Quasi-classical Trajectory Method Research Articles

Toward a Specific Reaction Parameter Density Functional for H2 + Ni(111): Comparison of Theory with Molecular Beam Sticking Experiments

Accurate barriers for rate controlling elementary surface reactions are key to understanding, controlling, and predicting the rate of overall heterogeneously catalyzed processes. The specific reaction parameter approach to density functional theory (SRP-DFT) in principle allows chemically accurate barrier heights to be obtained for molecules dissociating on metal surfaces, and such accurate barriers are now available for four H2–metal and three CH4–metal systems. Also, there is some evidence that SRP density functionals (SRP-DFs) may be transferable among systems in which the same molecule interacts with a low-index face of metals belonging to the same group. To extend the SRP database, here we take a first step to obtain an SRP-DF for H2 + Ni(111) by comparing sticking probabilities (S0) computed with the quasi-classical trajectory method with S0 measured in several molecular beam experiments, using potential energy surfaces computed with several density functionals. We find that the SRP-DF for H2 + Pt(111) is not transferable to H2 + Ni(111). On the other hand, the PBE-vdW2 functional describes the molecular beam experiments on H2 + Ni(111), which we deem to be most accurate with chemical accuracy and may therefore be considered a candidate SRP-DF for this system, of which the quality still needs to be confirmed through comparison with an experiment to which it was not fitted. However, the different molecular beam sticking measurements that we considered showed discrepancies with one another and with the theory for incidence energies > 0.2 eV, and it would be good if better defined and more accurate experiments would be done for these energies to resolve these differences.

Theoretical Study for the Ground Electronic State of the Reaction OH + SO → H + SO2.

The reaction OH + SO → H + SO2 plays an important role in the combustion of sulfur-containing fuels and the environment. Its reaction profile resembles that of OH + CO → H + CO2, which presents a prototypical reaction with the formation of deep complexes. In this work, a new potential energy surface (PES) for the OH + SO → H + SO2 reaction is developed based on ca. 39 200 data points calculated at the level of the explicitly correlated unrestricted coupled cluster method with single, double, and perturbative triple excitations with the augmented correlation-consistent polarized triple zeta basis set (CCSD(T)-F12a/AVTZ). The PES is invariant with respect to the permutation of the two identical oxygen atoms, which is guaranteed by the permutation-invariant polynomials as the input layer of the neural network. Using this PES, the quasiclassical trajectory method is employed to study the collision energy transfer between H and SO2 at the experimental translational energy of 59 kcal mol-1. The predicted large integral cross sections for trajectories producing SO2 with high vibrational energy and populations of the SO2 vibrational energy are in good agreement with the recent experimental and theoretical results. Detailed analysis shows that there are two possible mechanisms, a direct mechanism (without passing through HOSO or the HSO2 well) and an indirect one (passing through one or both wells). The latter dominates in producing SO2 with high vibrational energy.

The effect of collision energy on the stereodynamics of the reaction triatomic NH2 system

The stereodynamics of the reaction H(2S) + NH (v = 0, 1, 2, 3; j = 0) → N(4S) + H2 are studied using the quasi-classical trajectory method on a double many-body expansion potential energy surface to understand the alignment and orientation of the product molecules in the collision energy range of 2–20 kcal·mol−1. The vibrational–rotational quantum number of the NH molecules is specifically investigated for v = 0, 1, 2, and 3 and j = 0. The differential cross section [DCS; ], and average rotational alignment factor are calculated. The stereodynamics results indicate that the reagent vibrational quantum number and initial collision energy significantly affect the distributions of the k–j′, k–k′–j′ and k–k′ vector correlations along with In addition, while DCS is extremely sensitive to the collision energy, it is not significantly affected by the vibrational excitation of the reagents.

