Norcaradiene-Cycloheptatriene Equilibrium: A Heavy-Atom Quantum Tunneling Case.

The equilibrium between norcaradiene and cycloheptatriene, which has captivated chemists for more than half a century, is revisited by state-of-the-art quantum chemical calculations. Our theoretical data significantly deviate from the experimental results (J. Am. Chem. Soc., 1981, 26, 7791-7792), especially at low temperatures, where isomerization is dominated by heavy-atom tunneling. This effect results in an extremely short half-life for norcaradiene, rendering it undetectable. This work sheds light on this equilibrium, updating the kinetic and thermodynamic data while also expanding the repertoire of organic reactions controlled by this exotic quantum effect.

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.

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.

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.

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.

VTST and RPMD kinetics study of the nine-body X + C2H6 (X ≡ H, Cl, F) reactions based on analytical potential energy surfaces.

Thermal rate constants of nine-atom hydrogen abstraction reactions, X + C2H6 → HX + C2H5 (X ≡ H, Cl, F) with qualitatively different reaction paths, have been investigated using two kinetics approaches - variational transition state theory with multidimensional tunnelling (VTST/MT) and ring polymer molecular dynamics (RPMD) - and full dimensional analytical potential energy surfaces. For the H + C2H6 reaction, which proceeds through a noticeable barrier height of 11.62 kcal mol-1, kinetics approaches showed excellent agreement between them (with differences less than 30%) and with the experiment (with differences less than 60%) in the wide temperature range of 200-2000 K. For X = Cl and F, however, the situation is very different. The barrier height is either low or very low, 2.44 and 0.23 kcal mol-1, respectively, and the presence of van der Waals complexes in the entrance channel leads to a very flat topography and, consequently, imposes theoretical challenges. For the Cl(2P) reaction, VTST/MT underestimates the experimental rate constants (with differences less than 86%), and RPMD demonstrates better agreement (with differences less than 47%), although the temperature dependence is opposite to the experiment at low temperatures. Finally, for the F(2P) reaction, available experimental information shows discrepancies, both in the absolute values of the rate constants and also in the temperature dependence. Unfortunately, kinetics theories did not resolve this discrepancy. Different possible causes of these theory/experiment discrepancies were analyzed.

The hydrogen abstraction reaction H + C2H6→ H2(v,j) + C2H5. Part II. Theoretical kinetics and dynamics study.

Two important issues motivated the present study: the role of the tunnelling contribution at low temperatures and the role of the alkyl fragment in the dynamics. Using a recently developed full-dimensional analytical potential energy surface (PES), named PES-2018 (Part I), kinetics and dynamics studies were performed. The kinetics study was performed using the variational transition-state theory with multidimensional tunnelling over the temperature range of 200-2000 K. At high temperatures, T≥ 400 K, the calculated thermal rate constants reproduce the experimental evidence, with differences of 25%, with respect to experimental measures, while at low temperatures, T≤ 300 K, the tunnelling effect plays an important role although, unfortunately, no experimental information is available for comparison. We found that the tunnelling contribution is strongly dependent on the theoretical approach used to calculate it, with differences of a factor of about ∼30. For the dynamics, quasi-classical trajectory calculations were performed at different collision energies in the range of 10-50 kcal mol-1, taking into account the zero-point energy violation problem in the final analysis. Excitation function increased with collision energy, reproducing the experimental values, and the H2(v,j) product showed cold vibrational and rotational distributions, thus again simulating experiments. We found that the ethyl radical product presents small internal energy, similar to the methyl radical product in the H + CH4 reaction, indicating that a priori the size of the alkyl radical does not play an important role in the dynamics.

The hydrogen abstraction reaction H + C2H6→ H2(v,j) + C2H5. Part I. A full-dimensional analytical potential energy surface based on ab initio calculations.

