Previous Quasiclassical Trajectory Research Articles

Ring-Polymer Molecular Dynamics Calculations of Thermal Rate Coefficients and Branching Ratios for the Interstellar H3+ + CO → H2 + HCO+/HOC+ Reaction and Its Deuterated Analogue.

The reaction between H3+ and CO is important in understanding the H3+ destruction mechanism in the interstellar medium. In this work, thermal rate coefficients for the H3+ + CO and D3+ + CO reactions are calculated using ring-polymer molecular dynamics (RPMD) on a high-level machine-learning potential energy surface. The RPMD results agree well with the classical molecular dynamics results, where nuclear quantum effects are completely ignored, whereas the agreement between the RPMD results and the previous quasi-classical trajectory is good only at low temperatures. The calculated [HCO+]/[HOC+] product branching ratios decrease as the temperature increases, and the product branching is exclusively determined by the initial collisional orientation, which governs the formation of an ion-dipole complex, H3+···CO or H3+···OC, that dissociates into H2 + HCO+ or H2 + HOC+, respectively, via a direct mechanism. However, the contribution of the indirect mechanism via the rearrangement between H3+···CO and H3+···OC increases as the temperature increases, although its absolute fraction is small.

Mechanism analysis of reaction based on the quantum state-to-state dynamics**Project supported by the National Natural Science Foundation of China (Grant No. 11674198), the Taishan Scholar Project of Shandong Province, China (Grant No. ts201511025), and the Science Fund from the Shandong Provincial Laboratory of Biophysics.

We present a state-to-state dynamical calculation on the reaction S++H2→ SH+ + H based on an accurate X2A″ potential surface. Some reaction properties, such as reaction probability, integral cross sections, product distribution, etc., are found to be those with characteristics of an indirect reaction. The oscillating structures appearing in reaction probability versus collision energy are considered to be the consequence of the deep potential well in the reaction. The comparison of the present total integral cross sections with the previous quasi-classical trajectory results shows that the quantum effect is more important at low collision energies. In addition, the quantum number inversion in the rotational distribution of the product is regarded as the result of the heavy–light–light mass combination, which is not effective for the vibrational excitation. For the collision energies considered, the product differential cross sections of the title reaction are mainly concentrated in the forward and backward regions, which suggests that there is a long-life intermediate complex in the reaction process.

Quantum dynamics calculations reveal temperature independence of kinetic isotope effect of the OH + HBr/DBr reaction.

The reaction of OH radicals with HBr plays a key role in atmospheric chemistry as the reaction, OH + HBr → Br + H2O, produces Br atoms that destroy ozone. The experimental measurements of the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) found that the kinetic isotope effects are temperature-independent. However, previous quasi-classical trajectory calculations on an accurate ab initio potential energy surface showed that the kinetic isotope effect is temperature-dependent. By contrast, the present full-dimensional time-dependent quantum dynamics calculations on the same potential energy surface find that the kinetic isotope effect is temperature-independent, agreeing well with the experimental studies both qualitatively and quantitatively. Furthermore, the rate constants from both quantum dynamics and quasi-classical trajectory calculations have a peak at around 15 K whereas the experimental data are not available in this low temperature range. The good agreement of the temperature-dependence of kinetic isotope effects between the present quantum dynamics calculations and the experimental measurements indicates that the kinetic isotope effect of k(OH + HBr)/k(OH + DBr) should be temperature-independent and the peak of the rate constants from the theoretical calculations call for experimental measurements at a very low temperature range.

Zero-point energy conservation in classical trajectory simulations: Application to H2CO.

