Quasiclassical Trajectory Calculations Research Articles

Zero-dimensional simulations of DC ns-pulsed plasma jet in N2 at near atmospheric pressure: validation of the vibrational kinetics

Abstract A Direct Current (DC) nanosecond (ns)-pulsed plasma jet fed with N2 at near atmospheric pressure (20 000 Pa) is studied using a transient zero-dimensional (0-D) model coupled with a two-term Boltzmann equation solver. Good agreement is observed between the simulated and measured plasma properties: including the electron density and the ratios of the N2(v = 1, 2, 3, 4) densities to the gas density. A variety of theoretical approaches are considered to determine the Vibrational-Vibrational (V-V) and Vibrational-Translational (V-T) rate coefficients. For the V-V kinetics, the simple form of an Harmonic Oscillator (sfHO), the Schwartz–Slawsky–Herzfeld (SSH) and the Forced Harmonic Oscillator (FHO) approaches are used. The SSH approach used in this study is an improved version based on the pure SSH approach. For the V-T kinetics, the sfHO, a fit function of the Semi-Classical (ffSC) calculations and a fit function of the Quasi-Classical Trajectory (ffQCT) calculations are used. The influence of these different approaches on the calculated temporal evolution profiles of the vibrational distribution functions (VDFs) within one pulse modulation cycle is revealed. It is observed that the use of these different approaches does not strongly affect the densities of the low vibrational levels (v < 5), whereas larger influences on the higher level densities are found. In addition, it is found that the simulated evolution of the VDFs are sensitive to the probabilities of the neutral wall reaction N2(v) + wall → N2(v − 1) in the range of 1 × 10−2 to 1 × 10−4. A further analysis of the wall quenching probabilities of N2(0 < v < 58) is of importance for a more accurate prediction of the VDFs.

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.

Calculations of Dissociation Dynamics of CH3OH on a Global Potential Energy Surface Reveal the Mechanism for the Formation of HCOH; Roaming Plays a Role.

The experimental observation of hydroxymethylene, HCOH, following excitation of methanol at 193 nm, was reported recently (Hockey, E. K.; McLane, N.; Martí, C.; Duckett, L.; Osborn, D. L.; Dodson, L. G. Direct Observation of Gas-Phase Hydroxymethylene: Photoionization and Kinetics Resulting from Methanol Photodissociation. J. Am. Chem. Soc. 2024, 146, 14416-14421, 10.1021/jacs.4c03090). This stimulated us to investigate a dynamic mechanism for its formation using a global potential energy surface for the ground electronic state (S0) of methanol. We show via quasi-classical trajectory calculations that hydroxymethylene is indeed formed under the reasonable assumption that the initially excited state undergoes rapid internal conversion to S0. From the trajectories, fractional yields of the six major product channels are determined as a function of excitation energy, and the rate of production of each is determined from the fractions and rate of methanol disappearance. Roaming is observed in trajectories leading to the OH and CH3 products as well as in those leading to CH2OH + H and non-reactive trajectories. A "frustrated" roaming accounts for roughly 20% of the HCOH production.

Computational study on the bifurcation mechanism in the H2CO− + CH3Cl →CH3CH2O + Cl−/H2CO + CH3 + Cl− reaction: The importance of intramolecular vibrational redistributions

We have investigated the bifurcation dynamics of the H2CO− + CH3Cl →CH3CH2O + Cl− (C-substitution channel)/H2CO + CH3 + Cl− (electron transfer channel) reaction using three different molecular dynamics (MD) methods: quasi-classical trajectory (QCT), classical MD, and ring-polymer MD simulations. All MD calculations were performed using the on-the-fly approach at the ab initio molecular orbital theory level. We found that the C-substitution channel is dominant in the classical and ring-polymer MD calculations, while the electron transfer channel is dominant in the QCT calculations. The different bifurcation mechanisms in the types of MD simulations were investigated using supervised machine-learning classification. This difference is attributed to the varying efficiency of the intramolecular vibrational redistribution process among the different MD methods. Thus, in the bifurcation mechanism of the H2CO− + CH3Cl reaction, the bifurcation fractions are primarily determined by the vibrational dynamics occurring in the later stages of the reaction.

Mode-Specific Dynamics Studies for the Multichannel C2H2 + OH Reaction.

