Product Rotational Angular Momentum Research Articles

Inelastic scattering of NO(A2Σ+) + CO2: rotation-rotation pair-correlated differential cross sections.

A crossed beam velocity-map ion-imaging apparatus has been used to determine differential cross sections (DCSs) for the rotationally inelastic scattering of NO(A2Σ+, v = 0, j = 0.5) with CO2, as a function of both NO(A, v = 0, N') final state and the coincident final rotational energy of the CO2. The DCSs are dominated by forward-peaked scattering for all N', with significant rotational excitation of CO2, and a small backward scattered peak is also observed for all final N'. However, no rotational rainbow scattering is observed and there is no evidence for significant product rotational angular momentum polarization. New ab initio potential energy surface calculations at the PNO-CCSD(T)-F12b level of theory report strong attractive forces at long ranges with significant anisotropy relative to both NO and CO2. The absence of rotational rainbow scattering is consistent with removal of low-impact-parameter collisions via electronic quenching, in agreement with the literature quenching rates of NO(A) by CO2 and recent electronic structure calculations. We propose that high-impact-parameter collisions, that do not lead to quenching, experience strong anisotropic attractive forces that lead to significant rotational excitation in both NO and CO2, depolarizing product angular momentum while leading to forward and backward glory scattering.

Imaging rotational energy transfer: comparative stereodynamics in CO + N2 and CO + CO inelastic scattering.

State-to-state rotational energy transfer in collisions of ground ro-vibrational state 13CO molecules with N2 molecules has been studied using the crossed molecular beam method under kinematically equivalent conditions used for 13CO + CO rotationally inelastic scattering described in a previously published report (Sun et al., Science, 2020, 369, 307-309). The collisionally excited 13CO molecule products are detected by the same (1 + 1' + 1'') VUV (Vacuum Ultra-Violet) resonance enhanced multiphoton ionization scheme coupled with velocity map ion imaging. We present differential cross sections and scattering angle resolved rotational angular momentum alignment moments extracted from experimentally measured 13CO + N2 scattering images and compare them with theoretical predictions from quasi-classical trajectories (QCT) on a newly calculated 13CO-N2 potential energy surface (PES). Good agreement between experiment and theory is found, which confirms the accuracy of the 13CO-N2 potential energy surface for the 1460 cm-1 collision energy studied by experiment. Experimental results for 13CO + N2 are compared with those for 13CO + CO collisions. The angle-resolved product rotational angular momentum alignment moments for the two scattering systems are very similar, which indicates that the collision induced alignment dynamics observed for both systems are dominated by a hard-shell nature. However, compared to the 13CO + CO measurements, the primary rainbow maximum in the DCSs for 13CO + N2 is peaked consistently at more backward scattering angles and the secondary maximum becomes much less obvious, implying that the 13CO-N2 PES is less anisotropic. In addition, a forward scattering component with high rotational excitation seen for 13CO + CO does not appear for 13CO-N2 in the experiment and is not predicted by QCT theory. Some of these differences in collision dynamics behaviour can be predicted by a comparison between the properties of the PESs for the two systems. More specific behaviour is also predicted from analysis of the dependence on the relative collision geometry of 13CO + N2 trajectories compared to 13CO + CO trajectories, which shows the special 'do-si-do' pathway invoked for 13CO + CO is not effective for 13CO + N2 collisions.

Quantum and quasiclassical dynamics of Coriolis coupling effects and stereodynamics

The dynamics of C + H2 → H + CH reaction is theoretically studied using the quasiclassical trajectory and quantum mechanical wave packet methods. The analysis of reaction probabilities, integral cross sections, and rate coefficients reveal the essential Coriolis coupling effects in the quantum mechanical wave packet calculations. The calculated polarization-dependent differential cross section, P(θr ) and P(ϕr ) show that the j ′ of product rotational angular momentum is not only aligned along the y axis and the direction of the vector x + z , but also strongly oriented along the positive y axis.

Examining the isotope effect on CH decay and H exchange reactions: H(2S) + CH(D/T)(2Π)

The influence of the isotope substitution on the H + CH(D, T) reactions is analyzed in detail by the method of quasi-classical trajectory on the potential energy surface. By calculating the integral cross sections (ICSs), rate constants, and product vibrational and rotational state resolved ICSs, we find that when the isotope substitution effect promotes the R1 (CH decay) reaction, it can inhibit the R2 (H exchange) reaction. The analysis of differential cross sections (DCSs) indicates that H + CH(D/T) for R1 reaction is dominated by indirect reaction mechanism in the lower collision energy region, and governed by direct reaction mechanism in the high collision energy region. Finally, the calculated distributions of P(θ r ) and P(ϕ r ) show that the product rotational angular momentum is slightly oriented along the positive y-axis for R1 reaction, but for R2 reaction, there are no clear peak structures, so the polarization is not significant.

