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.

Kinetics and dynamics study of the Cl(2P) + CH3OH reaction based on an analytical potential energy surface.

The reaction of chlorine atoms with methanol plays a central role in atmospheric and combustion processes and is a prototype of multi-channel reaction with two paths, HCl(v,j) + CH2OH (R1) and HCl(v,j) + CH3O (R2). In order to understand the kinetics and dynamics of the title reaction, using a valence-bond (VB) strategy we developed a new full-dimensional potential energy surface, named PES-2023, fitted to high-level ab initio calculations. Given that the (R2) path shows a noticeable barrier height, 12.7 kcal mol-1, while the (R1) path presents a submerged transition state with respect to the reactants, the latter is the kinetically favoured path on which most experimental kinetics and dynamics studies have focused. The PES-2023 surface presents a smooth and continuous behavior and is free of spurious features. Quasi-classical trajectory calculations were performed on this surface in order to shed light on the reaction kinetics and dynamics. The thermal rate constants in the temperature range 200-1000 K are practically independent of temperature, reproducing recent experimental evidence, although the experimental kinetics isotope effects are not well simulated. In the dynamics study the product distribution energy and the HCl(v,j) product roto-vibrational energy reasonably simulate the experimental data, where only the v = 0 and v = 1 vibrational states are populated, 80-20%, respectively. We found that both HCl(v) vibrational states present similar forward scattering distributions, associated with a stripping mechanism. This theoretical result contrasts with some of the previous experimental measurements. Finally, PES-2023 was compared with a recent and accurate full-dimensional surface based on a different strategy, a molecular orbital (MO) based surface, fitted to a very large number of ab initio points, concluding that both surfaces present similar behaviour, where some kinetics and dynamics properties are better reproduced by one surface and other properties by the other.

The CN(X 2Σ+) + C2H6 reaction: Dynamics study based on an analytical full-dimensional potential energy surface.

The hydrogen abstraction reaction of the cyano radical with molecules of ethane presents some interesting points in the chemistry from ultra-cold to combustion environments especially with regard to HCN(v) product vibrational distribution. In order to understand its dynamics, a new analytical full-dimensional potential energy surface was developed, named PES-2023. It uses a combination of valence bond and mechanic molecular terms as the functional form, fitted to high-level ab initio calculations at the explicitly correlated CCSD(T)-F12/aug-cc-pVTZ level on a reduced and selected number of points describing the reactive process. The new surface showed a continuous and smooth behavior, describing reasonably the topology of the reaction: high exothermicity, low barrier, and presence of intermediate complexes in the entrance and exit channels. Using quasi-classical trajectory calculations (QCT) on the new PES-2023, a dynamics study was performed at room temperature with special emphasis on the HCN(v1,v2,v3) product stretching and bending vibrational excitations, and the results were compared with the experimental evidence, which presented discrepancies in the bending excitation. The available energy was mostly deposited as HCN(v) vibrational energy with the vibrational population inverted in the CH stretching mode and not inverted in the CN stretching and bending modes, thus simulating the experimental evidence. Other dynamics properties at room temperature were also analyzed; cold rotational energy distribution was found, associated with a linear and soft transition state, and backward scattering distribution was found, associated with a rebound mechanism.

Full-dimensional potential energy surface for the H + CH3OH reaction. Theoretical kinetics and dynamics study.

The dynamics and kinetics of the abstraction reactions of hydrogen atoms with methanol have been studied using quasi-classical trajectory calculations and variational transition state theory with tunnelling corrections, based on a new analytical potential energy surface (PES). The new PES is a valence-bond/molecular mechanics (VB/MM) expression that provides us with the potential energy for any set of Cartesian coordinates. Two reaction channels are considered: hydrogen abstraction from the methyl group (R1) and hydrogen abstraction from the alcohol group (R2), R1 being much more likely to occur in the wide temperature range under study (250-1000 K), as expected from the lower barrier height. Our dynamic calculations at a collision energy of 20 kcal mol-1 show that the H2 co-product is produced mainly in its vibrational ground-state and little rotation excitation is found. As for our kinetic results, they agree with those from previous theoretical studies as well as with those from kinetic experimental results (rate constants and kinetic isotopic effects), lending confidence to the analytical PES presented here. Thus, we expect this PES to be a simple yet powerful tool to understand such an important reaction in combustion chemistry at very high temperatures and interstellar chemistry at very low temperatures.