Hypersonic flow over Stardust Re-entry Capsule using ab-initio based chemical reaction model

Hypersonic air flow around the Stardust Re-entry Vehicle for diverse ambient conditions is investigated using the Direct Simulation Monte Carlo (DSMC) method. In the present work, the flow field and surface properties on the re-entry vehicle are compared for simulations employing two different chemical reaction models: the traditional phenomenological Total Collision Energy (TCE) model and a new chemical reaction model based on ab-initio principles. The reactive cross-section used in the new chemical reaction model are calculated using Quasi-Classical Trajectory method and employs highly accurate Potential Energy Surfaces. Conditions prevailing at 68 km, 80 km and 100 km are simulated and for two re-entry speeds. It is found that the DSMC simulations with the new ab-initio based chemical reaction model predicts higher heat flux and heat load on the re-entry vehicle surface compared to the simulations employing the TCE model. The difference in the heat flux predicted by the two models is most evident at 80 km. This is a significant inference for engineers designing the Thermal Protection Systems. It is observed that there are significant differences in the estimation of mole fraction of NO by the two models. The limitations of the present model and future scope are discussed in detail.

Stereo-dynamics of the reaction C + SH(D,T)(v = 0, j = 0) → H(D,T) + CS based on a recent excited state potential energy surface

The isotopic substitution effect on title reactions based on a recently developed potential energy surface of the HCS(A2A″) is studied by the quasi-classical trajectory method. The total integral cross sections (ICSs) and rate constant are presented for C + SH(D,T) → H(D,T) + CS reactions, while the vibrational state resolved ICSs, differential cross sections(DCSs), as well as two angle distribution functions P(θr), P(Φr) of products at different collision energies are also investigated. At high collision energies, the DCS for C + SH → H + CS reaction has obvious backward scattering characteristic, while for other two reactions the forward scattering feature is displayed. The distribution P(θr) of products is symmetric for all the reactions, but molecular orientation of the products becomes weaker when the mass of reactants gets greater. By analyzing P(Φr), the isotopic substitution dependence of the orientation and alignment for product molecules are also found. This kind of stereo-dynamics provides the foundation for manipulating chemical reactions.

Vibrational quenching and reactive processes of weakly bound molecular ions colliding with atoms at cold temperatures

We present a study of vibrational quenching and chemical processes of molecular ions immersed in an ultracold atomic gas by means of the quasi-classical trajectory (QCT) method. In particular, BaRb$^+(v)$ + Rb collisions are studied at cold temperatures revealing a highly efficient energy transfer between the translational degrees of freedom and internal degrees of the molecular ion. Thus leading to a large vibrational quenching cross section which follows the Langevin capture model prediction. These results play a key role on the understanding of relaxation phenomena of cold molecular ions in ultracold gases as well as in the fate of the molecules emerging trough ion-neutral-neutral three-body recombination in an cold and dense environment.

Transferability of the Specific Reaction Parameter Density Functional for H2 + Pt(111) to H2 + Pt(211).

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD3 + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H2 + Pt(111) with chemical accuracy is also capable of accurately describing H2 + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H2 + Pt(111). Our calculations used the Born–Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H2. The theoretical results for sticking of H2 and D2 on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron–hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron–hole pair excitation on sticking are found.

Dissection of the multichannel reaction of acetylene with atomic oxygen: from the global potential energy surface to rate coefficients and branching dynamics.

The O(3P) + C2H2 reaction is the first step in acetylene oxidation. The accurate kinetic data and the understanding of the reaction dynamics is of great importance. To this end, a full-dimensional global potential energy surface (PES) for the ground triplet state of the O(3P) + C2H2 reaction is constructed based on approximately 85 000 ab initio points calculated at the level of explicitly correlated unrestricted coupled cluster single, double, and perturbative triple excitations with the explicitly correlated polarized valence triple zeta basis set (UCCSD(T)-F12b/VTZ-F12). The PES is fit using the permutation invariant polynomial-neural network (PIP-NN) approach with a total root mean square error of 0.21 kcal mol-1. The key topographic features of the PES, including multiple potential wells and saddle points along different reaction pathways, are well represented by this fit PES. The kinetics and dynamics of the O(3P) + C2H2 reaction are investigated using the quasi-classical trajectory (QCT) method. The calculated rate coefficients are in good agreement with experimental data over a wide temperature range, especially when the temperature is lower than 1500 K. The product branch ratio has also been determined, which indicates the H + HCCO channel as the dominant reaction pathway at 298-3000 K, accounting for 80-90% of the overall rate coefficient, in agreement with experimental observations. The dynamics of the reaction is analyzed in detail.

