Product Vibrational Distributions Research Articles

Differential Cross-Sections for the Vibrationally Excited H + HOD(vOH = 1-4) → H2 + OD Reactions.

Using the time-dependent wave-packet approach, we calculate the first fully converged state-to-state differential cross-sections for the H + HOD(vOH = 1-4) → H2 + OD reactions on a highly accurate neural network PES. It is found that, unlike the loss of memory effect observed in the product distributions for low vibrational excitation reactions, high initial OH vibrational excitation significantly influences not only the product vibrational distribution but also the angular distribution. Furthermore, for the H + HOD(vOH = 3,4) reactions, the total integral cross-sections maintain the pronounced oscillatory structures in the J = 0 probabilities at low collision energies, which originate from the prereactive van der Waals resonances. Notably, the product angular distributions exhibit forward-backward peaked behavior at these energies, akin to those observed in the complex-forming system with deep potential wells. This is attributed to the much longer lifetimes of these resonances compared to those of conventional transition state resonances.

Product State-Resolved Reactive Scattering Studies of the H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl Reaction by the Time-Dependent Wave Packet Method.

The typical hydrogen atom plus halogen molecule reaction H + Cl2 → HCl + Cl has implications across many fields. In this paper, product state-resolved quantum dynamics calculations for the vibrationally excited reaction H + Cl2 (v0 = 1-3, j0 = 0) → HCl + Cl were conducted using the time-dependent wave packet method on a newly developed accurate potential energy surface. Numerical results indicate that the initial vibrational excitation of Cl2 does enhance the reactivity for this early barrier reaction, although less than the enhancement of the translational energy. The calculated product vibrational state-resolved integral cross sections and rate constants reveal that the product vibrational state distribution and the initial vibrational state of Cl2 are highly correlated. The thermal rate constant in the temperature range from 100 to 1000 K was given and is found to be in reasonable agreement with the experimental measurements.

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.

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π) → H + NO+(X1Σ+): Influence of ro-vibrational excitation of NO

Quantum state-to-state nonadiabatic dynamics of the charge transfer reaction H+ + NO(X2Π, vi = 1, 3, ji = 0, 1) → H + NO+(X1Σ+) has been studied based on the recently constructed diabatic potential energy matrix. It was found that the vibrational excitation of reactant NO inhibits the reactivity, while the rotational excitation of reactant NO has little effect on the reaction probability. These attributes were also observed in the semi-classical trajectory calculations employed in the adiabatic representation. Such an inhibitory effect of the vibrational excitation of reactant NO was owing to lower accessibility of the conical intersection and avoided crossing regions, which are located in the wells with respect to the Π diabat, as evidenced by the analysis of the population of the time-independent wave functions. Calculated vibrational state distributions of the product show that the decrease of the reaction mainly leads to the less formation of low vibrational states (vf < 6), and the product vibrational state distributions are more evenly populated for vi = 1 and 3, suggesting a non-statistical behavior. However, the overall shapes of the product rotational distributions remain unchanged, indicating that the redistribution of energy into the rotation of product NO is sufficient in the charge transfer process between H+ and NO. While the reaction is dominated by the forward and backward scattering in differential cross sections (DCSs), consistent with the complex-forming mechanism, a clear forward bias in the DCSs appears, indicating that the occurrence of the reaction is not sufficiently long to undergo the whole phase space of the interaction configurations.

Detailed quasiclassical dynamics of the F- + SiH3Cl multi-channel reaction.

We report a detailed quasiclassical trajectory study on the F- + SiH3Cl multi-channel reaction using a full-dimensional ab initio analytical potential energy surface. Reaction probabilities, cross sections, initial attack and scattering angle distributions as well as product relative translational, internal, vibrational, and rotational energy distributions are obtained in the collision energy range of 1-40 kcal mol-1 for the following channels: SiH3F + Cl-, SiH2Cl- + HF, SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, and SiHFCl- + H2. All the channels are translationally cold indicating indirect mechanisms, except proton transfer (SiH2Cl- + HF), which shows mixed direct-indirect character. The angular distributions vary depending on collision energy and inversion/retention for SiH3F + Cl-. In the case of SiH2Cl- + HF front-side/back-side attack backward-forward/forward scattering preference is found at low/high collision energy. SiH2F- + HCl is formed with isotropic scattering and the preferred angle of attack is similar to the SiH3F + Cl- channel. SiH2FCl + H-/SiH2 + FHCl- favors back-side attack and isotropic/backward scattering, whereas SiHFCl- + H2 does not show significant angular preference.

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111).

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

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 abinitio 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.

Photodissociation dynamics of the ethyl radical via the Ã2A'(3s) state: H-atom product channels and ethylene product vibrational state distribution.

