State-resolved Differential Cross Research Articles

High-Resolution Crossed-Beam Dynamics Studies of the D + Para-H2 → HD + H Reaction at 1.21 eV.

Understanding kinetic isotope effects is important in the study of the reaction dynamics of elementary chemical reactions, particularly those involving hydrogen atoms and molecules. As one of the isotopic variants of the hydrogen exchange reaction, the D + para-H2 reaction has attracted much attention. However, experimental studies of this reaction have been limited primarily due to its strong experimental background noise. In this study, by using the velocity map ion imaging method and the near-threshold ionization technique, together with improvements on the vacuum condition in the vicinity of the collision zone, background noise was reduced significantly, and quantum state-resolved differential cross sections (DCSs) for the D + para-H2 reaction at a collision energy of 1.21 eV were acquired in a crossed molecular beams experiment. Interestingly, clear rotational state-dependent angular distributions were noticed in the quantum state-resolved DCSs. The most intense peak's positions for HD (v', j') products shift to different scattering directions as the product's ro-vibrational quantum number increases. Two different microscopic reaction mechanisms are found to be involved in this reaction for HD products in different vibrational states. The results show a direct correlation between the scattering angle and the product's rotational quantum number, revealing that the contributions of impact parameters are strongly influenced by the corresponding centrifugal barrier.

Strong Angular Oscillation of Rotationally Resolved Differential Cross Section in the H + HD → H2 + D Reaction at the Collision Energy of 2.07 eV: Evidence of Geometric Phase Effects.

Geometric phase (GP) effects in chemical reactions are subtle quantum phenomena that are challenging to identify. In this work, we report a joint experimental and theoretical study of the H + HD → H2 + D reaction at a collision energy of 2.07 eV, which is far below the energy of the conical intersection of 2.53 eV. The rotationally state-resolved differential cross sections were measured by a crossed-beam experiment with the scheme of D-atom Rydberg tagging time-of-flight detection. Experimental angular distributions of three rotational states of H2 products exhibit notable variation near the backward scattering direction. Time-dependent quantum mechanics calculations (TDQMs) were carried out at the same collision energy, with and without the inclusion of GP. The experimental angular distributions are in good agreement with TDQM results with the inclusion of GP but do not agree with TDQM results without the inclusion of GP. This work demonstrates the existence of GP effects at energy far below the conical intersection.

Effects of single quantum rotational excitation on reaction of F+D2 at collision energies between 44 and 164 cm−1

There is no general picture to describe the influences of reagent rotational excitation on the reaction, which proceeds via the tunnelling mechanism at collision energies far below the reaction barrier. Here we report a crossed beam study on the prototypical reaction of F + D2(v=0, j=0,1) → DF(v′) + D at collision energies between 44 and 164 cm−1 with the scheme of multichannel D-atom Rydberg tagging time-of-flight detection. Vibrational state resolved differential cross sections are obtained at v′=2, 3, 4 levels. The effects of reagent rotational excitation were investigated at an equivalent amount of total energy by precise tuning of translational energies. Compared with translation, the rotation of D2 is found to be more efficient to promote the title reaction. Profound differences introduced by rotation of D2 are also observed on the angular distribution and quantum state distribution of DF products. We hope the present work could provide an example for understanding the effects of reagent rotational excitation on the chemical reaction at energies that are much lower than the reaction barrier.

Signature of shape resonances on the differential cross sections of the S(1D)+H2 reaction.

Shape resonances appear when the system is trapped in an internuclear potential well after tunneling through a barrier. They manifest as peaks in the collision energy dependence of the cross section (excitation function), and in many cases, their presence can be observed experimentally. High-resolution crossed-beam experiments on the S(1D) + H2(j = 0) reaction in the 0.81-8.5 meV collision energy range reaction revealed non-monotonic behavior and the presence of oscillations in the reaction cross section as a function of the collision energy, as predicted by quantum mechanical (QM) calculations. In this work, we have analyzed the effect of shape resonances on the differential cross sections for this insertion reaction by performing additional QM calculations. We have found that, in some cases, the resonance gives rise to a large enhancement of extreme backward scattering for specific final states. Our results also show that, in order to yield a significant change in the state-resolved differential cross section, the resonance has to be associated with constructive interference between groups of partial waves, which requires not getting blurred by the participation of many product helicity states.

