First-principles mode-specific reaction dynamics

Controlling the outcome of chemical reactions by exciting specific vibrational and/or rotational modes of the reactants is one of the major goals of modern reaction dynamics studies. In the present Perspective, we focus on first-principles vibrational and rotational mode-specific dynamics computations on reactions of neutral and anionic systems beyond six atoms such as X + C2H6 [X = F, Cl, OH], HX + C2H5 [X = Br, I], OH- + CH3I, and F- + CH3CH2Cl. The dynamics simulations utilize high-level ab initio analytical potential energy surfaces and the quasi-classical trajectory method. Besides initial state specificity and the validity of the Polanyi rules, mode-specific vibrational-state assignment for polyatomic product species using normal-mode analysis and Gaussian binning is also discussed and compared with experiment.

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.

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.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

Analytical potential energy surface and dynamics for the OH + CH3OH reaction

Using as functional form a combination of valence bond and mechanic molecular terms a new full-dimensional potential energy surface was developed for the title reaction, named PES-2022, which was fitted to high-level ab initio calculations at the coupled-cluster singles, doubles, and perturbative triples-F12 explicitly correlated level on a representative number of points describing the reactive system. This surface simultaneously describes the two reaction channels, hydrogen abstraction from the methyl group [(R1) path] and from the alcohol group [(R2) path] of methanol to form water. PES-2022 is a smooth and continuous surface, which reasonably describes the topology of this reactive system from reactants to products, including the intermediate complexes present in the system. Based on PES-2022 an exhaustive dynamics study was performed using quasi-classical trajectory calculations under two different initial conditions: at a fixed room temperature, for direct comparison with the experimental evidence and at different collision energies, to analyze possible mechanisms of reaction. In the first case, the available energy was mostly deposited as water vibrational energy, with the vibrational population inverted in the stretching modes and not inverted in the bending modes, reproducing the experimental evidence. In the second case, the analysis of different dynamics magnitudes (excitation functions, product energy partitioning, and product scattering distributions), allows us to suggest different mechanisms for both (R1) and (R2) paths: a direct mechanism for the (R2) path vs an indirect one, related with "nearly trapped" trajectories in the intermediate complexes, for the (R1) path.

Capturing quantum effects with quasi-classical trajectories in the D + H+3 → H2D+ + H reaction

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H+3 → H₂D⁺ + H reaction. Using the same H+4 potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H₂D⁺ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H+3, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.

Global potential energy surface and product pair-correlated distributions for the F(2P) + SiH4 reaction - comparison with experiments

In this paper we study the gas-phase hydrogen abstraction reaction between fluorine atoms and silane in a three-step process: potential energy surface, kinetics and dynamics. Firstly, we developed for the first time an analytical full-dimensional surface, named PES-2021, using high-level explicitly-correlated ab initio data as the input. PES-2021 represents a continuous and smooth potential with analytical gradients and includes intuitive concepts (stretching and bending nuclear motions). Based on the PES-2021 quasi-classical trajectory (QCT) calculations were performed to analyse the kinetics and dynamics. Secondly, in the kinetics study at room temperature we observed a very fast reaction with a rate constant of 3.90 × 10^-10 cm³ molecule^-1 s^-1, reproducing the scarce experimental evidence. Finally, the third step is the dynamics study, which was performed under two different conditions, a temperature of 77 K and a collision energy of 2.5 kcal mol^-1, for direct comparison with experiments. In the first case, we found the largest fraction, 44%, deposited as HF(v) vibration, where the most populated states were HF(v = 2, 3), both results reproducing the experimental evidence. The largest discrepancy with the experiment was found in the HF(j) rotational distribution, where hotter distributions were found, this discrepancy being associated with limitations of the QCT method. The second case, E = 2.5 kcal mol^-1, was a state-to-state correlated study and, therefore, more difficult. The theory overestimates (again) and consequently underestimates, respectively, the rotational and vibrational fractions of the HF(v,j) product as compared with experiments. While experimentally the SiH₃ product appears excited only in the umbrella mode, ν₂ = 0-5, correlated with the HF(v) co-product vibrational excited in v = 3 and 4, theoretically a wider vibrational distribution is found in both products, and these distributions have, obviously, an influence on the product correlated speed distributions. However, the product correlated angular distribution is well reproduced. In general, these results allowed us to test the capacity of PES-2021 + QCT tools to simulate the experimental evidence, revealing that agreement is better when average properties are compared, making the comparison worse when state-to-state properties are compared. Different causes of the theory/experiment discrepancies were analysed, and it was found that they are due, mainly, to limitations of the QCT method.