Using as input data high-level structure electronic calculations, a new full-dimensional analytical potential energy surface (PES), named PES-2018, was developed for the title reaction, which is a valence bond/molecular mechanics based surface that depends on a set of adjustable parameters. The title reaction is practically thermoneutral, -0.18 kcal mol-1, with a high barrier, 11.62 kcal mol-1, and it presents features that make it very interesting for kinetics and dynamics studies. The PES simulates the high-level ab initio calculations used in the fitting process, with differences of less than 0.5 kcal mol-1. The quality of the fitting and the analytical expression was tested by comparing the results from this PES to different ab initio data. In the light of these results we believe that the new PES-2018 surface presents great versatility and satisfactory behaviour for the description of the nine-body reactive system. Based on this PES, in a forthcoming paper (Part II) an exhaustive kinetics and dynamics study of the title reaction will be presented.

Theoretical Study of the Pair-Correlated F + CHD3(v = 0,ν1 = 1) Reaction: Effect of CH Stretching Vibrational Excitation.

The F + CHD3(v) reaction is a benchmark system in polyatomic reactions. Theoretical/experimental comparisons have been reported in recent years that present some controversies, specifically the role of the reactant CH stretching vibrational excitation, CHD3(ν1 = 1), on the reactivity of both isotope channels, DF(v) + CHD2(v') and HF(v) + CD3(v'). However, in many cases, these comparisons are not made on an equal footing. Previous theoretical studies were concerned with overall reactivity of each isotope channel, while fine velocity map imaging experiments provided results in a product pair-correlated manner. In order to shed some light on these controversies, we perform here a pair-correlated theory/experiment comparison for the title reaction, using quasi-classical trajectory calculations on a full dimensional potential energy surface. When these calculations are analyzed in a quantum spirit, i.e., by discarding those trajectories whose results do not meet quantum-mechanical requirements and aiming to reproduce stringent experimental constraints, some of the discrepancies on overall reactivity and the effect of the CH vibrational excitation are now resolved. Agreement with the available experimental studies, though still qualitative in some aspects, has noticeably improved.

Product Translational and Vibrational Distributions for the OH/OD + CH4/CD4 Reactions from Quasiclassical Trajectory Calculations. Comparison with Experiment.

For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H2O and HOD) product vibrational distributions experimentally reported by Liu's group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser's experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more "local" character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods.

A new QM/MM method oriented to the study of ionic liquids.

The interest on room temperature ionic liquids has grown in the last decades because of their use as all-purpose solvent and their low environmental impact. In the present work, a new theoretical procedure is developed to study pure ionic liquids within the framework of the quantum mechanics/molecular mechanics method. Each type of ion (cation or anion) is considered as an independent entity quantum mechanically described that follows a differentiated path in the liquid. The method permits, through an iterative procedure, the full coupling between the polarized charge distribution of the ions and the liquid structure around them. The procedure has been tested with 1-ethyl-3-methylimidazolium tetrafluoroborate. It was found that, similar to non-polar liquids and as a consequence of the low value of the reaction field, the cation and anion charge distributions are hardly polarized by the rest of molecules in the liquid. Their structure is characterized by an alternance between anion and cation shells as evidenced by the coincidence of the first maximum of the anion-anion and cation-cation radial distribution functions with the first minimum of the anion-cation. Some degree of stacking between the cations is also found.

Final state-resolved mode specificity in HX + OH → X + H2O (X = F and Cl) reactions: a quasi-classical trajectory study.

The state-to-state dynamics of the title reactions are investigated using a quasi-classical trajectory method on recently developed accurate global potential energy surfaces. Although both produce the H2O product, these two reactions have very different characteristics in the reaction energy, barrier location, and barrier height. It is shown that the H2O product is moderately excited in its three vibrational modes in the HF + OH reaction, but its stretching modes are highly excited in the HCl + OH reaction. For both reactions, the OH vibrational degree of freedom is essentially a spectator, which sequesters its energy throughout the reaction. On the other hand, the HF vibrational excitation has almost no impact on the H2O vibrational distribution while HCl converts some of its vibrational energy into the stretching modes of H2O. These mode specific correlations can be rationalized by the recently proposed Sudden Vector Projection model.

Theoretical study of solvent effects on the ground and low-lying excited free energy surfaces of a push-pull substituted azobenzene.