The dynamics of the Br + HgBr (v = 0, j = 0) → Br2 + Hg reaction based on quasi-classical trajectory calculations

To investigate the dynamics mechanism of the Br + HgBr → Br2 + Hg reaction, the quasi-classical trajectory calculations are performed on Balabanov’s potential energy surface (PES) of ground electronic state. Both the scalar and vector properties are investigated to recognize the dynamics of the title reaction. Reaction probability for the total angular momentum quantum number J = 0 is determined at the collision energies (denoted as Ec) in a range of 1–25 kcal/mol, and the product vibrational distributions are given and compared between Ec = 20 and 40 kcal/mol. Other calculation values characterizing product polarizations including polarization-dependent differential cross sections (PDDCSs), distributions of P(θr), P([Formula: see text]), and P(θr, [Formula: see text]), are all discussed and compared between the two different collision energies in detail to analyze the alignment and orientation characteristics. It is revealed that the products prefer forward scattering and the PDDCSs are anisotropic in the whole range of the scattering angle. The product rotational angular momentum j′ shows a tendency to align perpendicular to the reagent relative velocity k. In fact, the product polarization of the title reaction is weak at both collision energies. In terms of horizontal comparison, the alignment is slightly stronger but the orientation is even less remarkable at higher collision energy.

Low-energy stereodynamics in the ion–molecule reactions D+ + D2/HD and H+ + H2/HD: reagent vibrational excitation effect and mass factor effect

The low-energy chemical stereodynamics of these ion–molecule reactions D+ + D2 → D2 + D+, D+ + HD → DH + D+/D2 + H+, H+ + HD → H2 + D+/HD + H+ and H+ + H2 → H2 + H+ has been investigated by performing the quasi-classical trajectory calculations on the ground electronic state potential energy surface (11A′ PES). The polarization-dependent differential cross sections and the probability distributions of P(θ r ) and P(ϕ r ) have been calculated, compared and discussed within the center-of-mass frame and at the low collision energy of 100 meV. The calculation results indicate that the product scattering and the polarization of the product rotational angular momentum are sensitive to the reactant vibrational quantum number. Such sensitivity increases with the increasing value of mass factor. Moreover, the products from the reaction H+ + HD → HD + H+ show quite different scattering and polarization behaviors with reagent vibration excitation.

The harpooning mechanism as evidenced in the oxidation reaction of the Al atom.

The harpooning mechanism has long been proposed for elementary reaction dynamics involving metals. It is characterized by an initial electron transfer (ET) process from the metal to the oxidant molecule. For the titled reaction Al + O2, the ET distance can be predicted to be 2.6 Å by simply calculating the energy difference between the ionization energy of the Al atom and the electron affinity of the O2 molecule. Hereby we experimentally derived the maximum impact parameter bmax of 2.5 ± 0.2 Å for the titled reaction, in consistency with the predicted ET distance. This derivation of bmax was achieved by using the crossed molecular beam experiment at a collision energy of 507 cm-1 (i.e. 1.45 kcal mol-1) with a high resolution time-sliced ion velocity imaging detection of the state-selective AlO products based on the (1 + 1) resonance-enhanced multiphoton ionization. The small rotational constant of the AlO(X2Σ+) radical (Be = 0.6413 cm-1) facilitated the formation of the AlO(v = 0) products in high rotational levels up to the energetically limited state, Nmax = 52, with an almost zero velocity mapping. Hence, in this extreme angular momentum disposal case, the collisional orbital angular momentum l was nearly completely channeled into the product rotational angular momentum as a consequence of the conservations of energy and angular momentum, offering a reaction system that breaks the restriction of kinematically favored mass combination in order to obtain information on the impact parameters. The present study yields the first direct derivation of bmax from the maximum rotational level of products under the experimental condition with the recoil energy E'T ≈ 0. This, in turn, provides solid evidence in supporting the harpooning mechanism.