The C2H2 + OH reaction is a key elementary reaction in acetylene oxidation, and the products forming in different reaction channels, such as C2H and CH3 radicals, are also important for subsequent reaction processes in the combustion process. In this work, we investigated the dynamics of the C2H2 + OH reaction with specific vibrational mode excitations and analyzed the mode specificity based on quasi-classical trajectory calculations on a recently developed full-dimensional potential energy surface. It is found that exciting OH stretching mode can promote the production of H + OCCH2 and CO + CH3, while the excitation of C-H symmetric/antisymmetric stretching mode of C2H2 can facilitate the H2O + C2H channel. Based on the prediction of vibrationally adiabatic and sudden vector projection models, the mode specificity in the C2H2 + OH reaction can be attributed to the difference in the degree of coupling between the initial motion mode and the reaction coordinate of each reaction path, which ultimately leads to the changes in rate constants and the product branching ratios. These findings can offer theoretical insights to regulate the branching ratio of the multichannel C2H2 + OH reaction.

State-to-State Rate Constants for the O(3P)H2(v) System: Quasiclassical Trajectory Calculations

State-to-State Rate Constants for the O(3P)H2(v) System: Quasiclassical Trajectory Calculations

Absolute rate coefficient measurements of the reactions of vibrationally cold HD+ and H3+ ions with neutral C atoms

Ion-neutral reactions are driving the formation of small molecules in the gas phase of interstellar clouds, where hydrogen molecules and their ions are by far the most important collision partners for any species in the astrochemical network. Here we present absolute rate coefficient measurements for the reactions HD++C→CH+/CD++D/H and H3++C→CH+/CH2++H2/H obtained using a recently commissioned ion-neutral collision setup at the Cryogenic Storage Ring. Our measurements with vibrationally cold ions result in significantly higher rate coefficients when compared with previous studies using internally excited ions, bringing them in better agreement with classical capture theories. Moreover, we have performed detailed quasiclassical trajectory (QCT) calculations for the HD++C reaction, using new potential energy surfaces. Our experimental results and the QCT calculations show very good agreement for the absolute cross section of the reactions, as well as for the isotope effect. These results have great potential relevance for the chemistry of the interstellar medium and the onset of organic chemistry in space. Published by the American Physical Society 2024

Merged-Beams Study of the Reaction of Cold HD+ with C atoms Reveals a Pronounced Intramolecular Kinetic Isotope Effect

We present a merged-beams study of reactions between HD+ ions, stored in the Cryogenic Storage Ring (CSR), and laser-produced ground-term C atoms. The molecular ions are stored for up to 20 s in the extreme vacuum of the CSR, where they have time to relax radiatively until they reach their vibrational ground state (within 0.5 s of storage) and rotational states with J≤3 (after 5 s). We combine our experimental studies with quasiclassical trajectory calculations based on two reactive potential energy surfaces. In contrast to previous studies with internally excited H2+ and D2+ ions, our results reveal a pronounced isotope effect, favoring the production of CH+ over CD+ across all collision energies, and a significant increase in the absolute rate coefficient of the reaction. Our experimental results agree well with our theoretical calculations for vibrationally relaxed HD+ ions in their lowest rotational states. Published by the American Physical Society 2024

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).

State-to-state dynamics and machine learning predictions of inelastic and reactive O(3P) + CO(1∑+) collisions relevant to hypersonic flows.

The state-to-state (STS) inelastic energy transfer and O-atom exchange reaction between O and CO(v), as two fundamental processes in non-equilibrium air flow around spacecraft entering Mars' atmosphere, yield the same products and both make significant contributions to the O + CO(v) → O + CO(v') collisions. The inelastic energy transfer competes with the O-atom exchange reaction. The detailed reaction mechanisms of these two elementary processes and their specific contributions to the CO relaxation process are still unclear. To address these concerns, we performed systematic investigations on the 3A' and 3A″ potential energy surfaces (PESs) of CO2 using quasi-classical trajectory (QCT) calculations. Analysis of the collision mechanisms reveals that inelastic collisions have an apparent PES preference (i.e., they tend to occur on the 3A' PES), while reactive collisions do not. Reactive rates decrease significantly when the total collision energy approaches dissociation energy, which differs from the inelastic process. Inelastic rates are generally lower than the reactive rates below ∼10 000K, except for single quantum jumps, whereas the reverse is observed above ∼10 000K. In addition, by combining QCT with convolutional neural networks, we have established neural network (NN)-STS1 (inelastic) and NN-STS2 (reactive) models to generate all possible STS cross sections. The NN-based models accurately reproduce the results calculated from QCT calculations. In this study, all calculations have been focused on analyzing collisions at the ground rotational level.