The photodissociation dynamics of jet-cooled ethyl radical (C2H5) via the Ã2A'(3s) states are studied in the wavelength region of 230-260nm using the high-n Rydberg H-atom time-of-flight (TOF) technique. The H + C2H4 product channels are reexamined using the H-atom TOF spectra and photofragment translational spectroscopy. A prompt H + C2H4(X̃1Ag) product channel is characterized by a repulsive translational energy release, anisotropic product angular distribution, and partially resolved vibrational state distribution of the C2H4(X̃1Ag) product. This fast dissociation is initiated from the 3s Rydberg state and proceeds via a H-bridged configuration directly to the H + C2H4(X̃1Ag) products. A statistical-like H + C2H4(X̃1Ag) product channel via unimolecular dissociation of the hot electronic ground-state ethyl (X̃2A') after internal conversion from the 3s Rydberg state is also examined, showing a modest translational energy release and isotropic angular distribution. An adiabatic H + excited triplet C2H4(ã3B1u) product channel (a minor channel) is identified by energy-dependent product angular distribution, showing a small translational energy release, anisotropic angular distribution, and significant internal excitation in the C2H4(ã3B1u) product. The dissociation times of the different product channels are evaluated using energy-dependent product angular distribution and pump-probe delay measurements. The prompt H + C2H4(X̃1Ag) product channel has a dissociation time scale of <10ps, and the upper bound of the dissociation time scale of the statistical-like H + C2H4(X̃1Ag) product channel is <5ns.

Quasi-Classical Trajectory Dynamics Study of the Reaction OH + H2S→H2O + SH and Its Isotopic Variants: Comparison with Experiment

The hydrogen abstraction reaction OH + H2S→H2O + SH plays an important role in acid rain formation, air pollution and climate change. In this work, the product energy disposals of the reaction and its isotopic variants OD + H2S and OD + D2S are calculated on a new ab-initio-based ground electronic state potential energy surface (PES) using the quasi-classical trajectory method. The PES is developed by fitting a total of 72,113 points calculated at the level of UCCSD(T)-F12a/aug-cc-pVTZ and using the fundamental invariant-neural network method, resulting in a total RMSE of 4.14 meV. The product H2O formed in the OH + H2S reaction at 298 K is found to be largely populated in the first overtone states of its symmetric and asymmetric stretching modes, while the vibrational distributions of the products HOD and D2O in the isotopically substituted reactions are visibly different. The computed product vibrational state distributions agree reasonably well with experimental results and are rationalized by the sudden vector projection model.

Theoretical study on photodissociation dynamics of vibrational excited states of H2S in the first absorption band

The photodissociation quantum dynamics for the first absorption band of H2S in different initial vibrational states have been investigated using Chebyshev real wave packet method. Because of the difference of the wave functions for the initial vibrational states, the calculated absorption spectra and the distributions of vibrational and rotational state of the products display different dynamic characteristics. The width and peak position of the absorption spectra for initial stretching excited states (1,0,0) and (0,0,1) are different from that of the vibrational ground state, while the (0,1,0) vibrational state has two almost equally high peaks in its absorption spectrum because of the change of wave function in angular coordinate. The product vibrational state distribution for (0,1,0) initial state weakly depends on the excitation energy and is dominated by the products of v=0, but SH(v=1) fragment is dominant at lower energy for (1,0,0) and (0,0,1) vibrational states. The rotational state distributions of products are very cold with the peak at j=l for these four states and weakly depend on the total energy. Besides, the rotational state distribution from (0,1,0) vibrational state displays strong oscillation, and its anisotropic parameter with rotational quantum numbers is also different from that of the other three vibrational states.

Combining Machine Learning and Spectroscopy to Model Reactive Atom + Diatom Collisions.

The prediction of product translational, vibrational, and rotational energy distributions for arbitrary initial conditions for reactive atom + diatom collisions is of considerable practical interest in atmospheric re-entry. Because of the large number of accessible states, determination of the necessary information from explicit (quasi-classical or quantum) dynamics studies is impractical. Here, a machine-learned (ML) model based on translational energy and product vibrational states assigned from a spectroscopic, ro-vibrational coupled energy expression based on the Dunham expansion is developed and tested quantitatively. All models considered in this work reproduce final state distributions determined from quasi-classical trajectory (QCT) simulations with R2 ∼ 0.98. As a further validation, thermal rates determined from the machine-learned models agree with those from explicit QCT simulations and demonstrate that the atomistic details are retained by the machine learning which makes them suitable for applications in more coarse-grained simulations. More generally, it is found that ML is suitable for designing robust and accurate models from mixed computational/experimental data which may also be of interest in other areas of the physical sciences.

Reaction Pathway Control via Reactant Vibrational Excitation and Impact on Product Vibrational Distributions: The O + HO2 → OH + O2 Atmospheric Reaction.