A new approach for preventing zero-point energy (ZPE) violation in quasi-classical trajectory (QCT) simulations is presented and applied to H2CO "roaming" reactions. Zero-point energy may be problematic in roaming reactions because they occur at or near bond dissociation thresholds and these channels may be incorrectly open or closed depending on if, or how, ZPE has been treated. Here we run QCT simulations on a "ZPE-corrected" potential energy surface defined as the sum of the molecular potential energy surface (PES) and the global harmonic ZPE surface. Five different harmonic ZPE estimates are examined with four, on average, giving values within 4 kJ/mol-chemical accuracy-for H2CO. The local harmonic ZPE, at arbitrary molecular configurations, is subsequently defined in terms of "projected" Cartesian coordinates and a global ZPE "surface" is constructed using Shepard interpolation. This, combined with a second-order modified Shepard interpolated PES, V, allows us to construct a proof-of-concept ZPE-corrected PES for H2CO, V eff, at no additional computational cost to the PES itself. Both V and V eff are used to model product state distributions from the H + HCO → H2 + CO abstraction reaction, which are shown to reproduce the literature roaming product state distributions. Our ZPE-corrected PES allows all trajectories to be analysed, whereas, in previous simulations, a significant proportion was discarded because of ZPE violation. We find ZPE has little effect on product rotational distributions, validating previous QCT simulations. Running trajectories on V, however, shifts the product kinetic energy release to higher energy than on V eff and classical simulations of kinetic energy release should therefore be viewed with caution.

Quasiclassical trajectory study of the C(¹D) + H₂ → CH + H reaction on a new global ab initio potential energy surface.

Quasiclassical trajectory (QCT) calculations have been performed on a new global ab initio potential energy surface (PES) for the singlet ground state (1(1)A') of the CH2 reactive system. Our new PES can give a very good description of the well and asymptote regions, and particularly regions around conical intersections (CIs) and of van der Waals (vdW) interactions. The integral cross sections, differential cross sections, and product rovibrational state distributions for the C((1)D) + H2 → CH + H reaction have been investigated in a wide range of collision energies. The present integral cross sections are much larger than the previous QCT results at low collision energies, which can be attributed to the differences of the PESs in the regions around the CIs and vdW complexes. The thermal rate coefficients in the temperature range 200-1500 K have also been calculated and very good agreement with experiment is obtained.

Adiabatic Quantum Dynamics of CH(X2Π) + H(2S) Reactions on the CH2(X̃3A″) Surface and Role of the Excited Electronic States

We present the Born-Oppenheimer (BO) quantum mechanical (QM) dynamics of the CH decay (d) CH(X2Π) + H(2S) → C(3P) + H2(X1Σ(g)(+)) and of the H exchange reaction (e) CH(X2Π) + H′(2S) → CH′(X2Π) + H(2S) on the CH2 X̃3A″ adiabatic potential energy surface (PES) of Harding et al. (J. Phys. Chem. 1993, 97, 5472). A thorough analysis of the correlation diagram of the four lowest CH2 electronic states, as well as Renner-Teller and spin–orbit nonadiabatic test calculations on the X̃3A″, ã1A′, and b̃1A″ coupled PESs, validate the X̃3A″ BO results, confirming that these reactions occur essentially on the uncoupled X̃3A″ ground surface. We consider the CH molecule in the ground vibrational state and in the four lowest rotational states j0. Thus, we obtain initial-state resolved reaction probabilities, cross sections, and rate constants by propagating coupled-channel real wave packets and performing flux analyses. If J is the total angular momentum quantum number and K is its projection along the body-fixed z axis, CH + H gives essentially the C + H2 products via a barrierless K-inhibited insertion, CH2 resonances at low J, and large cross sections near the threshold. These cross sections decrease strongly with collision energy and depend slightly on j0. On the other hand, the small cross sections obtained for the (e) channel are nearly independent of energy. From initial-state resolved rate constants and Boltzmann populations at temperature T, we obtain QM thermal rate constants from 100 to 400 K: at 300 K, k(d) = (9.57 ± 0.96) × 10(-11) and k(e) = (1.41 ± 0.14) × 10(-11) cm(3) s(-1) for (d) and (e) reactions, respectively. The k(d) value is in good agreement with previous quasi-classical trajectory (QCT) results on the same PES, but it is larger than that observed at 297 K by a factor of 7. On the contrary, and in agreement with the small role of CH2 excited electronic states, X̃3A″ QCT and experimental rate constants agree at high temperatures. Thus, the discrepancy obtained at room T between theory and experiment should be due to an experimental error or to some theoretical effects that we have not been considered in this work. At the present state of the art, an experimental error is more likely and suggests a new measurement of the rate constant.