Current Status of the X + C2H6 [X ≡ H, F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review.

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C2H6 → HX + C2H5; X ≡ H, F(2P), Cl(2P), O(3P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(3P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.

Quasi-Classical Trajectory Study of the CN + NH3 Reaction Based on a Global Potential Energy Surface.

Based on a combination of valence-bond and molecular mechanics functions which were fitted to high-level ab initio calculations, we constructed an analytical full-dimensional potential energy surface, named PES-2020, for the hydrogen abstraction title reaction for the first time. This surface is symmetrical with respect to the permutation of the three hydrogens in ammonia, it presents numerical gradients and it improves the description presented by previous theoretical studies. In order to analyze its quality and accuracy, stringent tests were performed, exhaustive kinetics and dynamics studies were carried out using quasi-classical trajectory calculations, and the results were compared with the available experimental evidence. Firstly, the properties (geometry, vibrational frequency and energy) of all stationary points were found to reasonably reproduce the ab initio information used as input; due to the complicated topology with deep wells in the entrance and exit channels and a "submerged" transition state, the description of the intermediate complexes was poorer, although it was adequate to reasonably simulate the kinetics and dynamics of the title reaction. Secondly, in the kinetics study, the rate constants simulated the experimental data in the wide temperature range of 25-700 K, improving the description presented by previous theoretical studies. In addition, while previous studies failed in the description of the kinetic isotope effects, our results reproduced the experimental information. Finally, in the dynamics study, we analyzed the role of the vibrational and rotational excitation of the CN(v,j) reactant and product angular scattering distribution. We found that vibrational excitation by one quantum slightly increased reactivity, thus reproducing the only experimental measurement, while rotational excitation strongly decreased reactivity. The scattering distribution presented a forward-backward shape, associated with the presence of deep wells along the reaction path. These last two findings await experimental confirmation.

Full-dimensional analytical potential energy surface describing the gas-phase Cl + C2H6 reaction and kinetics study of rate constants and kinetic isotope effects.

Within the Born-Oppenheimer approximation a full-dimensional analytical potential energy surface, PES-2017, was developed for the gas-phase hydrogen abstraction reaction between the chlorine atom and ethane, which is a nine body system. This surface presents a valence-bond/molecular mechanics functional form dependent on 60 parameters and is fitted to high-level ab initio calculations. This reaction presents little exothermicity, -2.30 kcal mol-1, with a low height barrier, 2.44 kcal mol-1, and intermediate complexes in the entrance and exit channels. We found that the energetic description was strongly dependent on the ab initio level used and it presented a very flat topology in the entrance channel, which represents a theoretical challenge in the fitting process. In general, PES-2017 reproduces the ab initio information used as input, which is merely a test of self-consistency. As a first test of the quality of the PES-2017, a theoretical kinetics study was performed in the temperature range 200-1400 K using two approaches, i.e. the variational transition-state theory and quasi-classical trajectory calculations, with spin-orbit effects. The rate constants show reasonable agreement with experiments in the whole temperature range, with the largest differences at the lowest temperatures, and this behaviour agrees with previous theoretical studies, thus indicating the inherent difficulties in the theoretical simulation of the kinetics of the title reaction. Different sources of error were analysed, such as the limitations of the PES and theoretical methods, recrossing effects, and the tunnelling effect, which is negligible in this reaction, and the manner in which the spin-orbit effects were included in this non-relativistic study. We found that the variation of spin-orbit coupling along the reaction path, and the influence of the reactivity of the excited Cl(2P1/2) state, have relative importance, but do not explain the whole discrepancy. Finally, the activation energy and the kinetics isotope effects reproduce the experimental information.

Quasi-Classical Trajectory Dynamics Study of the Cl(2P) + C2H6 → HCl(v,j) + C2H5 Reaction. Comparison with Experiment.