Rainbow scattering in rotationally inelastic collisions of HCl and H2.

We examine rotational transitions of HCl in collisions with H2 by carrying out quantum mechanical close-coupling and quasi-classical trajectory (QCT) calculations on a recently developed globally accurate full-dimensional ab initio potential energy surface for the H3Cl system. Signatures of rainbow scattering in rotationally inelastic collisions are found in the state resolved integral and differential cross sections as functions of the impact parameter (initial orbital angular momentum) and final rotational quantum number. We show the coexistence of distinct dynamical regimes for the HCl rotational transition driven by the short-range repulsive and long-range attractive forces whose relative importance depends on the collision energy and final rotational state, suggesting that the classification of rainbow scattering into rotational and l-type rainbows is effective for H2 + HCl collisions. While the QCT method satisfactorily predicts the overall behavior of the rotationally inelastic cross sections, its capability to accurately describe signatures of rainbow scattering appears to be limited for the present system.

A fundamental invariant-neural network representation of quasi-diabatic Hamiltonians for the two lowest states of H3.

The fundamental invariant neural network (FI-NN) approach is developed to represent coupled potential energy surfaces in quasidiabatic representations with two-dimensional irreducible representations of the complete nuclear permutation and inversion (CNPI) group. The particular symmetry properties of the diabatic potential energy matrix of H3 for the 1A' and 2A' electronic states were resolved arising from the E symmetry in the D3h point group. This FI-NN framework with symmetry adaption is used to construct a new quasidiabatic representation of H3, which reproduces accurately the ab initio energies and derivative information with perfect symmetry behaviors and extremely small fitting errors. The quantum dynamics results on the new FI-NN diabatic PESs give rise to accurate oscillation patterns in the product state-resolved differential cross sections. These results strongly support the accuracy and efficiency of the FI-NN approach to construct reliable diabatic representations with complicated symmetry problems.

Imaging the State-to-State Dynamics of the H + D2 → HD + D Reaction at 1.42 eV.

High-resolution state-resolved differential cross sections (DCSs) are of great importance in understanding quantum reaction dynamics, and they are the most detailed observables that can be experimentally measured. Here we report a synergic crossed molecular beam and quantum reaction dynamics study on the H + D2 reaction. With the time-sliced velocity map ion imaging (VMI) technique and the near-threshold ionization scheme, we acquired the product rovibrational state-resolved DCSs of the H + D2 (v = 0, j = 0) → HD (v', j') + D reaction at a collision energy of 1.42 eV. For HD products with small j' quantum numbers, significant forward scattering with clear angular oscillations was observed. The forward scattering disappears for the rotational states with large j' quantum numbers. Interestingly, as the j' number increases, the peak of the DCS shifts from backward to sideways systematically. The experimental observation agrees very well with theoretical quantum mechanical dynamics results, which reveals that the systematic shift of the peak in the DCS from backward scattering to sideways scattering can be understood very well with the strong correlation between the product rotational quantum number j' and the specific partial waves (J = 3-12), whereas the forward angular oscillations are from the coherent summation of larger partial waves.

Crossed beam study on the F+D2→DF+D reaction at hyperthermal collision energy of 23.84 kJ/mol

We presented an experimental apparatus combining the H-atom Rydberg tagging time-of-flight technique and the laser detonation source for studying crossed beam reactions at hyperthermal collision energies. The preliminary study of the F+D2 DF+D reaction at hyperthermal collision energy of 23.84 kJ/mol was performed. Two beam sources were used in this study: one is the hyperthermal F beam source produced by a laser detonation process, and the other is D2 beam source generated by liquid-N2 cooled pulsed valve. Vibrational state-resolved differential cross sections (DCSs) of product for the title reaction were determined. From the product vibrational state-resolved DCS, it can be concluded that products DF(v′=0, 1, 2, 3) are predominantly distributed in the sideway and backward scattering directions at this collision energy. However, the highest vibrational excited product DF(v′=4), is clearly peaked in the forward direction. The probable dynamical origins for these forward scattering products were analyzed and discussed.

Reaction mechanism of and its state-to-state quantum dynamics**Project supported by the National Natural Science Foundation of China (Grant Nos. 11674198 and 11504206), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2016AP14), and the Taishan Scholar Project of Shandong Province, China.