Temperature Dependence of the Reaction HCl + OH → Cl + H2O between 140 and 1100 K

Temperature dependence of the molecule‐radical reaction HCl + OH → Cl + H2O at temperatures between 140 and 1100 K is studied using a quasiclassical trajectory method. Potential energy surfaces are formulated using pair‐wise additive two‐body, nonadditive three‐body, and four‐body analytic forms and long‐range interactions. At temperatures above 300 K, the reaction occurs by direct collisions and the calculated rate constant fits the Arrhenius equation kdir = 4.85 × 10−12 exp.(−631 ± 10/T) cm3/molecule/s. At temperatures below 300 K, the reaction is driven by an attractive potential and occurs through the formation of a ClH…OH collision complex, which is sufficiently long‐lived to enhance quantum mechanical tunneling of the H atoms. The sum of the direct and complex‐mode reaction rates effectively describes the reaction occurring at temperatures in the 140–1100 K temperature range.

A new potential energy surface of the LiHO+ system and the dynamics studies of the O + LiH+ reaction

A potential energy surface (PES) for the lowest 2A′ state of LiHO+ is constructed using ab initio calculations. The MRCI method with AVQZ and AV5Z basis sets is employed during the calculations. The artificial neural network is utilized to fit the analytical PES based on 28,552 energy points which are extrapolated to the complete basis set limit. The reaction dynamics of the O + LiH+ ⟶ Li+ + HO reaction is investigated by means of quasi-classical trajectory method. The dynamics results show that the reaction mechanism dominating the title reaction changes from indirect to direct mechanism with increasing collision energy.

Accurate potential energy surface of H2S+(X 2 A″) via extrapolation to the complete basis set limit and its use in dynamics study of reaction.

The single-sheeted potential energy surface (PES) of is developed based on the ab initio energies calculated by the multi-reference configuration interaction method including the Davidson correction. All the ab initio energies are first calculated using aug-cc-pVQdZ and aug-cc-pV5dZ basis sets, which are then extrapolated to the complete basis set (CBS) limit. A switching function is developed to model the transition of to . The many-body expansion formalism is employed to obtain the PES by fitting such CBS energies and the root-mean square derivation is 0.0367 eV. The topographical features of the present PES are examined in detail, which are well consistent with previous studies. The quasiclassical trajectory method is subsequently utilized to study the reaction. The capture time, integral cross sections, and rovibrational distributions are calculated. By examining the capture time, it can be concluded that the title reaction is mainly controlled by the indirect mechanism for lower collision energies, while the direct and indirect mechanisms coexist and the latter plays a dominant role for higher collision energies.

Comparison of Potential Energy Surface and Computed Rate Coefficients for Dissociation

Comparisons are made between potential energy surfaces (PESs) for and collisions and between rate coefficients for dissociation that were computed using the quasi-classical trajectory (QCT) method on these PESs. For , Laganà’s empirical London–Eyring–Polanyi–Sato surface is compared with one from NASA Ames Research Center based on ab initio quantum chemistry calculations. For , two ab initio PESs (from NASA Ames and from the University of Minnesota) are compared. These use different methods for computing the ground state electronic energy for but give similar results. Thermal dissociation rate coefficients, for the 10,000–30,000 K temperature range, have been computed using each PES, and the results are in excellent agreement. Quasi-stationary state (QSS) rate coefficients using both PESs have been computed at these temperatures using the direct molecular simulation method (DMS) of Schwartzentruber and coworkers. The QSS rate coefficients are up to a factor of 5 lower than the thermal ones, and the thermal and QSS values bracket the results of shock-tube experiments. It is concluded that the combination of ab initio quantum chemistry PESs and QCT calculations provides an attractive approach for the determination of accurate high-temperature rate coefficients for use in aerothermodynamics modeling.