To understand and simulate the dynamics behavior of the title reaction, QCT calculations were performed on a recently developed global analytical potential energy surface, PES-2017. These calculations combine the classical description of the dynamics with pseudoquantization in the reactants and products to perform a theoretical/experimental comparison on the same footing. Thus, in the products a series of constraints are included to analyze the HCl(v = 0,j) product, which is experimentally detected. At collision energies of 5.5 and 6.7 kcal mol-1 the largest fraction of available energy is deposited as translation, 67%, while the ethyl radical shows significant internal energy, 27%, and so it does not act as a spectator of the reaction, thus reproducing recent experimental evidence. The HCl(v=0, j) rotational distribution is cold, peaking at j = 2, only one unit hotter than experiment, which represents an error of 0.12 kcal mol-1. At a collision energy of 5.5 kcal mol-1 product translational distribution is slightly hotter than experiment, but at 6.7 kcal mol-1 agreement with recent experiments is practically quantitative, suggesting that the first experiments should be revised. In addition, we observe that the HCl(v=0, j) scattering distribution shifts from isotropic at low values of j to backward at high values of j, which is in agreement with experimental data. Finally, no evidence was found for the "chattering" mechanism suggested to explain the low translational energy of the HCl product in the backward scattering region. In sum, agreement with experiments of a series of sensible dynamic properties permits us to be optimistic on the quality and accuracy of the theoretical tools used in the present work, QCT and PES-2017.

Kinetics study of the CN + CH4 hydrogen abstraction reaction based on a new ab initio analytical full-dimensional potential energy surface.

We have developed an analytical full-dimensional potential energy surface, named PES-2017, for the gas-phase hydrogen abstraction reaction between the cyano radical and methane. This surface is fitted using high-level ab initio information as input. Using the PES-2017 surface, a kinetics study was performed via two theoretical approaches: variational transition-state theory with multidimensional tunnelling (VTST-MT) and ring polymer molecular dynamics (RPMD). The results are compared with the experimental data. In the whole temperature range analysed, 300-1500 K, both theories agree within a factor of <2, reproducing the experimental behaviour taking into account the experimental uncertainties. At high temperatures, where the recrossing effects dominate and the RPMD theory is exact, both theories differ by a factor of about 20%; while at low temperatures this difference is larger, 45%. Note that in this temperature regime, the tunnelling effect is negligible. The CN + CH4/CD4 kinetic isotope effects are important, reproducing the scarce experimental evidence. The good agreement with the ab initio information used in the fitting process (self-consistency test) and with the kinetic behaviour in a wide temperature range gives confidence and strength to the new surface.

Quasi-classical trajectory calculations in asymmetrically substituted polyatomic systems of the type A + CX3Y --> products: the H + CH3Cl hydrogen abstraction reaction channel.

A state-to-state dynamics study was performed for the first time for asymmetrically substituted reactions of the type H + CX3Y --> products, and was applied to the H + CH3Cl gas-phase hydrogen abstraction reaction, analyzing the influence of CH3Cl reactant vibrational stretching and bending excitations. Quasi-classical trajectory calculations were performed on an analytical potential energy surface constructed previously by our group. The strong coupling between different vibrational modes in the entry channel makes the reaction non-adiabatic and the reactant vibrational excitation increases the reactivity of the vibrational ground-state by factors of approximately 2-3 depending on the excited mode. While the H2 and CH2Cl products appear with similar moderate amounts of internal energy, about 25% of the total available energy, most of this energy appears as translational energy, and the reactant vibrational excitation has little influence. The two products appear vibrationally cold, and in the case of the H2 product, also rotationally cold. The product angular distribution is predominantly sideways-backward, the sideways component increasing with the vibrational excitation of the H2 product. The reactant vibrational excitations have little effect on this behaviour. Finally, comparison with theoretical results for the analogue H + CH4 reaction shows that the dynamic behaviour of the two reactions is similar, with the chlorine substituent effect being small or negligible.

Potential energy surface for asymmetrically substituted reactions of type CWXYZ + A. Kinetics study.

