Cumulative reaction probabilities: A comparison between quasiclassical and quantum mechanical results

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.

Li + HF and Li + HCl Reactions Revisited I: QCT Calculations and Simulation of Experimental Results

The Li + HF and Li + HCl reactions share some common features. They have the same kinematics, relatively small barrier heights, bent transition states, and are both exothermic when the zero point energy is considered. Nevertheless, the pioneering crossed beam experiments by Lee and co-workers in the 80s (Becker et al., J. Chem. Phys. 1980, 73, 2833) revealed that the dynamics of the two reactions differ significantly, especially at low collision energies. In this work, we present theoretical simulations of their results in the laboratory frame (LAB), based on quasiclassical trajectories and obtained using accurate potential energy surfaces. The calculated LAB angular distributions and time-of-flight spectra agree well with the raw experimental data, although our simulations do not reproduce the experimentally derived center-of-mass (CM) differential cross section and velocity distributions. The latter were derived by forward convolution fitting under the questionable assumption that the CM recoil velocity and scattering angle distribution were uncoupled, while our results show that the coupling between them is relevant. Some important insights into the reaction mechanism discussed in the article by Becker et al. had not been contrasted with those that can be extracted from the theoretical results. Among them, the correlation between the angular momenta involved in the reactions has also been examined. Given the kinematics of both systems, the reagent orbital angular momentum, l , is almost completely transformed into the rotation of the product diatom, j'. However, contrary to the coplanar mechanism proposed in the original paper, we find that the initial and final relative orbital angular momenta are not necessarily parallel. Both reactions are found to be essentially direct, although about 15% of the LiFH complexes live longer than 200 fs.

The long-lived reactive nitrogen species in the troposphere: DFTB model for atmospheric applications

The longest lived reactive NO₂ molecule formation in a dry and clean air environment under a high-temperature shock wave was investigated under three basic reactions (R2 for the O + NO system, R6 for the NO + NO₃ system, and R7 for the NO + O₃ system) in the atmospheric environment. With certain approaches, a DFTB3 model was used, which gave results close to the density functional theory. In the calculations, the related reactions up to 250 ps were examined at individual specific temperatures, and the temperature ranges that contributed to the formation of the NO₂ molecule were determined. Moreover, a shock wave with both heating and cooling channels was applied only on R2 to see whether molecular concentrations were in good agreement with atmospheric information. The reaction products were examined under a shock wave of about 20 ps. At the end of the study, the applicability of the DFTB model to atmospheric systems was demonstrated by comparing it with experimental data and information. QCT approach was also used for the calculation of reaction rate constants of only O₂-formation on the O + NO system. Here, all systems are focused on nitrogen species containing oxygen. In particular, the highest-population NO molecule that emerged in the lightning flash event was used as the reactant, while systems existing with the longest lived NO₂ in the atmosphere after the lightning flash were focused in the product channel. As a result of the study, the hypothesis of geophysicists that almost all NO₂ formed in the lightning flash event originates from the NO + O system was disproved. It has been proven that the presence of NO₃ molecules that can withstand high temperatures in such systems should be evaluated.

Oxygen Molecule Formation and the Puzzle of Nitrogen Dioxide and Nitrogen Oxide during Lightning Flash

Unlike the compounds of the natural air atmosphere, the lightning systems are primarily focused on NO(X²Π), NO₂(1²A'), and O(³P) concentrations that occurred newly and highly in the ground electronic structure. While the NO/NO₂ concentrations ratio is about 2000 during the lightning flash, this ratio becomes about 0.8 right after the lightning flash. The reason for this decrease in the ratio is the disappearance of the high temperature that prevents the formation of NO₂ (with the combination of NO and O) and of the photon energy that causes its dissociation (NO₂ + hv → NO + O) right after the lightning flash. However, this study will focus on the reactions that contribute to the NO concentration, except for the combination of N and O atoms during lightning flash. To do this, it was focused on the reactive scattering states (especially the NO-exchange) of the NO + O collision and the photo-dissociation of NO₂, which provide the formation of the NO molecule in the ground electronic state. This case raises important questions. To what extent do the NO-exchange reaction and the photo-dissociation of NO₂ contribute to the atmospherically observed NO molecules? or how can the vibrational quantum states of the NO molecules formed by the photo-dissociation be effected on the NO + O¹ collision to produce a NO¹ molecule? These conditions may contribute to the concentrations of NO high during lightning flashes. Under low collision energy (between 0.1 and 0.3 eV), the NO (v = 0) population dissociated by a photon can act as reactants in the NO-exchange reactive scattering on the doublet electronic state. Since it is assumed that all of the NO₂ molecules are due to NO in the lightning flash system, this is one of the reasons that makes the NO population so high during lightning flash. Therefore, in the light of considering that the lightning system supports the formation of highly vibrating molecular groups, it might also support the formation of O₂ molecules. In particular, it was shown that the v = 4 quantum state of the NO molecule over the doublet state between collision energies of 0.9-1.5 eV and the v = 5 quantum state of the NO molecule over the quartet state between collision energies of 1.0-1.5 eV contribute to O₂ formation.