The ground and low-lying excited free energy surfaces of 4-amino-4'-cyano azobenzene, a molecule that has been proposed as building block for chiroptical switches, are studied in gas phase and a variety of solvents (benzene, chloroform, acetone, and water). Solvent effects on the absorption and emission spectra and on the cis-trans thermal and photo isomerizations are analyzed using two levels of calculation: TD-DFT and CASPT2/CASSCF. The solvent effects are introduced using a polarizable continuum model and a QM/MM method, which permits one to highlight the role played by specific interactions. We found that, in gas phase and in agreement with the results found for other azobenzenes, the thermal cis-trans isomerization follows a rotation-assisted inversion mechanism where the inversion angle must reach values close to 180° but where the rotation angle can take almost any value. On the contrary, in polar solvents the mechanism is controlled by the rotation of the CN═NC angle. The change in the mechanism is mainly related to a better solvation of the nitrogen atoms of the azo group in the rotational transition state. The photoisomerization follows a rotational pathway both in gas phase and in polar and nonpolar solvents. The solvent introduces only small modifications in the nπ* free energy surface (S1), but it has a larger effect on the ππ* surface (S2) that, in polar solvents, gets closer to S1. In fact, the S2 band of the absorption spectrum is red-shifted 0.27 eV for the trans isomer and 0.17 eV for the cis. In the emission spectrum the trend is similar: only S2 is appreciably affected by the solvent, but in this case a blue shift is found.

Theoretical kinetics study of the O(³P) + CH4/CD4 hydrogen abstraction reaction: the role of anharmonicity, recrossing effects, and quantum mechanical tunneling.

Using a recently developed full-dimensional accurate analytical potential energy surface [Gonzalez-Lavado, E., Corchado, J. C., and Espinosa-Garcia, J. J. Chem. Phys. 2014, 140, 064310], we investigate the thermal rate coefficients of the O((3)P) + CH4/CD4 reactions with ring polymer molecular dynamics (RPMD) and with variational transition-state theory with multidimensional tunneling corrections (VTST/MT). The results of the present calculations are compared with available experimental data for a wide temperature range 200-2500 K. In the classical high-temperature limit, the RPMD results match perfectly the experimental data, whereas VTST results are smaller by a factor of 2. We suggest that this discrepancy is due to the harmonic approximation used in the present VTST calculations, which leads to an overestimation of the variational effects. At low temperatures the tunneling plays an important role, which is captured by both methods, although they both overestimate the experimental values. The analysis of the kinetic isotope effects shows a discrepancy between both approaches, with the VTST values smaller by a factor about 2 at very low temperatures. Unfortunately, no experimental results are available to shed any light on this comparison, which keeps it as an open question.

The hydrogen abstraction reaction O(3P) + CH4: a new analytical potential energy surface based on fit to ab initio calculations.

Based exclusively on high-level ab initio calculations, a new full-dimensional analytical potential energy surface (PES-2014) for the gas-phase reaction of hydrogen abstraction from methane by an oxygen atom is developed. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath, taking especial caution respecting the location and characterization of the intermediate complexes in the entrance and exit channels. By comparing with the reference results we show that the resulting PES-2014 reproduces reasonably well the whole set of ab initio data used in the fitting, obtained at the CCSD(T) = FULL/aug-cc-pVQZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical surface we perform an extensive dynamics study using quasi-classical trajectory calculations, comparing the results with recent experimental and theoretical data. The excitation function increases with energy (concave-up) reproducing experimental and theoretical information, although our values are somewhat larger. The OH rotovibrational distribution is cold in agreement with experiment. Finally, our results reproduce experimental backward scattering distribution, associated to a rebound mechanism. These results lend confidence to the accuracy of the new surface, which substantially improves the results obtained with our previous surface (PES-2000) for the same system.

CO2 vibrational state distributions from quasi-classical trajectory studies of the HO + CO → H + CO2 reaction and H + CO2 inelastic collision.

Quasi-classical trajectory studies have been carried out for the HO + CO → H + CO2 reaction and H + CO2 inelastic collision on a recently developed global potential energy surface based on a large number of high-level ab initio points. The CO2 vibrational state distributions for these processes have been determined using an original normal-mode analysis method. It was found that the CO2 product of the reaction is highly excited in both the Fermi-linked bending and symmetric stretching modes, but little population was found in the antisymmetric stretching mode. The substantial excitation of the CO2 vibration, while consistent with the geometry of the transition state in the exit channel, is in disagreement with available experimental data. For the inelastic collision, the CO2 is much less excited despite much higher total energies. In addition, excitations in all vibrational modes were found, in good agreement with experiment.