Chemical reactions often have multiple pathways, the control of which is of fundamental and practical importance. In this Letter, we examine the dynamics of the O + HO2 → OH + O2 reaction, which plays an important role in atmospheric chemistry, using quasi-classical trajectories on a recently developed full-dimensional potential energy surface (PES). This reaction has two pathways leading to the same products: the H abstraction pathway (Oa + HObOc → OaH + ObOc) and the O abstraction pathway (Oa + HObOc → ObH + OaOc). Under thermal conditions, the reaction is dominated by the latter channel, which is barrierless, leading to vibrational excitation of the O2 product. However, we demonstrate that excitation of the HO2 reactant in its O-H (v1) vibrational mode results in dramatic switching of the reaction pathway to the activated H abstraction channel, which leads to a highly excited OH product vibrational state distribution. The implications of such dynamical effects in the atmospheric chemistry are discussed.

Product vibrational state distributions of F+CH3OH reaction on full-dimensional accurate potential energy surface

The hydrogen abstraction reaction of methanol with fluorine atoms can produce HF and CH3O or CH2OH radicals, which are important in the environment, combustion, radiation, and interstellar chemistry. In this work, the dynamics of this typical reaction is investigated by the quasi-classical trajectory method based on a recently developed globally accurate full-dimensional potential energy surface. Particularly, the vibrational state distributions of the polyatomic products CH3O and CH2OH are determined by using the normal mode analysis method. It is found that CH3O and CH2OH are dominantly populated in the ground state when the reactants are at the ground ro-vibrational state. The OH stretching mode, torsional mode, H2CO out-of-plane bending mode and their combination bands in the CH2OH product can be effectively excited once the OH stretching mode of the reactant CH3OH is excited to the first vibrationally excited state. Most of the available energy flows into the HF vibrational energy and the translational energy in both channels, while the radical products, CH3O or CH2OH, receive a small amount of energy, consistent with experiment, which is an indication of its spectator nature.

Non-adiabatic couplings induced complex-forming mechanism in H+MgH+ → Mg++H2 reaction

A chemical process may involve multiple adiabatic electronic states, and non-adiabatic couplings play an important role in the reaction mechanism. In this work, the effect of non-adiabatic couplings in the H+MgH+ → Mg+ + H2 reaction are studied using the time-dependent wave packet method and trajectory surface hopping method. The calculated results show that the reaction follows a direct abstraction process when the non-adiabatic couplings are neglected. However, when non-adiabatic couplings are included in the calculations, a long-lived excited state complex (MgH2+)* can be formed during the reaction. These direct and complex-forming reaction pathways are revealed by trajectory surface hopping calculations. The non-adiabatic couplings induced complex-forming mechanism not only increases the reactivity but also has significant effect on the product vibrational state 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.

Effect of Reagent Vibration and Rotation on the State-to-State Dynamics of the Hydrogen Exchange Reaction, H + H2 → H2 + H.

State-to-state dynamics of the benchmark hydrogen exchange reaction H + H2 (v = 0-4, j = 0-3) → H2 (v', j') + H is investigated with the aid of the real wave packet approach of Gray and Balint-Kurti (J. Chem. Phys. 1998, 108, 950-962) and electronic ground BKMP2 potential energy surface of Boothroyd et al. (J. Chem. Phys. 1996, 104, 7139-7152). Initial state-selected and product state-resolved reaction probabilities, integral cross section, and product diatom vibrational and rotational level populations at a few collision energies are reported to elucidate the energy disposal mechanism. State-specific thermal rate constants are also calculated and compared with the available literature results. Coriolis coupling terms of the nuclear Hamiltonian are included, and calculations are parallelized over the helicity quantum number, Ω'. Attempts are made, in particular, to study the effect of reagent vibrational and rotational excitations on the dynamical attributes. It is found that the calculations become computationally expensive with reagent vibrational and rotational excitation. Reagent vibrational excitation is found to enhance the reactivity and has significant impact on the energy disposal to the vibrational and rotational degrees of freedom of the product. The interplay of reagent translational and vibrational energy on the product vibrational distribution unfolds an important aspect of the energy disposal mechanism. The effect of reagent rotation on the state-to-state dynamics is found not to be very significant, and the weak effect turns out to be specific to v'.

Theoretical study of the O(3P) + C2H6 reaction based on a new ab initio-based global potential energy surface.