Cross sections and rate constants for OH + H2 reaction on three different potential energy surfaces for ro-vibrationally excited reagents

A systematic study of the reagent ro-vibrational excitations in H(2) + OH reaction is presented on three different potential energy surfaces using the multiconfiguration time-dependent Hartree method. An exact form of the kinetic energy operator including Coriolis coupling has been used. Coupled channel results on WDSE surface for vibrational excitation of H(2) produce very large cross sections in accordance with the previous approximate results. The rate constant obtained for H(2)(v = 1) at 300 K on the YZCL2 surface shows an excellent agreement with the most recent experimental result. Quantum dynamical results for ro-vibrational excitation of reagents obtained on the WSLFH surface show similar behavior to previous quasiclassical trajectory studies. The integral cross sections obtained for excited reagent rotations exhibit contrasting trends on the three surfaces. The effects are explained considering the different orientations of the transition state structure and the individual surface characteristics.

Quantitative (υ, N, Ka) Product State Distributions near the Triplet Threshold for the Reaction H2CO → H + HCO Measured by Rydberg Tagging and Laser-Induced Fluorescence

In this paper, we report quantitative product state distributions for the photolysis of H2CO --> H + HCO in the triplet threshold region, specifically for several rotational states in the 2(2)4(3) and 2(3)4(1) H2CO vibrational states that lie in this region. We have combined the strengths of two complementary techniques, laser-induced fluorescence for fine resolution and H atom Rydberg tagging for the overall distribution, to quantify the upsilon, N, and Ka distributions of the HCO photofragment formed via the singlet and triplet dissociation mechanisms. Both techniques are in quantitative agreement where they overlap and provide calibration or benchmarks that permit extension of the results beyond that possible by each technique on its own. In general agreement with previous studies, broad N and Ka distributions are attributed to reaction on the S0 surface, while narrower distributions are associated with reaction on T1. The broad N and Ka distributions are modeled well by phase space theory. The narrower N and Ka distributions are in good agreement with previous quasi-classical trajectory calculations on the T1 surface. The two techniques are combined to provide quantitative vibrational populations for each initial H2CO vibrational state. For dissociation via the 2(3)4(1) state, the average product vibrational energy (15% of E(avail)) was found to be about half of the rotational energy (30% of E(avail)), independent of the initial H2CO rotational state, irrespective of the singlet or triplet mechanism. For dissociation via the 2(2)4(3) state, the rotational excitation remained about 30% of E(avail), but the vibrational excitation was reduced.

A quantum wave-packet study of intersystem crossing effects in the O(P2,1,3,D21)+H2 reaction

We present for the first time an exact quantum study of spin-orbit-induced intersystem crossing effects in the title reaction. The time-dependent wave-packet method, combined with an extended split operator scheme, is used to calculate the fine-structure resolved cross section. The calculation involves four electronic potential-energy surfaces of the 1A' state [J. Dobbyn and P. J. Knowles, Faraday Discuss. 110, 247 (1998)], the 3A' and the two degenerate 3A" states [S. Rogers, D. Wang, A. Kuppermann, and S. Wald, J. Phys. Chem. A 104, 2308 (2000)], and the spin-orbit couplings between them [B. Maiti, and G. C. Schatz, J. Chem. Phys. 119, 12360 (2003)]. Our quantum dynamics calculations clearly demonstrate that the spin-orbit coupling between the triplet states of different symmetries has the greatest contribution to the intersystem crossing, whereas the singlet-triplet coupling is not an important effect. A branch ratio of the spin state Pi32 to Pi12 of the product OH was calculated to be approximately 2.75, with collision energy higher than 0.6 eV, when the wave packet was initially on the triplet surfaces. The quantum calculation agrees quantitatively with the previous quasiclassical trajectory surface hopping study.

DYNAMICS OF THE N(2D)+H2 REACTION ON THE $\tilde{X}^2 A^{\prime\prime}$ SURFACE, PROPAGATING REAL WAVE PACKETS WITH AN ARCCOS MAPPING OF THE HAMILTONIAN

We have investigated the dynamics of the title reaction with the Gray and Balint-Kurti approach, which propagates real wave packets (WP) under an arccos mapping of a scaled and shifted Hamiltonian. We have considered H 2 rotational quanta j=0 and 1 and obtained reaction probabilities using reactant coordinates and the flux analysis. We have calculated accurate reaction probabilities for total angular momentum quantum number J=0, centrifugal-sudden probabilities for J>0, cross sections, and the room temperature rate constant. The present cross sections are in good agreement with previous quasiclassical trajectory (QCT) results and the theoretical rate constant compares rather well with that observed. WP snapshots show that the reaction occurs via a C2v insertion mechanism, confirming previous QCT calculations.