State-to-state quantum dynamics studies of the H + LiH+ → Li+ + H2 reaction

ABSTRACTQuantum dynamical calculations of the H + LiH+ → Li+ + H2 reaction were performed based on the potential energy surface (PES) reported by Dong et al. (RSC Adv. 7, 7008 (2017)) using the time-dependent quantum wave packet method in collision energy range from 0.01 to 1.0 eV. Dynamics properties such as reaction probability, integral cross section, differential cross section (DCS), and thermal rate constant of the H + LiH+ → Li+ + H2 reaction were reported at the state-to-state level of theory and compared with available theoretical calculations. The results indicated that present values are in good agreement with results obtained from the quasi-classical trajectory method. However, large differences can be found between present values and previous quantum results. This can be attributed to the different PESs used in the calculation and the CS approximation was adopted in previous theoretical studies. In addition, the ‘rebound’ reaction mechanism was proposed in previous theoretical studies in a high collision energy range. However, the DCS scattering signals calculated in the present work indicated that complex-forming and direct abstract reaction mechanisms are dominant in low and high collision energies, respectively.

Mode-specific and bond-selective dissociative chemisorption of CHD3 and CH2D2 on Ni(111) revisited using a new potential energy surface

Dissociative chemisorption of methane on a nickel surface is a prototypical system for studying mode-specific chemistry in gas-surface reactions. We recently developed a fifteen-dimensional potential energy surface for this system which has proven to be chemically accurate in reproducing the measured absolute dissociative sticking probabilities of CHD3 in thermal conditions and with vibrational excitation on Ni(111) at high incident energies. Here, using this new potential energy surface, we explored mode specificity and bond selectivity for CHD3 and CH2D2 dissociative chemisorption at low incidence energies down to ~50 kJ/mol via a quasi-classical trajectory method. Our calculated dissociation probabilities are consistent with previous theoretical and experimental ones with an average shift in translational energy of ~8 kJ/mol. Our results very well reproduce the C–H/C–D branching ratio upon the C–H local mode excitation, which can be rationalized by the sudden vector projection model. Quantitatively, however, the calculated dissociative sticking probabilities are systematically larger than experimental ones, due presumably to the artificial zero point energy leakage into reaction coordinate. Further high-dimensional quantum dynamics calculations are necessary for acquiring a chemically accurate description of methane dissociative chemisorption at low incident energies.

Vibrational enhancement in the dynamics of ammonia dissociative chemisorption on Ru(0001).

The vibrationally selective dissociative chemisorption dynamics of ammonia on the Ru(0001) surface is investigated using a quasi-classical trajectory (QCT) method on a new global potential energy surface (PES) with twelve dimensions. The PES is constructed by fitting 92 524 density functional theory points using the permutation invariant polynomial-neural network method, which rigorously enforces the permutation symmetry of the three hydrogen atoms as well as the surface periodicity. The PES enables highly efficient QCT simulations as well as future quantum dynamical studies of the scattering/dissociation dynamics. The QCT calculations yield satisfactory agreement with experiment and suggest strong activation of dissociation by both translational and vibrational excitations.

Scattering of CO with H2O: Statistical and classical alternatives to close-coupling calculations.

Energy transfer in inelastic atom-molecule and molecule-molecule collisions can be described theoretically using the quantum-mechanical close-coupling method. Unfortunately, for bimolecular collisions implying heavy colliders and/or for which the potential energy surface has a deep well, the resulting coupled equations become numerically intractable and approximate methods have to be employed. H2O-CO collisions provide an important example for which close-coupling calculations are not feasible. In this paper, we investigate the accuracy of three approximate methods (the coupled states method, the quasi-classical trajectory method, and the statistical adiabatic channel model) to describe inelastic collisions of H2O with CO. We perform scattering calculations on a recent 5D potential energy surface, and we compare the results of the three approximate methods to fully converged close-coupling calculations at energies below 300 cm-1 and at low values of the total angular momentum. We show that the statistical method provides an attractive alternative to fully quantum mechanical close-coupling calculations at low collision energies, while the quasi-classical method is more advantageous at high energies.