Quasi-Classical Trajectory Calculation of Rate Constants Using an Ab Initio Trained Machine Learning Model (aML-MD) with Multifidelity Data.

Machine learning (ML) provides a great opportunity for the construction of models with improved accuracy in classical molecular dynamics (MD). However, the accuracy of a ML trained model is limited by the quality and quantity of the training data. Generating large sets of accurate ab initio training data can require significant computational resources. Furthermore, inconsistent or incompatible data with different accuracies obtained using different methods may lead to biased or unreliable ML models that do not accurately represent the underlying physics. Recently, transfer learning showed its potential for avoiding these problems as well as for improving the accuracy, efficiency, and generalization of ML models using multifidelity data. In this work, ab initio trained ML-based MD (aML-MD) models are developed through transfer learning using DFT and multireference data from multiple sources with varying accuracy within the Deep Potential MD framework. The accuracy of the force field is demonstrated by calculating rate constants for the H + HO2 → H2 + 3O2 reaction using quasi-classical trajectories. We show that the aML-MD model with transfer learning can accurately predict the rate constants while reducing the computational cost by more than five times compared to the use of more expensive quantum chemistry training data sets. Hence, the aML-MD model with transfer learning shows great potential in using multifidelity data to reduce the computational cost involved in generating the training set for these potentials.

Role of the Vibrational and Translational Energies in the CN(v)+C2H6(ν1, ν2, ν5 and ν9) Reactions. A Theoretical QCT Study.

Quasi-classical trajectory (QCT) calculations were conducted on the newly developed full-dimensional potential energy surface, PES-2023, to analyse two critical aspects: the influence of vibrational versus translational energy in promoting reactivity, and the impact of vibrational excitation within similar vibrational modes. The former relates to Polanyi's rules, while the latter concerns mode selectivity. Initially, the investigation revealed that independent vibrational excitation by a single quantum of ethane's symmetric and asymmetric stretching modes (differing by only 15 cm-1) yielded comparable dynamics, reaction cross-sections, HCN(v) vibrational product distributions, and scattering distributions. This observation dismisses any significant mode selectivity. Moreover, an equivalent amount of energy provided as translational energy (at total energies of 9.6 and 20.0 kcal mol-1) gave rise to slightly lower reactivity compared to the same amount of energy provided as vibrational energy. This effect is more evident at low energies, presenting a counterintuitive scenario in an 'early transition state' reaction. These findings challenge the straightforward application of Polanyi's rules in polyatomic systems. Regarding CN(v) vibrational excitation, our calculations reveal that the reaction cross-section remains practically unaffected by this vibrational excitation, suggesting that the CN stretching mode is a spectator mode. The results were rationalized by considering several factors: the strong coupling between different vibrational modes, and between vibrational modes and the reaction coordinate; and a significant vibrational energy redistribution within the ethane reactant before collision. This redistribution creates an unphysical energy flow, resulting in loss of adiabaticity and vibrational memory before the reactants' collision. These theoretical findings require future confirmation through experimental or theoretical quantum mechanical studies, which are currently unavailable.

Non-IRC Mechanism of Bimolecular Reactions with Submerged Barriers: A Case Study of Si+ + H2O Reaction.

Chemical reactions with submerged barriers may feature interesting dynamic behaviors that are distinct from those with substantial barriers or those entirely dominated by capture. The Si+ + H2O reaction is a prototypical example, involving even two submerged saddle points along the reaction path: one for the direct dissociation of H (H-dissociation SP) and another for H migration from the O-side to the Si-side (H-migration SP). We investigated the intricacies of this process by employing quasi-classical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface. Through careful trajectory analysis, an interesting nonintrinsic reaction coordinate mechanism was found to play an important role in producing SiOH+ and H. This new pathway is featured as that the H atoms do not form HSiOH+ complexes along the minimum-energy path but directly dissociate into the products after passing through the H-migration SP. Furthermore, based on artificially scaled potential energy surfaces (PESs), the impact of barrier height on the reaction is also explored. This work provides new insights into the dynamics of the Si+ + H2O reaction and enriches our understanding of reactions with submerged barriers.