A new analytical potential energy surface was developed for the first time for the nine-body O(3P) + C2H6 hydrogen abstraction reaction, named PES-2020, which was fitted to explicitly-correlated high-level electronic structure calculations. This surface simulates the topography of the reactive system, from reactants to products, OH(v,j) + C2H5. The adiabatic energy of reaction, ΔHr(0 K) = -2.33 kcal mol-1, reproduces the experimental evidence, and the barrier height, 10.70 kcal mol-1, agrees with the ab initio calculations used as input. In addition, an intermediate complex in the exit channel is observed, which is stabilized with respect to the products of the reaction. Based on PES-2020 a dynamics study was carried out, where quasi-classical trajectory calculations were performed for collision energies in the range of 7.0-60.0 kcal mol-1, which covers high collision energy regions. The reaction cross section increases with collision energy; the largest fraction of available energy is deposited as translational energy (44-66%), and the scattering distribution evolves from backward to forward with collision energy. These findings reproduce previous theoretical calculations using electronic structure calculations of lower levels. However, where these previous studies failed, viz. in rotational and vibrational OH(v,j) distributions, PES-2020 reproduces practically quantitatively the experimental evidence, i.e., cold vibration and rotation, the rotational distribution peaking at j = 1-3 depending on the collision energy. In sum, this behaviour is typical of gas-phase hydrogen abstraction reactions with direct mechanism and high reaction barrier.

Insights into the Mechanism of Nonadiabatic Photodissociation from Product Vibrational Distributions. The Remarkable Case of Phenol.

The fate of a photoexcited molecule is often strongly influenced by electronic degeneracies, such as conical intersections, which break the Born-Oppenheimer separation of electronic and nuclear motion. Detailed information concerning internal energy redistribution in a nonadiabatic process can be extracted from the product state distribution of a photofragment in photodissociation. Here, we focus on the nonadiabatic photodissociation of phenol and discuss the internal excitation of the phenoxyl fragment using both symmetry analysis and wave packet dynamics. It is shown that unique and general selection rules exist, which can be attributed to the geometric phase in the adiabatic representation. Further, our results provide a reinterpretation of the experimental data, shedding light on the impact of conical intersections on the product state distribution.

QCT study of the vibrational and translational role in the H + C2H6(ν1, ν2, ν5, ν7, ν9 and ν10) reactions

Two important issues were analysed in the title reaction: the effects of vibrational excitation, associated with mode selectivity, and the role of translational energy, associated with Polanyi’s rules. Based on a global analytical potential energy surface, PES-2018, recently developed in our group, quasi-classical trajectory (QCT) calculations were performed at total energy of 35 kcal mol−1, either as translation or as a combination of translation and vibration energy. Independent vibrational excitation by one quantum of any of the CH3 stretching modes in ethane leads to similar dynamics pictures of reaction cross sections and H2(v′, j′) rotovibrational and scattering distributions, ruling out mode selectivity. Normal mode analysis showed a cold, non-inverted, H2(v′) product vibrational distribution, while the C2H5(v′) co-product presented many vibrational states, all of them with a low population, practically simulating a classical behaviour. An equivalent amount of energy as translation raises reactivity somewhat less effective than vibrational energy, contrary to that found for the O(3P) + CH4 reaction. Both reactions present “central” barriers, so this opposite behaviour shows the difficulties for a straightforward application of the Polanyi′s rules. The role of vibrational and translational energy on dynamics has been rationalized by the coupling between vibrational modes, which makes analysis of vibrational excitation difficult in polyatomic systems. Finally, the role of the total energy on reactivity and mode selectivity was analysed, concluding that at lower energy, 15 kcal mol−1, translational energy is much more effective than vibrational energy to enhance reactivity, while at intermediate energy, 20 kcal mol−1, the situation is more confusing and strongly dependent on the counting methods used in the QCT calculations. Therefore, very small mode selectivity is found, and translation seems to be more effective in enhancing reactivity than vibration at low collision energies, while this behaviour is reversed as we increase the collision energy, being the turning point around 20 kcal mol−1.

A theoretical study on the C + OH reaction dynamics and product energy disposal with vibrationally excited reagent

State-to-state dynamics of the C(3 P) + OH(X2 Π , v = 0– 2, j = 0) → CO (a3 Π ) + H (2 S), reaction on the first (12 A″ ) and second (14 A″ ) excited states is studied by the real wave packet method of Gray and Balint-Kurti [S.K. Gray et al., J. Chem. Phys. 108 , 950 (1998)]. Product state-resolved (both vibrational and rotational) and total reaction probabilities are calculated for the total angular momentum, J = 0. Product vibrational and rotational distributions are also examined at five different collision energies to elucidate the reaction mechanism. Reagent vibrational excitation is found to decrease the reactivity on the 12 A″ state and enhance the same on the 14 A″ state. While the excess reagent vibrational energy releases mainly as product translation on the 12 A″ state, the same releases as product vibration and rotation on the 14 A″ state. The product rotational distribution is relatively cold on the 14 A″ state. Despite same mass combination and same exoergicity, the drastic differences of the dynamics of the reaction on the two excited states are related to the microscopic topology of the underlying reaction path. The late barrier present on the 14 A″ state plays crucial role on the reaction dynamics at the state-to-state level. The results of the present study are compared with the available literature data.