Effect of reagent vibrational excitation on reaction of H+CH+C++H2

The effect of reagent vibrational excitation on the stereodynamical properties of H(2S)+CH+(X1+)C+(2P)+H2(X1g+)reaction is investigated by quasi-classical trajectory method on a globally smooth ab initio potential surface of the 2A' state at a collision energy of 500 meV. The reaction probability and the reaction cross-section are also studied. In the calculation, the vibrational levels of the reactant molecules are taken as v = 0, 1, 3, 5 and j = 0, respectively, where v is the vibrational quantum number and j is the rotational quantum number. The calculation results show that the reaction probability reaches a maximum when v = 1, and then decreases with the vibrational quantum number increasing. The integral cross-section decreases sharply with the increase of vibrational quantum number. The potential distribution P(r), the dihedral angle distribution P(r), and the polarization-dependent generalized differential cross sections are calculated. P(r) represents the relation between the reagent relative velocity k and the product rotational angular momentum j'. P(r) describes the correlation of k-k'-j', in which k' is the product reagent relative velocity. The peak of P(r) is at r = 90 and symmetric with respect to 90, which shows that the product rotational angular momentum vector is strongly aligned along the direction perpendicular to the relative velocity direction. The peak of P(r) distribution becomes increasingly obvious with the increase of the rotational quantum number. The dihedral angle distribution P(r) tends to be asymmetric with respect to the k-k' scattering plane (or about r= 180), directly reflecting the strong polarization of the product angular momentum for the title reaction. Each curve has two evident peaks at about r = 90 and r = 270, but the two peak intensities are obviously different, which suggests that j' is not only aligned, but also strongly orientated along the Y-axis of the center-of-mass frame. The peak at r= 90 is apparently stronger than that at r = 270, which indicates that j' tends to be oriented along the positive direction of Y-axis. In order to validate more information, we also plot the angular momentum polarization in the forms of polar plots r and r. The distribution of P(r; r) is well consistent with the distribution P(r) and also the distribution P(r) of the products at different vibrational quantum states. In addition, the polarization-dependent differential cross section is quite sensitive to the reagent vibrational excitation. Based on the obtained results, we find that the observed excess of the methylidyne cation CH+ is closely related to the reactant of vibrational excitation in interstellar chemistry.

Influence of collision energy on the stereodynamics of the H+CH+→C++H2 reaction

The reactive cross section and stereodynamics at selected collision energies for the H(2S)+CH+(X1Σ+)→C+(2P)+H2(X1Σg+) reaction on a globally smooth ab initio potential surface of the 2A' state are calculated in detail by the quasi-classical trajectory(QCT) method. The calculated cross section decreases with the increase of the collision energy, which is found to be in overall good agreement with the previous time-dependent quantum results in the high collision energy regime (Ec>20 meV). The discrepancy between the QCT and previous quantum cross section below 20 meV can be attributed to the limitations of the classical trajectory method, because the QCT method cannot handle the effect of zero point energy. In general, QCT results show qualitative agreement with the quantum results, which confirmsthe validity of the QCT method. The research shows that the product rotational angular momentum vector is aligned and oriented. The alignment of the product rotational angular momentum vector j' depends very sensitively on the collision energy. With the increase of the collision energy, the alignment effect recedesin the low collision energy region (1500 meV), while it is enhanced in the high collision energy region (500-1000 meV). Moreover, the k-k'-j' distributions tend to be asymmetric with respect to the k-k' scattering plane (or about φr=180°), with two peaks appearing at φr=90° and φr=270°, respectively. This indicates that the product rotational angular momentum is not only in the Y-axis direction but also along the positive Y-axis direction. The peak intensity decreases with the collision energy increasing from 1 meV to 100 meV, while it increases with collision energy increasing from 100 meV to 1000 meV. Therefore the Y-axis orientation effect turns weak with the enhancement of the collision energy in the low energy region, while it becomes strong in the high energy region. In addition, the polarization dependent differential cross sections (PDDCSs) (2π/σ)(dσ00/dωt) and (2π/σ)(dσ20/dωt) are calculated. PDDCS (2π/σ)(dσ00/dωt) results indicate that the products have almost symmetrically scattered forward and backward, and the intensity of the scattering increases with the increase of the collision energy. The PDDCS (2π/σ)(dσ20/dωt) shows that the alignment effect of the rotational angular momentum of the products is stronger at the terminal of the scattering angle than at the other directions.