The CHClF(2) + Cl --> ClH + CClF(2) gas-phase abstraction reaction was chosen as a model of asymmetrically substituted polyatomic reactions of type CWXYZ + A --> products. The analytical potential energy surface for this reaction was constructed with suitable functional forms to represent vibrational modes, and calibrated with respect to experimental thermal rate constants which are available over the temperature range 296-410 K. On this surface, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wider temperature range, 200-2500 K, therefore obtaining kinetics information at lower and higher temperatures than are experimentally available. This surface was also used to analyze dynamical features, such as tunneling and reaction-path curvature. In the former, the influence of the tunneling factor was important since a light hydrogen atom passes through the barrier. In the latter, it was found that vibrational excitation of the C-F and C-Cl stretching modes can be expected in the exit channel.

Analytical potential energy surface describing abstraction reactions in asymmetrically substituted polyatomic systems of type CX3Y + A--> products.

The gas-phase reaction between chloromethane and hydrogen proceeds by two channels, Cl- and H-abstraction, and was chosen as a model of asymmetrically substituted polyatomic reactions of type CX3Y + A --> products. The analytical potential energy surface for this reaction was constructed with suitable functional forms to represent vibrational modes, and both channels were independently fitted to reproduce experimental and theoretical information only at the stationary points. The rate constants for the Cl- and H-channels and the overall reaction were calculated using variational transition-state theory with multidimensional tunneling effect over a wide temperature range, 298-3000 K. The Cl-abstraction reaction is preferred until 2100 K, while above this temperature the H-abstraction channel is favored. The theoretical overall rate constants agree with the experimental data in the common temperature range, 500-800 K, with a small curvature of the Arrhenius plot due mainly to the role of the tunneling in the H-abstraction channel. This surface was then used to analyze dynamical features, such as reaction-path curvature, and coupling between the reaction-coordinate and vibrational modes. It was found qualitatively that excitation of the C-Cl and C-H stretching reactive modes enhances the forward rate constants for the Cl- and H-abstraction channels, respectively, and only the Cl-H and H-H stretching modes in the products of the Cl- and H-abstraction reactions, respectively, appear vibrationally excited.

Quasi-classical trajectory calculations analyzing the reactivity and dynamics of asymmetric stretch mode excitations of methane in the H + CH4 reaction.

An exhaustive dynamics study was performed at two collision energies, 1.52 and 2.20 eV, analyzing the effects of the asymmetric (nu3) stretch mode excitation in the reactivity and dynamics of the gas-phase H + CH4 reaction. Quasi-classical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories, were performed on an analytical potential energy surface previously developed by our group. First, strong coupling between different vibrational modes in the entry channel was observed, indicating that energy can flow between these modes, and therefore that they do not preserve their adiabatic character along the reaction path; i.e., the reaction is nonadiabatic. Second, we found that the reactant vibrational excitation has a significant influence on the vibrational and rotational product distributions. With respect to the vibrational distribution, our results confirm the purely qualitative experimental evidence, although the theoretical results presented here are also quantitative. The rotational distributions are predictive, because no experimental data have been reported. Third, with respect to the reactivity, we found that the nu3 mode excitation by one quantum is more reactive than the ground state by a factor of about 2, independently of the collision energy, and in agreement with the experimental measurement of 3.0 +/- 1.5. Fourth, the state-to-state angular distributions of the products reproduce the experimental behavior at 1.52 eV, where the CH3 products scatter sideways and backward. At 2.20 eV this experimental information is not available, and therefore the results reported here are again predictive. The satisfactory reproduction of a great variety of experimental data by the present QCT study lends confidence to the potential energy surface constructed by our group and to those results whose accuracy cannot be checked by comparison with experiment.

Potential energy surface, kinetics, and dynamics study of the Cl+CH4-->HCl+CH3 reaction.

A modified and recalibrated potential energy surface for the gas-phase Cl+CH4-->HCl+CH3 reaction is reported and tested. It is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to updated experimental and theoretical stationary point properties and experimental forward thermal rate constants. From the kinetics point of view, the forward and reverse thermal rate constants and the activation energies were calculated using the variational transition-state theory with semiclassical transmission coefficients over a wide temperature range of 150-2500 K. The theoretical results reproduce the available experimental data, with a small curvature of the Arrhenius plot which indicates the role of tunneling in this hydrogen abstraction reaction. A dynamics study was also performed on this PES using quasiclassical trajectory (QCT) calculations, including corrections to avoid zero-point energy leakage along the trajectories. First, we found a noticeable internal energy in the coproduct methyl radical, both in the ground-state [CH4 (v=0)] and vibrationally excited [CH4 (v=1)] reactions. This CH3 internal energy was directly precluded in some experiments or oversimplified in previous theoretical studies using pseudotriatomic models. Second, our QCT calculations give HCl rotational distributions slightly hotter than those in experiment, but correctly describing the experimental trend of decreasing the HCl product rotation excitation in going from HCl (v'=0) to HCl (v'=1) for the CH4 (v=1) reaction. Third, the state specific scattering distributions present a reasonable agreement with experiment, although they tend to make the reaction more forward and backward scattered than found experimentally probably because of the hotter rotational distribution and the deficiencies of the QCT methods.