The quantum state-to-state calculations of the reaction are performed on a potential energy surface of state. The state-resolved integral and differential cross sections and product state distributions are calculated and discussed. It is found that the rotational distribution, rather than the vibrational distribution, of the product has an obvious inversion. Due to the fact that it is a small-impact-parameter collision, its product D2 is mainly dominated by rebound mechanism, which can lead to backward scattering at low collision energy. As the collision energy increases, the forward scattering and sideward scattering begin to appear. In addition, the backward collision is also found to happen at high collision energy, through which we can know that both the rebound mechanism and stripping mechanism exist at high collision energy.

Quantum state-to-state study for (H-(D-),HD) collisions on two potential energy surfaces.

Quantum time-dependent wave-packet calculations have been carried out to explore the state-to-state dynamics of the ion-molecule (H-(D-),HD) collisions on two accurate ab initio potential energy surfaces in the collision energy range 0.2-1.2 eV. Total and final state-resolved integral and differential cross sections are elaborated in detail. The differential cross sections vary substantially with the collision energy, turning from predominantly backward-scattering at low collision energies to forward and sideways scattering bias at relatively high collision energies. The rebound, stripping and time-delayed mechanisms are found to be possible in (H-(D-),HD) collisions. A set of quasi-classical trajectory calculations were performed, and the results indicate that the backward-scattering peak is caused by the low impact parameter trajectories, while the trajectories of high impact parameter are responsible for the forward scattering. A set of representative state-to-state differential cross sections at collision energies 0.6 and 1.2 eV are also presented. Different reaction mechanisms are dominant in (H-(D-),HD) collisions at different collision energies, resulting in different product rovibrational state distributions. The differences between the dynamics results based on the two potential energy surfaces are also discussed.

State-to-state quantum dynamics of F(2P)+HO(2Π)→O(3P)+HF(1Σ+) reaction on 13A′ and 23A′′ surfaces

ABSTRACTThe state-to-state dynamics of reaction F + HO() is studied on the potential energy surfaces (PESs) of the and states. The time-dependent wave packet method, which is carried out on the graphics processing units, is used for this accurate calculation. The emphasis is on the exploration of different dynamical behaviours happening on the PESs of two excited states. The obvious vibrational and rotational inversion is found in the state-resolved integral cross section on PES, but the rotational inversion does not appear on PES. Both the total and state-resolved differential cross sections (DCSs) of the reaction on two PESs exhibit the behaviour of sideward and backward scattering, but the backward scattering of is much stronger because of its higher energy barrier, and the sideward scattering is enhanced with the increasing of collision energy. In addition, a multi-peak structure is discovered in the distribution of the product rotational state-resolved integral and DCSs, which is attributed to the quantum interference of the resonance wave functions.

Accurate Quantum Wave Packet Study of the Deep Well D+ + HD Reaction: Product Ro-vibrational State-Resolved Integral and Differential Cross Sections.

The H+ + H2 reaction and its isotopic variants as the simplest triatomic ion-molecule reactive system have been attracting much interests, however there are few studies on the titled reaction at state-to-state level until recent years. In this work, accurate state-to-state quantum dynamics studies of the titled reaction have been carried out by a reactant Jacobi coordinate-based time-dependent wave packet approach on diabatic potential energy surfaces constructed by Kamisaka et al. Product ro-vibrational state-resolved information has been calculated for collision energies up to 0.2 eV with maximal total angular momentum J = 40. The necessity of including all K-component for accounting the Coriolis coupling for the reaction has been illuminated. Competitions between the two product channels, (D+ + HD' → D'+ + HD and D+ + HD' → H+ + DD') were investigated. Total integral cross sections suggest that resonances enhance the reactivity of channel D+ + HD'→ H+ + DD', however, resonances depress the reactivity of the another channel D+ + HD' → D'+ + HD. The structures of the differential cross sections are complicated and depend strongly on collision energies of the two channels and also on the product rotational states. All of the product ro-vibrational state-resolved differential cross sections for this reaction do not exhibit rigorous backward-forward symmetry which may indicate that the lifetimes of the intermediate resonance complexes should not be that long. The dynamical observables of this deuterated isotopic reaction are quite different from the reaction of H+ + H2 → H2 + H+ reported previously.