Supercollisions of NaCl + NaCl on an Accurate Full-Dimensional Potential Energy Surface.

An accurate, global, full-dimensional potential energy surface (PES) of NaCl + NaCl has been constructed by the fundamental invariant-neural network (FI-NN) fitting based on roughly 13,000 ab initio energies at the level of CCSD(T)-F12a/aug-cc-pVTZ, with the small fitting error of 0.16 meV. Extensive quasiclassical trajectory (QCT) calculations were performed on this PES to investigate the energy transfer process of the NaCl + NaCl collision at four different collision energies. Various quantities were obtained, including the cross-sections, energy transfer probability, average energy transfer, and collision lifetime. The probabilities of energy transfer (P(ΔE)) for prompt trajectories, nonreactive trajectories, and reactive trajectories deviate from a simple exponential decay pattern. Instead, a noteworthy probability is observed in the high-energy transfer region, indicative of supercollisions. The formation of the (NaCl)2 complex, coupled with a comparatively extended collision lifetime, promotes vibrational excitation in NaCl molecules. The reactive trajectories exhibit enhanced energy transfer, attributed to the longer lifetime of the NaCl dimer. This study not only provides an accurate and extensive understanding of the NaCl + NaCl collision dynamics but also reveals intriguing phenomena, such as supercollisions and enhanced energy transfer in reactive trajectories, shedding light on the complex intricacies of molecular interactions.

High-level analytical potential-energy-surface-based dynamics of the OH- + CH3CH2Cl SN2 and E2 reactions in full (24) dimensions.

We develop a coupled-cluster full-dimensional global potential energy surface (PES) for the OH- + CH3CH2Cl reactive system, using the Robosurfer program package, which automatically samples configurations along PES-based trajectories as well as performs ab initio computations with Molpro and fitting with the monomial symmetrization approach. The analytical PES accurately describes both the bimolecular nucleophilic substitution (SN2) and elimination (E2) channels leading to the Cl- + CH3CH2OH and Cl- + H2O + C2H4 products, respectively, and allows efficient quasi-classical trajectory (QCT) simulations. QCT computations on the new PES provide accurate statistically-converged integral and differential cross sections for the OH- + CH3CH2Cl reaction, revealing the competing dynamics and mechanisms of the SN2 and E2 (anti, syn, β-α transfer) channels as well as various additional pathways leading to induced inversion of the CH3CH2Cl reactant, H-exchange between the reactants, H2O⋯Cl- complex formation, and H2O + CH3CHCl- products via proton abstraction.

Substitutional Control of Non-statistical Dynamics in the Thermal Deazetization of Tetracyclic Azo compounds

Dynamical control of reactivity for the deazetization of endo,endo-9,10-diazatetracyclo[3.3.2.02,4.06,8]dec-9-ene (3) is studied using on-the-fly quasi-classical trajectory (QCT) calculations at the density functional theory (DFT). Two degenerate homotropilidenes, 4 and 5...

Rate coefficients for the O + H2 and O + D2 reactions: how well ring polymer molecular dynamics accounts for tunelling.

We present here extensive calculations of the O(3P) + H2 and O(3P) + D2 reaction dynamics spanning the temperature range from 200 K to 2500 K. The calculations have been carried out using fully converged time-independent quantum mechanics (TI QM), quasiclassical trajectories (QCT) and ring polymer molecular dynamics (RPMD) on the two lowest lying adiabatic potential energy surfaces (PESs), 13A' and 13A'', calculated by Zanchet et al. [J. Chem. Phys., 2019, 151, 094307]. TI QM rate coefficients were determined using the cumulative reaction probability formalism on each PES including all of the total angular momenta and the Coriolis coupling and can be considered to be essentially exact within the Born-Oppenheimer approximation. The agreement between the rate coefficients calculated by using QM and RPMD is excellent for the reaction with D2 in almost the whole temperature range. For the reaction with H2, although the agreement is very good above 500 K, the deviations are significant at lower temperatures. In contrast, the QCT calculations largely underestimate the rate coefficients for the two isotopic variants due to their inability to account for tunelling. The differences found in the disagreements between RPMD and QM rate coefficients for the reactions for both the isotopologues are indicative of the ability of the RPMD method to accurately describe systems where tunelling plays a relevant role. Considering that both reactions are dominated by tunelling below 500 K, the present results show that RPMD is a very powerful tool for determining rate coefficients. The present QM rate coefficients calculated on adiabatic PESs slightly underestimate the best global fits of the experimental measurements, which we attribute to the intersystem crossing with the singlet 11A' PES.