Cross-sections for O2 + N system using the QCT method

Collision Induced Exchange cross-sections for the Zeldovich reaction N2+O⇌NO+N for high energy atom-molecular collisions are calculated using the Quasi-Classical Trajectory method. The dynamical study of O2+N collision is conducted using the 2A′ and 4A′ NO2 PESs reported Sayos et al. Cross-sections for the reverse exchange reaction involving NO + O collisions are also calculated and reported. In addition to these exchange reactions, Collision Induced Dissociation cross-sections for dissociation of molecules are also published. Overall, a cross-section database for four important atom-molecule reactions of the air chemistry is provided as supplementary material with this paper.

Flame Inhibition Chemistry: Rate Coefficients of the Reactions of HBr with CH3 and OH Radicals at High Temperatures Determined by Quasiclassical Trajectory Calculations

Reactions of HBr with radicals are involved in atmospheric chemistry and in the mechanism of operation of bromine-containing flame retardants. The rate coefficients for two such reactions, HBr + OH and HBr + CH3, are available from earlier experiments at near or below room temperature, relevant for atmospheric chemistry, and in this domain, the activation energy for both has been found to be negative. However, no experimental data are available at combustion temperatures. In this work, to provide reliable data needed for modeling the action of brominated flame suppressants, we used the quasiclassical trajectory (QCT) method in combination with high-level ab initio potential energy surfaces to evaluate the rate coefficients of the two title reactions at combustion temperatures. The QCT calculations have been validated by reproducing the experimental rate coefficients at room temperature. At temperatures between 600 and 3200 K, the QCT rate coefficients display positive activation energies. We recommend the...

Globally Accurate Potential Energy Surface for HCS(A2A″) by Extrapolation to the Complete Basis Set Limit.

A global potential energy surface (PES) representation of the C(3P) + SH(X 2Π) → H(2S) + CS(a 3Π) system is developed by fitting plenty of precise energies obtained through the ab initio calculation with aug-cc-pV QZ and aug-cc-pV5Z basis sets via extrapolation to the complete basis set limit. The topographical characteristics of the PES are examined in detail, and it is found that they agree well with previous calculations available in the literature. By utilizing the PES of HCS(A2A″), the corresponding reaction is investigated using the quasi-classical trajectory (QCT) method in the collision energy range of 0.08-1.0 eV. The minimum energy paths (MEPs) calculated on the basis of the present PES indicate that the C(3P) + SH(X 2Π) → H(2S) + CS(a 3Π) reaction is exothermic, with the exothermicity ∼0.204 eV. The calculation for the capture time indicates that the reaction is mainly governed by the indirect mechanism at the lower collision energy, while, for higher collision energy, the direct mechanism is in coexistence with the indirect mechanism, and the latter one plays a dominant role.

Dissociation cross section for high energy O2-O2 collisions.

Collision-induced dissociation cross section database for high energy O2-O2 collisions (up to 30 eV) is generated and published using the quasiclassical trajectory method on the singlet, triplet, and quintet spin ground state O4 potential energy surfaces. At equilibrium conditions, these cross sections predict reaction rate coefficients that match those obtained experimentally. The main advantage of the cross section database based on ab initio computations is in the study of complex flows with high degree of non-equilibrium. Direct simulation Monte Carlo simulations using the reactive cross section databases are carried out for high enthalpy hypersonic oxygen flow over a cylinder at rarefied ambient conditions. A comparative study with the phenomenological total collision energy chemical model is also undertaken to point out the difference and advantage of the reported ab initio reaction model.