Dissection of the Multichannel Reaction O(3P) + C2H2: Differential Cross-Sections and Product Energy Distributions

The O(³P) + C₂H₂ reaction plays an important role in hydrocarbon combustion. It has two primary competing channels: H + HCCO (ketenyl) and CO + CH₂ (triplet methylene). To further understand the microscopic dynamic mechanism of this reaction, we report here a detailed quasi-classical trajectory study of the O(³P) + C₂H₂ reaction on the recently developed full-dimensional potential energy surface (PES). The entrance barrier TS1 is the rate-limiting barrier in the reaction. The translation of reactants can greatly promote reactivity, due to strong coupling with the reaction coordinate at TS1. The O(³P) + C₂H₂ reaction progress through a complex-forming mechanism, in which the intermediate HCCHO lives at least through the duration of a rotational period. The energy redistribution takes place during the creation of the long-lived high vibrationally (and rotationally) excited HCCHO in the reaction. The product energy partitioning of the two channels and CO vibrational distributions agree with experimental data, and the vibrational state distributions of all modes of products present a Boltzmann-like distribution.

Theoretical study of the Cl(2P) + SiH4 reaction: global potential energy surface and product pair-correlated distributions. Comparison with experiment

For the theoretical study of the title reaction, an analytical full-dimensional potential energy surface named PES-2021 was developed for the first time, by fitting high-level explicitly-correlated ab initio data. This reaction presented high exothermicity, (298 K) = -11.6 kcal mol^-1, reproducing the experimental evidence; it is a barrierless reaction and no intermediate complexes were found. PES-2021 is a continuous and smooth potential energy surface, it includes intuitive concepts in its development and fitting, such as stretching and bending nuclear motions, and it presents analytical first energy derivatives. Based on PES-2021, kinetics and dynamics studies were carried out using quasi-classical trajectory calculations. In the kinetics study, over the temperature range 300-450 K, we observed that rate constants were practically independent of temperature, with an almost zero activation energy, as compared to 0.0 and -0.48 kcal mol^-1 experimentally reported. In this kinetics study the role of the spin-orbit effect on reactivity was analysed. In the dynamics study, different product pair-correlated dynamics properties were compared with the only experimental evidence: product energy partition, product vibrational distribution, product angular distribution and product speed distribution. We observed two mechanisms of reaction, a stripping mechanism associated with large impact parameters and forward scattering, and an indirect mechanism associated with sideways-backward scattering related with "nearly-trapped" trajectories due to the product rotation. In general, theoretical results reasonably simulate the experimental measurements when they consider some rotational and vibrational constraints as well as binning techniques to mimic a quantum-mechanical behaviour. Although the agreement is not quantitative, the present results shed light on the mechanism of this difficult polyatomic reactive system.

Kinetic and Dynamic Studies of the F(2P) + ND3 → DF + ND2 Reaction

The fast F reaction with NH₃ poses a big challenge to experimental studies because of secondary chemical and collisional reactions. The quasi-classical trajectory method is utilized to investigate the mode specificity, product energy disposal, and temperature dependence of the thermal rate coefficient of F + ND₃ → DF + ND₂ on a recently developed potential energy surface. The effect of isotopic substitution is explored by comparing the F + ND₃ reaction with the F + NH₃ reaction. The computed results permit a better understanding of the F + ammonia reaction. The DF vibrational state has a Λ-type distribution, in accordance with the experimental measurement by the fast flow reactor technique. The product ND₂ is dominantly populated in the ground state, and a considerable amount of ND₂ is produced in the fundamental states of the bending mode. The similar vibrational state distributions of HF and NH₂ in the F + NH₃ reaction indicate a weak isotopic substitution effect on the product energy disposal. Exciting the umbrella mode of ND₃ suppresses the reaction at low energies below 5 kcal mol^-1, in sharp contrast to the observation in the F + NH₃ reaction. These dynamical behaviors can be partially explained by the sudden vector projection model. In addition, the thermal rate coefficient of F + ND₃ shows no temperature dependence in the range between 150 and 2000 K. There exists an inverse kinetic isotope effect at temperatures from 150 to 1500 K.