Theoretical Study of the X+YCl (X, Y=H, D) Reactions

AbstractTime‐dependent wave packet calculations for the reaction H+HCl and its isotopic reactions are carried out on the potential energy surface (PES) of Bian and Werner (BW2) [Bain, W.; Werner, H.‐J. J. Chem. Phys. 2000, 112, 220]. Reaction probabilities for the exchanged and abstraction channels are calculated from various initial rotational states of the reagent. Those have then been used to estimate reaction cross sections and rate constants which also are calculated and explained by the zero‐point energy and the tunneling effect. The results of this work were compared with that of previous quasiclassical trajectory calculations and reaction dynamics experiments on the abstraction channel. In addition, the calculated rate constants are in reasonably good agreement with experimental measurements for both channels.

Close-Coupling Time-Dependent Quantum Dynamics Study of the H + HCl Reaction

The paper presents a theoretical study of the dynamics of the H + HCl system on the potential energy surface (PES) of Bian and Werner (Bian, W.; Werner, H. -J., J. Chem. Phys. 2000, 112, 220). A time-dependent wave packet approach was employed to calculate state-to-state reaction probabilities for the exchanged and abstraction channels. The most recent PES for the system has been used in the calculations. Reaction probabilities have also been calculated for several values of the total angular momentum J > 0. Those have then been used to estimate cross sections and rate constants for both channels. The calculated cross sections can be compared with the results of previous quasiclassical trajectory calculations and reaction dynamics experimental on the abstraction channel. In addition, the calculated rate constants are in the reasonably good agreement with experimental measurement.

The dynamics of the H+D2O→OD+HD reaction at 2.5 eV: Experiment and theory

The title reaction has been studied both experimentally and computationally at a mean collision energy of 2.48 eV. OD quantum state populations, rotational alignment parameters, rovibrational quantum state-resolved center-of-mass angular scattering distributions and HD co-product internal energy release distributions have been determined, along with OD quantum state averaged energy disposals. The experiments employ pulsed laser photolysis coupled with polarized Doppler-resolved laser induced fluorescence detection of the radical products. The OD angular scattering distributions show a preference for scattering in the forward direction, and are quite different from those observed previously at the lower collision energy of 1.4 eV. So too are the kinetic energy release distributions, which reveal that the HD co-products are born significantly more internally excited at 2.48 eV than at 1.4 eV. The HD internal energy distributions obtained from analysis of the Doppler resolved profiles are in reasonable accord with that derived from the direct HD population measurements performed by Zare and co-workers [J. Chem. Phys. 98, 4636 (1993)] at collision energies around 2.7 eV. The data are compared in detail with the results of new quasi-classical trajectory (QCT) calculations employing two alternative potential energy surfaces (PESs), as well as with the results from previous QCT studies of the title reaction by other workers. Refinements to the most recent of the PESs employed here, that developed using the iterative methods of Collins and Zhang and co-workers [J. Chem. Phys. 115, 174 (2001)], are also described. The theoretical results obtained using this refined PES agree very well with many of the experimental observables, and the surface appears to be a significant improvement on those previously developed. However, even with this new PES, the QCT calculations at 2.48 eV overestimate the internal excitation of the HD products.

Comment on “Reaction cross sections for the H+D2 (v=0,1) system for collision energies up to 2.5 eV: A multiconfiguration time-dependent Hartree wave-packet propagation study” [J. Chem. Phys. 110, 241 (1999)

Exact quantum mechanical (QM) scattering calculations for the H+D2 (v=0, j=0−2) reaction at 0.54 eV collision energy on the LSTH potential energy surface show that the reactivity increases with increasing initial j, in agreement with previous quasiclassical trajectory data, and in contrast with the time-dependent QM calculations by Jäckle et al. using the coupled states approximation.

