C2H5 product vibrations, respectively, whereas product rotations are not affected. The computed mode-specific H2O vibrational distributions show that initial OH excitation appears in the asymmetric stretching vibration of the H2O product and allow comparison with experiments.

Machine learning‐assisted study of correlation between post‐transition‐state bifurcation and initial phase information at the ambimodal transition state

AbstractThe Diels–Alder cycloaddition of cyclopentadiene and nitroethene, the intramolecular cycloaddition between a diene and triene, and the Diels–Alder cycloaddition of 2‐hydroxyacrolein with 1,3‐butadiene involving post‐transition‐state bifurcation (PTSB) were studied. These cycloaddition reactions were investigated using quasi‐classical trajectory (QCT), classical molecular dynamics (MD), ring‐polymer molecular dynamics (RPMD) simulations, and supervised machine‐learning binary classification techniques. Room‐temperature dynamics simulations started from the ambimodal transition state (TS) using the QCT, classical MD, and RPMD methods presented similar dynamics. Binary classification revealed that the initial geometry displacement from the ambimodal TS for the Diels–Alder cycloaddition of cyclopentadiene and nitroethene contributed to the branching dynamics and that the initial momenta for the intramolecular cycloaddition between a diene and triene and the Diels–Alder cycloaddition of 2‐hydroxyacrolein with 1,3‐butadiene played a significant role in the bifurcation dynamics.

Experimental and Theoretical Study of the Kinetics of the CH3 + HBr → CH4 + Br Reaction and the Temperature Dependence of the Activation Energy of CH4 + Br → CH3 + HBr.

The rate coefficient of the reaction of CH3 with HBr was measured and calculated in the temperature range 225-960 K. The results of the measurements performed in a flow apparatus with mass spectrometric detection agree very well with the quasiclassical trajectory calculations performed on a previously developed potential energy surface. The experimental rate coefficients are described well with a double-exponential fit, k1(exp) = [1.44 × 10-12 exp(219/T) + 6.18 × 10-11 exp(-3730/T)] cm3 molecule-1 s-1. The individual rate coefficients below 500 K accord with the available experimental data as does the slightly negative activation energy in this temperature range, -1.82 kJ/mol. At higher temperatures, the activation energy was found to switch sign and it rises up to about an order of magnitude larger positive value than that below 500 K, and the rate coefficient is about 50% larger at 960 K than that around room temperature. The rate coefficients calculated with the quasiclassical trajectory method display the same tendencies and are within about 8% of the experimental data between 960 and 300 K and within 25% below that temperature. The significant variation of the magnitude of the activation energy can be reconciled with the tabulated heats of formation only if the activation energy of the reverse CH4 + Br reaction also significantly increases with the temperature.