Kinetics and dynamics of the NH3 + H → NH2 + H2 reaction using transition state methods, quasi-classical trajectories, and quantum-mechanical scattering.

On a recent analytical potential energy surface developed by two of the authors, an exhaustive kinetics study, using variational transition state theory with multidimensional tunneling effect, and dynamics study, using both quasi-classical trajectory and full-dimensional quantum scattering methods, was carried out to understand the reactivity of the NH(3) + H → NH(2) + H(2) gas-phase reaction. Initial state-selected time-dependent wave packet calculations using a full-dimensional model were performed, where the total reaction probabilities were calculated for the initial ground vibrational state and for four excited vibrational states of ammonia. Thermal rate constants were calculated for the temperature range 200-2000 K using the three methods and compared with available experimental data. We found that (a) the total reaction probabilities are very small, (b) the symmetric and asymmetric N-H stretch excitations enhance the reactivity, (c) the quantum-mechanical calculated thermal rate constants are about one order of magnitude smaller than the transition state theory results, which reproduce the experimental evidence, and (d) quasi-classical trajectory calculations, which were performed with the main goal of analyzing the influence of the zero-point energy problem on the final dynamics results, reproduce the quantum scattering calculations on the same surface.

Quasi-classical trajectory calculations of the hydrogen abstraction reaction H + NH3.

On a new potential energy surface (PES-2009) recently developed by our group describing the H + NH(3) hydrogen abstraction reaction, we perform an exhaustive state-to-state dynamics study using quasi-classical trajectory (QCT) calculations at collision energies between 15 and 50 kcal mol(-1). The reaction cross section is very small, corresponding to a large barrier height and reproducing other theoretical measurements. Most of the available energy appears as product translational energy ( approximately 50%) with the H(2) diatomic product being vibrationally cold (v' = 0, 1). The vibrational distribution of the triatomic NH(2) product shows that it is mostly found in its vibrational ground state (approximately 80%), with a small vibrational excitation in the bending mode (approximately 12%). This distribution varies little with the collision energy. The product angular distribution shows sideways-backward behavior at low energies, shifting the scattering toward the sideways hemisphere when the energy increases. The effect of the zero-point energy constraint on these dynamical properties was analyzed.

Product vibrational distributions in polyatomic species based on quasiclassical trajectory calculations.

By including anharmonicity and Coriolis coupling terms, we have improved our earlier quasi-classical method for vibrational mode analysis in polyatomic species, which was based on a harmonic approach. Because accurate methods have been developed only for diatomic and triatomic systems, the new algorithm was tested against accurate methods for diatomic molecules, and against the semiclassical fast Fourier transform (FFT) method for triatomic species, finding excellent agreement. The new algorithm is designed to be used with dynamics studies based on quasi-classical trajectory (QCT) calculations, and it is general for any polyatomic species.

The hydrogen abstraction reaction H + CH4. I. New analytical potential energy surface based on fitting to ab initio calculations.

A new analytical potential energy surface is presented for the reaction of hydrogen abstraction from methane by a hydrogen atom. It is based on an analytical expression proposed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)], and its fittable parameters were obtained by a multibeginning optimization procedure to reproduce high-level ab initio electronic structure calculations obtained at the CCSD(T)/cc-pVTZ level. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath. No experimental information is used. By comparison with the reference results we show that the resulting surface reproduces well not only the ab initio data used in the fitting but also other thermochemical and kinetic results computed at the same ab initio level, such as equilibrium constants, rate constants, and kinetic isotope effects, which were not used in the fit. In this way we show that the new potential energy surface is correctly fitted and almost as accurate as the CCSD(T)/cc-pVTZ method in describing the kinetics of the reaction. We analyze the limitations of the functional form and the fitting method employed, and suggest some solutions to their drawbacks. In a forthcoming communication, we test the quality of the new surface by comparing its results with experimental values.