New Stress Test for Ring Polymer Molecular Dynamics: Rate Coefficients of the O(3P) + HCl Reaction and Comparison with Quantum Mechanical and Quasiclassical Trajectory Results

In the past decade, ring polymer molecular dynamics (RPMD) has emerged as a very efficient method to determine thermal rate coefficients for a great variety of chemical reactions. This work presents the application of this methodology to study the O(³P) + HCl reaction, which constitutes a stringent test for any dynamical calculation due to rich resonant structure and other dynamical features. The rate coefficients, calculated on the ³A' and ³A″ potential energy surfaces (PESs) by Ramachandran and Peterson [ J. Chem. Phys. 2003 , 119 , 9590 ], using RPMD and quasiclassical trajectories (QCT) are compared with the existing experimental and the quantum mechanical (QM) results by Xie et al. [ J. Chem. Phys. 2005 122 , 014301 ]. The agreement is very good at T > 600 K, although RPMD underestimates rate coefficients by a factor between 4 and 2 in the 200-500 K interval. The origin of these discrepancies lies in the large contribution from tunneling on the ³A″ PES, which is enhanced by resonances due to quasibound states in the van der Waals wells. Although tunneling is fairly well accounted for by RPMD even below the crossover temperature, the effect of resonances, a long-time effect, is not included in the methodology. At the highest temperatures studied in this work, 2000-3300 K, the RPMD rate coefficients are somewhat larger than the QM ones, but this is shown to be due to limitations in the QM calculations and the RPMD are believed to be more reliable.

Influence of vibration in the reactive scattering of D + MuH: the effect of dynamical bonding

The dynamics of the D + MuH(v = 1) reaction has been investigated using time-independent quantum mechanical calculations. The total reaction cross sections and rate coefficients have been calculated for the two exit channels of the reaction leading, respectively, to DMu + H and DH + Mu. Over the 100-1000 K temperature range investigated the rate coefficients for the DMu + H channel are of the order of 10(-10) cm(3) s(-1) and those for the DH + Mu channel vary between 1 × 10(-12) and 8 × 10(-11) cm(3) s(-1). These results point to a virtually barrierless reaction for the DMu + H channel and to the presence of a comparatively small barrier for the DH + Mu channel and are consistent with the profiles of their respective collinear vibrationally adiabatic potentials (VAPs). The effective barrier in the VAP of the DH + Mu channel is located in the reactant valley and, consequently, translation is found to be more efficient than vibration for the promotion of the reaction over a large energy interval in the post threshold region. Below this barrier, the DH + Mu channel can be accessible through an indirect mechanism implying crossing from the DMu + H pathway. The most salient feature found in the present study is revealed in the total reaction cross section for the DMu + H channel, which shows a sharp resonance caused by the presence of a deep well in the vibrationally adiabatic potential. This well has a dynamical origin, reminiscent of that found recently in the vibrationally bonded BrMuBr complex [Fleming, et al., Angew. Chem., Int. Ed., 2014, 53, 1], and is due to the stabilizing effect of the light Mu atom oscillating between the heavier H and D isotopes and to the bond softening associated with vibrational excitation of MuH.

Rate coefficients from quantum and quasi-classical cumulative reaction probabilities for the S(1D) + H2 reaction

Cumulative reaction probabilities (CRPs) at various total angular momenta have been calculated for the barrierless reaction S((1)D) + H(2) → SH + H at total energies up to 1.2 eV using three different theoretical approaches: time-independent quantum mechanics (QM), quasiclassical trajectories (QCT), and statistical quasiclassical trajectories (SQCT). The calculations have been carried out on the widely used potential energy surface (PES) by Ho et al. [J. Chem. Phys. 116, 4124 (2002)] as well as on the recent PES developed by Song et al. [J. Phys. Chem. A 113, 9213 (2009)]. The results show that the differences between these two PES are relatively minor and mostly related to the different topologies of the well. In addition, the agreement between the three theoretical methodologies is good, even for the highest total angular momenta and energies. In particular, the good accordance between the CRPs obtained with dynamical methods (QM and QCT) and the statistical model (SQCT) indicates that the reaction can be considered statistical in the whole range of energies in contrast with the findings for other prototypical barrierless reactions. In addition, total CRPs and rate coefficients in the range of 20-1000 K have been calculated using the QCT and SQCT methods and have been found somewhat smaller than the experimental total removal rates of S((1)D).