High-Temperature Nonequilibrium Air Chemistry from First Principles

We present first-principles calculations for chemically reacting five-species air (N2, N, O2, O, NO) over a range of gas temperatures (T=5000–30,000 K), relying exclusively on ab initio potential energy surfaces (PESs) from the University of Minnesota Computational Chemistry group to describe the forces between atoms. We use these PESs within direct molecular simulations (DMSs) and quasi-classical trajectory (QCT) calculations to determine the coupling of internal energy relaxation to chemical reactions. From DMS we extract the internal energy populations of diatomic species during the quasi-steady-state (QSS) dissociation phase and, for all diatomic species, observe depleted high-energy tails relative to corresponding Boltzmann distributions. A comparison of thermochemical equilibrium rate coefficients (from QCT) with those during QSS (from DMS) helps quantify the macroscopic effects of vibrationally depleted distributions on dissociation. In contrast, Zeldovich exchange reactions are almost unaffected by these vibrationally depleted distributions. Unlike dissociation, they do not exhibit significant vibrational bias and take place at near-thermal rates at all temperatures studied. Furthermore, we quantify the amount of vibrational and rotational energy removed and/or gained in exchange and dissociation reactions. Such macroscopic quantities are of interest for enhancing the fidelity of multitemperature nonequilibrium chemistry models used in computational fluid dynamics codes.

Two-color polarization spectroscopy measurements of Zeeman state-to-state collision induced transitions of nitric oxide in binary gas mixtures.

We investigated collision induced transitions in the (0, 0) band of the A2Σ+-X2Π electronic transition of nitric oxide (NO) using two-color polarization spectroscopy (TCPS). Two sets of TCPS spectra for 1% NO, diluted in different buffer gases at 295K and 1 atm, were obtained with the pump beam tuned to the R11(11.5) and OP12(1.5) transitions. The buffer gases were He, Ar, and N2. The probe was scanned while the pump beam was tuned to the line center. Theoretical TCPS spectra, calculated by solving the density matrix formulation of the time-dependent Schrödinger wave equation, were compared with the experimental spectra. A collision model based on the modified exponential-gap law was used to model the rotational level-to-rotational level collision dynamics. A model for collisional transfer from an initial to a final Zeeman state was developed based on the difference in cosine of the rotational quantum number J projection angle with the z-axis for the two Zeeman states. Rotational energy transfer rates and Zeeman state collisional dynamics were varied to obtain good agreement between theory and experiment for the two different TCPS pump transitions and for the three different buffer gases. One key finding, in agreement with quasi-classical trajectory calculations, is that the spin-rotation changing transition rate in the A2Σ+ level of NO is almost zero for rotational quantum numbers ≥8. It was necessary to set this rate to near zero to obtain agreement with the TCPS spectra.

Assessing the dynamics of CO adsorption on Cu(110) using the vdW-DF2 functional and artificial neural networks

In this work, we revisit the dynamics of carbon monoxide molecular chemisorption on Cu(110) by using quasi-classical trajectory calculations. The molecule–surface interaction is described through an atomistic neural network approach based on Density Functional Theory calculations using a nonlocal exchange–correlation (XC) functional that includes the effect of long-range dispersion forces: vdW-DF2 [Lee et al. Phys. Rev. B, 82, 081101 (2010)]. With this approach, we significantly improve the agreement with experiments with respect to a similar previous study based on a semi-local XC functional. In particular, we obtain excellent agreement with molecular beam experimental data concerning the dependence of the initial sticking probability on surface temperature and impact energy at normal incidence. For off-normal incidence, our results also reproduce two trends observed experimentally: (i) the preferential sticking for molecules impinging parallel to the [1̄10] direction compared to [001] and (ii) the change from positive to negative scaling as the impact energy increases. Nevertheless, understanding the origin of some remaining quantitative discrepancies with experiments requires further investigations.