Potential energy surface for the F(2P(3/2),2P(1/2)) + CH4 hydrogen abstraction reaction. kinetics and dynamics study.

A modified and recalibrated potential energy surface (PES) is reported for the gas-phase F(2P(3/2),2P(1/2)) + CH4 reaction and its deuterated analogue. This semiempirical surface is completely symmetric with respect to the permutation of the four methane hydrogen atoms and is calibrated with respect to the updated experimental and theoretical stationary point properties and experimental thermal rate constants. To take into account the two spin-orbit electronic states of the fluorine atom, two versions of the surface were constructed, the PES-SO and PES-NOSO surfaces, which differ in the choice of the zero reference level of the reactants. On both surfaces, the thermal rate constants were calculated using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 180-500 K. While the PES-SO surface overestimates the experimental rate constants, the PES-NOSO surface shows a better agreement, reproducing the experimental variation with temperature. The influence of the tunneling factor is negligible, due to the flattening of the surface in the entrance valley, and we found a direct dependence on temperature, and therefore positive and small activation energies, in agreement with experiment. The kinetic isotope effects calculated showed good agreement with the sparse experimental data at 283 and 298 K. Finally, on the PES-NOSO surface, other dynamical features, such as the coupling between the reaction coordinate and the vibrational modes, were analyzed. It was found qualitatively that the FH stretching and the CH3 umbrella bending modes in the products appear vibrationally excited. These kinetics and dynamics results seem to indicate that a single, adiabatic PES is adequate to describe this reaction.

Theoretical Study of the Antioxidant Activity of Vitamin E: Reactions of α-Tocopherol with the Hydroperoxy Radical.

The reactivity of the hydroperoxy radical with α-tocopherol [Formula: see text] a prototype of the chemical reactions involved in biological antioxidant actions [Formula: see text] was studied theoretically. Two pathways were analyzed: hydrogen abstraction from the phenolic hydrogen and hydroperoxy addition to the aromatic ring. The reaction paths for the two mechanisms were traced independently, and the respective thermal rate constants were calculated using variational transition-state theory with multidimensional small-curvature tunneling. The reactivity of the hydroperoxy radical was found to be dominated by the hydrogen abstraction mechanism on α-tocopherol, with a rate constant of 1.5 × 10(5) M(-1) s(-1) at 298 K. It was also found that the mechanism of the reaction is not direct but passes through two intermediates, one of which may have a significant role in preventing the pro-oxidant effects of α-tocopherol.

New hybrid method for reactive systems from integrating molecular orbital or molecular mechanics methods with analytical potential energy surfaces.

A computational approach to calculating potential energy surfaces for reactive systems is presented and tested. This hybrid approach is based on integrated methods where calculations for a small model system are performed by using analytical potential energy surfaces, and for the real system by using molecular orbital or molecular mechanics methods. The method is tested on a hydrogen abstraction reaction by using the variational transition-state theory with multidimensional tunneling corrections. The agreement between the calculated and experimental information depends on the quality of the method chosen for the real system. When the real system is treated by accurate quantum mechanics methods, the rate constants are in excellent agreement with the experimental measurements over a wide temperature range. When the real system is treated by molecular mechanics methods, the results are still good, which is very encouraging since molecular mechanics itself is not at all capable of describing this reactive system. Since no experimental information or additional fits are required to apply this method, it can be used to improve the accuracy of molecular orbital methods or to extend the molecular mechanics method to treat any reactive system with the single constraint of the availability of an analytical potential energy surface that describes the model system.