Dynamics of the reactions of muonium and deuterium atoms with vibrationally excited hydrogen molecules: tunneling and vibrational adiabaticity

Quantum mechanical (QM) and quasiclassical trajectory (QCT) calculations have been carried out for the exchange reactions of D and Mu (Mu = muonium) with hydrogen molecules in their ground and first vibrational states. In all the cases considered, the QM rate coefficients, k(T), are in very good agreement with the available experimental results. In particular, QM calculations on the most accurate potential energy surfaces (PESs) predict a rate coefficient for the Mu + H(2) (ν = 1) reaction which is very close to the preliminary estimate of its experimental value at 300 K. In contrast to the D + H(2) (ν = 0,1) and the Mu + H(2) (ν = 0) reactions, the QCT calculations for Mu + H(2) (ν = 1) predict a much smaller k(T) than that obtained with the accurate QM method. This behaviour is indicative of tunneling. The QM reaction probabilities and total reactive cross sections show that the total energy thresholds for the reactions of Mu with H(2) in ν = 0 and ν = 1 are very similar, whereas for the corresponding reaction with D the ν = 0 total energy threshold is about 0.3 eV lower than that for ν = 1. The results just mentioned can be explained by considering the vibrational adiabatic potentials along the minimum energy path. The threshold for the reaction of Mu with H(2) in both ν = 0 and ν = 1 states is the same and is given by the height of the ground vibrational adiabatic collinear potential, whereas for the D + H(2) reaction the adiabaticity is preserved and the threshold for the reaction in ν = 1 is very close to the height of the ν = 1 adiabatic collinear barrier. For Mu + H(2) (ν = 1) the reaction takes place by crossing from the ν = 1 to the ν = 0 adiabat, since the exit channel leading to MuH (ν = 1) is not energetically accessible. At the lowest possible energies, the non-adiabatic vibrational crossing implies a strong tunneling effect through the ν = 1 adiabatic barrier. Absence of tunneling in the classical calculations results in a threshold that coincides with the height of the ν = 1 adiabatic barrier. Most interestingly, the expected tunneling effect in the reaction of Mu with hydrogen molecules occurs for H(2) (ν = 1) but not for H(2) (ν = 0) where zero-point-energy effects clearly dominate.

Cumulative reaction probabilities and transition state properties: a study of the H+ + H2 and H+ + D2 proton exchange reactions

Cumulative reaction probabilities (CRPs) have been calculated by accurate (converged, close coupling) quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical QCT (SQCT) methods for the H(+) + H(2) and H(+) + D(2) reactions at collision energies up to 1.2 eV and total angular momentum J = 0-4. A marked resonance structure is found in the QM CRP, most especially for the H(3)(+) system and J = 0. When the CRPs are resolved in their ortho and para contributions, a clear steplike structure is found associated with the opening of internal states of reactants and products. The comparison of the QCT results with those of the other methods evinces the occurrence of two transition states, one at the entrance and one at the exit. At low J values, except for the quantal resonance structure and the lack of quantization in the product channel, the agreement between QM and QCT is very good. The SQCT model, that reflects the steplike structure associated with the opening of initial and final states accurately, clearly tends to overestimate the value of the CRP as the collision energy increases. This effect seems more marked for the H(+) + D(2) isotopic variant. For sufficiently high J values, the growth of the centrifugal barrier leads to an increase in the threshold of the CRP. At these high J values the discrepancy between SQCT and QCT becomes larger and is magnified with growing collision energy. The total CRPs calculated with the QCT and SQCT methods allowed the determination of the rate constant for the H(+) + D(2) reaction. It was found that the rate, in agreement with experiment, decreases with temperature as expected for an endothermic reaction. In the range of temperatures between 200 and 500 K the differences between SQCT and QCT rate results are relatively minor. Although exact QM calculations are formidable for an exact determination of the k(T), it can be reliably expected that their value will lie between those given by the dynamical and statistical trajectory methods.

A statistical quasiclassical trajectory model for atom-diatom insertion reactions

A statistical model based on the quasiclassical trajectory method is presented in this work for atom-diatom insertion reactions. The basic difference between this and the corresponding statistical quantum model (SQM) lies in the fact that trajectories instead of wave functions are propagated in the entrance and exit channels. Other than this the two formulations are entirely similar. In particular, it is shown that conservation of parity can be taken into account in a natural and precise way in the statistical quasiclassical trajectory (SQCT) model. Additionally, the SQCT model complies with the principle of detailed balance and overcomes the problem of the zero point energy in the products. As a test, the model is applied to the H3+ and H+D2 exchange reactions. The excellent agreement between the SQCT and SQM results, especially in the case of the differential cross sections, indicates that the effect of tunneling through the centrifugal barrier is negligible. The effect of ignoring quantum mechanical parity conservation is also investigated.

Constraints at the transition state of the D + H2 reaction: quantum bottlenecks vs. stereodynamics

This article presents a quasiclassical trajectory method for the calculation of cumulative reaction probabilities by sampling of the helicity quantum number of the reagents (k). The method is applied to the D + H(2) reaction at various total angular momentum (J) values, and the helicity-resolved quasiclassical cumulative reaction probabilities are compared to their quantum mechanical counterparts. The agreement between the two sets of results is fairly good. In particular, k-dependent, J-independent reaction thresholds found with quantum methods are reproduced by the quasiclassical calculations. The shift of these thresholds with increasing k, which has been previously attributed to the quantum bottleneck states taking part in the reaction, is revisited and discussed also in terms of the reaction stereodynamics.