Effects of bending excitation on the reaction dynamics of fluorine atoms with ammonia

Vibrational excitation has been established as an efficient way to control the chemical reaction outcome. Stretching vibration of polyatomic molecules is believed to be efficient to promote abstraction reactions since energy is placed directly into the breaking bond. In this work, we report on a counterexample showing that exciting the low-frequency umbrella bending mode of ammonia enhances its reaction with fluorine atoms much more than exciting the high-frequency symmetric or asymmetric stretching mode over a wide range of collision energy, validated using both quasiclassical trajectory simulations and full-dimensional quantum dynamics calculations under the centrifugal-sudden approximation. This interesting mode-specific reaction dynamic originates from the increased chance of capturing the fluorine atom by ammonia due to the enlarged attractive interaction between them and the enhancement of the direct stripping reaction mediated by two submerged barriers.

Final-State-Resolved Dynamics of the H3+ + CO → H2 +HCO+/HOC+ Reaction: A Quasi-Classical Trajectory Study

The ion-molecule reaction H₃⁺ + CO → H₂ + HCO⁺/HOC⁺, which initiates the formation of crucial organic molecules, plays a key role in interstellar and circumstellar environments. In this work, the quasi-classical trajectory method is employed to study the reaction dynamics on a recently developed full-dimensional global potential energy surface (PES). The calculated product internal energy distributions and relative internal excited fractions agree reasonably well with the experimental measurements. For the two reaction channels, most of the available energy flows into the vibrational modes of HCO⁺ or HOC⁺ at low collision energies, followed by the translational mode and the rotational modes of HCO⁺ or HOC⁺. As the collision energy increases, the proportion of the product translational energy increases while the proportion of the product vibrational energy decreases. Furthermore, the CH and CO stretching modes and their combination bands are effectively excited for the product HCO⁺ while the bending mode is remarkably excited for the product HOC⁺.

Theoretical study of the F(2P) + NH3→ HF + NH2 reaction on an accurate potential energy surface: dynamics and kinetics

The highly exothermic hydrogen abstraction reaction of the F atom with NH₃ is investigated using the quasi-classical trajectory method on a newly developed potential energy surface (PES) for the ground electronic state. The full-dimensional PES is constructed by fitting 41 282 ab initio energy points at the level of UCCSD(T)-F12/aug-cc-pVTZ. The flexible fundamental invariant-neural network method is applied in the fitting, resulting in a total root mean square error of 0.13 kcal mol^-1. On one hand, the calculated differential cross sections agree reasonably well with the experimental results and indicate that the reaction is dominated by the direct abstraction and stripping mechanisms while a considerable amount of reaction takes place by the indirect "yo-yo" mechanism. The product energy partition also reproduces well the experimental result, which can be understood according to the geometry change along the minimum energy path. On the other hand, the obtained vibrational state distribution of the product HF follows P_νHF=2≈P_νHF=1 > P_νHF=0 > P_νHF=3, less consistent with the scattered experimental results. In addition, the calculated thermal rate coefficients have practically no temperature dependence within the statistical errors.

Dynamics in reactions on metal surfaces: A theoretical perspective

Recent advances in theoretical characterization of reaction dynamics on metal surfaces are reviewed. It is shown that the widely available density functional theory of metals and their interactions with molecules have enabled first principles theoretical models for treating surface reaction dynamics. The new theoretical tools include methods to construct high-dimensional adiabatic potential energy surfaces, to characterize nonadiabatic processes within the electronic friction models, and to describe dynamics both quantum mechanically and classically. Three prototypical surface reactions, namely, dissociative chemisorption, Eley-Rideal reactions, and recombinative desorption, are surveyed with a focus on some representative examples. While principles governing gas phase reaction dynamics may still be applicable, the presence of the surface introduces a higher level of complexity due to strong interaction between the molecular species and metal substrate. Furthermore, most of these reactive processes are impacted by energy exchange with surface phonons and/or electron-hole pair excitations. These theoretical studies help to interpret and rationalize experimental observations and, in some cases, guide experimental explorations. Knowledge acquired in these fundamental studies is expected to impact many practical problems in a wide range of interfacial processes.

Origin of Thermal and Hyperthermal CO2 from CO Oxidation on Pt Surfaces: The Role of Post-Transition-State Dynamics, Active Sites, and Chemisorbed CO2

The post-transition-state dynamics in CO oxidation on Pt surfaces are investigated using DFT-based ab initio molecular dynamics simulations. While the initial CO₂ formed on a terrace site on Pt(111) desorbs directly, it is temporarily trapped in a chemisorption well on a Pt(332) step site. These two reaction channels thus produce CO₂ with hyperthermal and thermal velocities with drastically different angular distributions, in agreement with recent experiments (Nature, 2018, 558, 280-283). The chemisorbed CO₂ is formed by electron transfer from the metal to the adsorbate, resulting in a bent geometry. While chemisorbed CO₂ on Pt(111) is unstable, it is stable by 0.2 eV on a Pt(332) step site. This helps explain why newly formed CO₂ produced at step sites desorbs with far lower translational energies than those formed at terraces. This work shows that steps and other defects could be potentially important in finding optimal conditions for the chemical activation and dissociation of CO₂ .