Dynamics of the N(4S)+NO(X 2Π)→N2(X 1Σ+g)+O(3P) atmospheric reaction on the 3A″ ground potential energy surface. III. Quantum dynamical study and comparison with quasiclassical and experimental results

A detailed reactive–infinite-order sudden approximation (R-IOSA) study of the reactivity of the N+NO→N2+O system has been carried out in the 0.0038 to 1.388 eV translational energy range and the results have been compared with the existing quasiclassical trajectory (QCT) and experimental data available. The general features already observed in the previous QCT studies are reproduced qualitatively in the quantum study, even though some differences arise in the product vibrational distributions and state-to-state opacity functions in the low energy range. The observed differences have been justified in terms of the anisotropy of the potential energy surface and the vibrational barriers to reaction at fixed angles. A strong vibrational adiabaticity is observed quantally in the low translational energy range, disappearing at moderately high collision energies (around 0.3 eV), where a simple Franck–Condon type model is capable of describing the evolution of the vibrational distribution with translational energy. The vibrational distributions at fixed angles have been discussed within the context of Polanyi’s and Light’s correlation between products vibrational excitation and the features of the potential energy surface. The validity of extending the conclusions drawn from collinear to three-dimensional (3D) collisions is discussed. Finally, the detailed reaction mechanism is examined in light of the vibrational matrix elements of the close-coupling interaction matrix.

Reaction dynamics on barrierless reaction surfaces. II. Microcanonical variational transition states

A previous quasiclassical trajectory investigation of a generic proton-transfer reaction [Lim and Brauman, J. Chem. Phys. 94, 7164 (1991)] suggested the existence of both the usual centrifugal barrier transition state and a ‘‘dynamic’’ nonenergetic transition state for association on a barrierless potential surface. This paper reports a microcanonical variational transition state theory investigation of the same potential surface. The dynamic transition state is found to fulfill the variational criterion of a minimum in the sum of states. Implications for ion/molecule reactions are discussed.

Effects of translational, rotational, and vibrational energy on the dynamics of the D+H2 exchange reaction. A classical trajectory study

Quasiclassical trajectory (QCT) calculations for the D+H2(v,j)→HD+H system have been performed on the Liu, Siegbahn, Truhlar, Horowitz (LSTH) potential energy surface in order to study the combined effects of translation, rotation, and vibration on the reactivity. The range of initial conditions covered has been ET =0.25–1 eV, v=0, 1, and 2 and j=0–12. Integral cross sections, opacity functions, solid angle differential cross sections, and the energy partitioning among the products’ degrees of freedom have been obtained. The minimum in the dependence of the total cross section with rotational excitation observed in previous QCT calculations for v=0 and v=1 at low collision energies is here verified also for v=2. The center-of-mass (c.m.) angular distributions of the scattered HD product are predominantly backward with respect to the direction of the D incoming atom, at low energies, but they broaden markedly and become more forward with increasing total energy. Translational and vibrational excitation in the reactants are largely adiabatic and tend to remain as translation and vibration in the products. Where they can be compared, present results are in good agreement with recent quantum mechanical calculations and with experimental measurements.

Reaction path and variational transition state theory rate constant for Li++H2O→Li+(H2O) association

Canonical variational transition state theory rate constants are calculated for Li++H2O→Li+(H2O) recombination. Temperature dependence transition states are determined by finding the maxima in the free energy along the reaction path. Only one maximum is found at each temperature. The transition state theory rate constants are larger than those determined in a previous quasiclassical trajectory study of Li++H2O recombination. This results from a dynamical recrossing of the transition state dividing surface in the trajectory calculations.

Quantum resonance structure in the three-dimensional F + H 2 reaction

Evidence for a quantum resonance in the three-dimensional F + H 2 ( v = 0, i = 0) → FH( v = 2, all i) + H reaction is presented. Relative to the collinear reaction, this resonance is much broader and is shifted by about 0.1 eV to higher energies. This resonance has not been predicted in previous quasiclassical trajectory computations, or in approximate quantum calculations.

Quantum mechanical scattering calculations on a spline-fitted ab initio surface: the He + H+2 (ν = 0, 1, 2) → HeH+ + H reaction

All-channel time-dependent quantum mechanical reaction probabilities are reported for the collinear He + H+2(ν = 0, 1, 2) → HeH+ + H reaction at a total energy of 1.2 eV on previously reported diatomics-in-molecule (DIM) and spline fitted ab initio (SAI) surfaces. These results are in agreement with the previous quasiclassical trajectory results in that there is vibrational enhancement of the reaction probability on the SAI surface but not on the DIM surface. This agreement lends support to our previously drawn conclusion that small differences in the potential-energy surface can lead to substantially different dynamic results.