State-to-state dynamics of reaction on potential energy surface**Project supported by the National Natural Science Foundation of China (Grant Nos. 11504206 and 11404049), the China Postdoctoral Science Foundation (CPSF) (Grant No. 2014M561259), and the Ph. D. Research Start-up Fund of Shandong Jiaotong University.

State-to-state time-dependent quantum dynamics calculations are carried out to study reaction on ground potential energy surface (PES). The vibrationally resolved reaction probabilities and the total integral cross section agree well with the previous results. Due to the heavy–light–heavy (HLH) system and the large exoergicity, the obvious vibrational inversion is found in a state-resolved integral cross section. The total differential cross section is found to be forward–backward scattering biased with strong oscillations at energy lower than a threshold of 0.10 eV, which is the indication of the indirect complex-forming mechanism. When the collision energy increases to greater than 0.10 eV, the angular distribution of the product becomes a strong forward scattering, and almost all the products are distributed at . This forward-peaked distribution can be attributed to the larger J partial waves and the property of the F atom itself, which make this reaction a direct abstraction process. The state-resolved differential cross sections are basically forward-backward symmetric for , 1, and 2 at a collision energy of 0.07 eV; for a collision energy of 0.30 eV, it changes from backward/sideward scattering to forward peaked as increasing from 0 to 3. These results indicate that the contribution of differential cross sections with more highly vibrational excited states to the total differential cross sections is principal, which further verifies the vibrational inversion in the products.

Analysis of the state-to-state dynamics mechanism of H + HBr (v = 0,1, j = 0) → H2 + Br reaction

The dynamics of the H + HBr(v = 0, 1, j = 0) → H2 + Br reaction was investigated in detail at the state-to-state level on a new ab initio potential energy surface (Y Kurosaki and T Takayanagi, private communication). A newly developed graphics processing unit (GPU)-accelerated time-dependent wave packet program was applied to calculate product vibrational state-resolved integral cross sections and differential cross sections for collision energies ranging from 0.05 eV to 1.4 eV. The reaction mechanism was also fully analyzed with respect to the structures of the differential cross sections. The state specific integral cross section and differential cross section of H + HBr(v = 0, j = 0) is remarkably different from that for H + HBr(v = 1, j = 0).

State-to-State Mode Specificity in F + CHD3 → HF/DF + CD3/CHD2 Reaction.

The F + CHD3 → HF/DF + CD3/CHD2 reaction is studied using a state-to-state quasi-classical trajectory method on a recently developed ab initio based full-dimensional potential energy surface. Consistent with sudden vector projection model predictions, the HF/DF products are highly excited in both vibrational and rotational modes, while the CD3/CHD2 product internal excitation is mostly in the umbrella/out-of-plane mode. Furthermore, the C-H stretching vibration in the CHD3 reactant is found to behave as an active mode for the HF + CD3 channel, leading to additional excitation in the HF product but having almost no impact on CD3 vibrational state distributions. On the other hand, this mode acts as a spectator for the DF + CHD2 channel, exerting little influence on the DF and other CHD2 vibrational modes except an extra quantum excitation in the C-H stretching mode. The calculated vibrational state resolved differential cross sections are in good agreement with available experimental results at Ec = 9.00 kcal/mol.

State-resolved differential and integral cross sections for the Ne + H2 (+) (v = 0-2, j = 0) → NeH(+) + H reaction.

State-to-state quantum dynamic calculations for the proton transfer reaction Ne + H2 (+) (v = 0-2, j = 0) are performed on the most accurate LZHH potential energy surface, with the product Jacobi coordinate based time-dependent wave packet method including the Coriolis coupling. The J = 0 reaction probabilities for the title reaction agree well with previous results in a wide range of collision energy of 0.2-1.2 eV. Total integral cross sections are in reasonable agreement with the available experiment data. Vibrational excitation of the reactant is much more efficient in enhancing the reaction cross sections than translational and rotational excitation. Total differential cross sections are found to be forward-backward peaked with strong oscillations, which is the indication of the complex-forming mechanism. As the collision energy increases, state-resolved differential cross section changes from forward-backward symmetric peaked to forward scattering biased. This forward bias can be attributed to the larger J partial waves, which makes the reaction like an abstraction process. Differential cross sections summed over two different sets of J partial waves for the v = 0 reaction at the collision energy of 1.2 eV are plotted to illustrate the importance of large J partial waves in the forward bias of the differential cross sections.