Uncovering the role of the stationary points in the dynamics of the F- + CH3I reaction

We describe an analysis method which assigns geometries to stationary points along (quasi)classical trajectories. The method is applied to the F^- + CH₃I reaction, thereby uncovering the role of the minima and transition states in the dynamics of the S_N2 inversion, S_N2 retention via front-side attack and double inversion, induced inversion, and proton-transfer channels. Stationary-point probability distributions, stationary-point-specific trajectory orthogonal projections, root-mean-square distance distributions, transition probability matrices, and time evolutions of the stationary points reveal long-lived front-side (F^-ICH₃) and hydrogen-bonded (F^-HCH₂I) complexes in the entrance channel and significant post-reaction ion-dipole complex (FCH₃I^-) formation in the S_N2 exit channel. Most of the proton-transfer stationary points (FHCH₂I^-) participate in all the reaction channels with larger distance deviations than the double-inversion transition state. Significant forward-backward transitions are observed between the minima and transition states indicating complex, indirect dynamics. The utility of distance and energy constraints is also investigated, thereby restricting the assignment into uniform configuration or energy ranges around the stationary points.

New Method To Extract Final-State Information of Polyatomic Reactions Based on Normal Mode Analysis

State-to-state reaction dynamics provides a comprehensive insight into reaction mechanisms of chemical reactions at the atomic level. A new scheme to extract final-state information based on normal mode analysis is proposed in this work. Different from the traditional scheme extracting the coordinates and momenta from the last step of each trajectory, they are taken in the new scheme from a specific step of each reactive trajectory within the last vibrational period of the product molecule by demanding the corresponding geometry of the step to have the minimum potential energy. Test calculations on the collisions between the atom H and the molecules H₂O, H₂S, and NH₃ show that the new scheme works much better than the traditional one. In addition, the new scheme is applied to calculate the vibrational state distribution of the product NH₂ in the reaction H + NH₃ → H₂ + NH₂.

Tracking the energy flow in the hydrogen exchange reaction OH + H2O → H2O + OH

The prototypical hydrogen exchange reaction OH + H2O → H2O + OH has attracted considerable interest due to its importance in a wide range of chemically active environments. In this work, an accurate global potential energy surface (PES) for the ground electronic state was developed based on ∼44 000 ab initio points at the level of UCCSD(T)-F12a/aug-cc-pVTZ. The PES was fitted using the fundamental invariant-neural network method with a root mean squared error of 4.37 meV. The mode specific dynamics was then studied by the quasi-classical trajectory method on the PES. Furthermore, the normal mode analysis approach was employed to calculate the final vibrational state distribution of the product H2O, in which a new scheme to acquire the Cartesian coordinates and momenta of each atom in the product molecule from the trajectories was proposed. It was found that, on one hand, excitation of either the symmetric stretching mode or the asymmetric stretching mode of the reactant H2O promotes the reaction more than the translational energy, which can be rationalized by the sudden vector projection model. On the other hand, the relatively higher efficacy of exciting the symmetric stretching mode than that of the asymmetric stretching mode is caused by the prevalence of the indirect mechanism at low collision energies and the stripping mechanism at high collision energies. In addition, the initial collision energy turns ineffectively into the vibrational energy of the products H2O and OH while a fraction of the energy transforms into the rotational energy of the product H2O. Fundamental excitation of the stretching modes of H2O results in the product H2O having the highest population in the fundamental state of the asymmetric stretching mode, followed by the ground state and the fundamental state of the symmetric stretching mode.

Dynamics and kinetics of the reaction OH + H2S → H2O + SH on an accurate potential energy surface

Mode specificity and product energy disposal are unveiled in the reaction OH + H₂S → H₂O + SH.

QCT dynamics study of OH/OD + GeH4 reactions. The problem of water bending excitation

The difficulties in the description of the water bending population could be related to the zero-point violation problem in QCT calculations.

HCN elimination from vinyl cyanide: product energy partitioning, the role of hydrogen–deuterium exchange reactions and a new pathway

A schematic diagram of HCN elimination channels from vinyl cyanide including a new CCdiss pathway.