Quantum and classical dynamics of H + CaCl(X (2)Σ(+)) → HCl + Ca((1)S) reaction and vibrational energy levels of the HCaCl complex.

We carried out accurate quantum wave packet as well as quasi-classical trajectory (QCT) calculations for H + CaCl (νi = 0, ji = 0) reaction occurring on an adiabatic ground state using the recent ab initio potential energy surface to obtain the quantum and QCT reaction probabilities for several partial waves (J = 0, 10, and 20) as well as state resolved QCT integral and differential cross sections. The complete list of vibrational energy levels supported by the intermediate HCaCl complex is also obtained using the Lanczos algorithm. The QCT reaction probabilities show excellent agreement with the quantum ones except for the failure in reproducing the highly oscillatory resonance structure. Despite the fact that the reaction is exothermic and the existence of a barrier that is energetically lower than the bottom of the reactant valley, the reaction probability for J = 0 shows threshold-like behavior and the reactivity all through the energies is very low (<0.1). The dynamical features at two different energy regions (<0.35 eV and >0.35 eV) are found to be different drastically from each other. The analyses of these results suggest that the reaction is governed by one of the two different types of reaction mechanism, one is the direct mechanism at the high energy region and the other is the indirect mechanism at the low energy region by which the reaction proceeds through the long-lived intermediate complex followed by a statistical dissociation into asymptotic channels.

Quantum state-resolved differential cross sections for complex-forming chemical reactions: Asymmetry is the rule, symmetry the exception.

We argue that statistical theories are generally unable to accurately predict state-resolved differential cross sections for triatomic bimolecular reactions studied in beam experiments, even in the idealized limit where the dynamics are fully chaotic. The basic reason is that quenching of interferences between partial waves is less efficient than intuitively expected, especially around the poles.

Rotational Orientation Effects in NO(X) + Ar Inelastic Collisions.

Rotational angular momentum orientation effects in the rotationally inelastic collisions of NO(X) with Ar have been investigated both experimentally and theoretically at a collision energy of 530 cm(-1). The collision-induced orientation has been determined experimentally using a hexapole electric field to select the ϵ = -1 Λ-doublet level of the NO(X) j = 1/2 initial state. Fully quantum state resolved polarization-dependent differential cross sections were recorded experimentally using a crossed molecular beam apparatus coupled with a (1 + 1') resonance-enhanced multiphoton ionization detection scheme and subsequent velocity-map imaging. To determine the NO sense of rotation, the probe radiation was circularly polarized. Experimental orientation polarization-dependent differential cross sections are compared with those obtained from quantum mechanical scattering calculations and are found to be in good agreement. The origin of the collision-induced orientation has been investigated by means of close-coupled quantum mechanical, quantum mechanical hard shell, quasi-classical trajectory (QCT), and classical hard shell calculations at the same collision energy. Although there is evidence for the operation of limiting classical mechanisms, the rotational orientation cannot be accounted for by QCT calculations and is found to be strongly influenced by quantum mechanical effects.

Effect of Reagent Vibrational Excitation on the Dynamics of F + H2(v = 1, j = 0) → HF(v', j') + H Reaction.

The reaction of fluorine atom with vibrationally excited H2 at v = 1 has been studied using a high resolution crossed molecular beam apparatus at collision energies of 0.52 and 0.90 kcal/mol. Product HF rotational state-resolved differential cross sections (DCSs) were measured at v' = 2, 3, 4 levels. The product angular distributions are predominantly backward scattered except for a small forward signal of HF(v' = 4) at 0.90 kcal/mol. At the collision energy of 0.52 kcal/mol, the forward scattering peak of the HF(v' = 2) product, which arises in F + H2(v = 0) reaction from the Feshbach resonances, disappears in F + H2(v = 1) reaction. Oscillatory structures do not appear in the backward direction of the scattering as the collision energy increases from 0.4 to 2.0 kcal/mol, indicating there are no explicit reaction resonances in the F + H2(v = 1, j = 0) → HF + H reaction in the studied energy range. Quantum dynamics calculations on a highly accurate potential energy surface are in good agreement with the experimental results and reveal that the reaction occurs via likely a direct abstraction mechanism, not via long-lived reactive resonances.