Effects of collision energy on the stereodynamics of the reaction O + H2+ → OH + H+

Quasi-classical trajectories calculations have been carried out to study the stereodynamics of the reaction O+H2+(v=0, j=0)→OH+H+ on the first excited-state potential energy surface (12A′) of Paniagua et al. (2014). The reaction probability for the total angular momentum J=0 and the integral cross section are presented at the collision energies of 0.1–1.2eV. Furthermore, the product rotational alignment factor 〈P2(j′·k)〉 has also been obtained. To show the collision-energy dependence on the chemical stereodynamics of the title reaction, the PDDCSs and the angular distributions of P(θr) and P(ϕr) are investigated. The results indicate that the product rotational angular momentum j′ is not only aligned, but also oriented along the positive y-axis. The stereodynamics of the reaction O+H2+→OH+H+ depend sensitively on the collision energy.

Theoretical study of stereodynamics for the N + H2/D2/T2 reactions

The effects of isotopic variants on stereodynamic properties for the title reactions have been investigated using a quasi-classical trajectory method based on the first excited state NH2(12A′) potential energy surface [Li Y Q and Varandas A J C 2010 J. Phys. Chem. A 114 9644]. The forward—backward symmetry scattering of the differential cross section can be observed, which demonstrates that all these reactions follow the insertion mechanism. Three angle distribution functions P(θr), P(φr), and P(θr, φr) with different collision energies and target molecules H2/D2/T2 are calculated. It is shown that the product rotational angular momentum is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The title reaction is mainly governed by the “in-plane” mechanism through the calculated distribution function P(θr, θpr). The observable influences on the rotational polarization of the product by the isotopic substitution of H/D/T can be demonstrated.

Stereodynamics investigation of F + HO → HF + O(1D) on the ground singlet potential energy surface by means of the quasi-classical trajectory method

The stereodynamics calculation of F + HO → HF + O(1D) was carried out using the quasi-classical trajectory method on the 11A′ potential energy surface provided by Gomez-Carrasco et al. (Chem. Phys. Lett. 2007, 435, 188). The effect of the collision energy, isotopic substitution, and different initial ro-vibrational states on the reaction is discussed. It is found that for the initial ground state of HO (v = 0, j = 0), the degree of the forward scattering and the product polarizations remarkably change as the collision energy varies. Isotopic effect leads to the increase of alignment and decrease of orientation of product rotational angular momentum. Moreover, the P(θr) distribution and P(φr) distribution change noticeably by varying the initial vibrational number. The initial vibrational excitation plays a more important role in the enhancement of alignment and orientation distribution of j′ for the title reaction. Although the influence of the initial rotational excitation effect on the aligned and oriented distribution of product is not stronger than that of the initial vibrational excitation effect, the initial rotational excitation makes the alignment of the product rotational angular momentum decrease to some extent. The probabilities show that the reactivity of the title reaction strongly depends on the initial vibrational state.

Dynamics for the reaction O+DCl→OD+Cl

With the quasi-classical trajectory method the stereodynamics of the O+DCl→OD+Cl reaction on the ground potential energy surface is investigated. The characteristic of calculated integral cross-section is consistent with that of the non-energy barrier reaction path on the potential energy surface, which implies that the title reaction is a typical exothermic reaction. The obtained differential reaction cross-section shows that the products tend to both forward and backward scattering, and the forward scattering is stronger than the backward one. So we can infer that the reaction follows the indirect reaction mechanism that has been verified by the randomly abstractive reaction trajectories. The distribution curves of P(θr) and 2(J'· K)> reflect that the degree of rotational alignment of the product OD first increases and then decreases with collision energy increasing. The product rotational angular momentum vector J' is aligned along the y-axis direction but is oriented along the positive direction of y-axis at higher collision energy. With the increase of the collision energy the rotation mechanism of the product molecules transits from the “in-plane” mechanism to the “out-of-plane” mechanism.

Stereodynamics study of the H′(2S) + NH(X3Σ−) → N(4S) + H2 reaction

The stereodynamics and reaction mechanism of the H′(2S) + NH (X3Σ−) → N(4S) + H2 reaction are thoroughly studied at collision energies in the 0.1 eV–1.0 eV range using the quasiclassical trajectory (QCT) on the ground 4A″ potential energy surface (PES). The distributions of vector correlations between products and reagents P(θr), P(φr) and P(θr, φr) are presented and discussed. The results indicate that product rotational angular momentum j′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane; further, the product H2 presents different rotational polarization behaviors for different collision energies. Furthermore, four polarization-dependent differential cross sections (PDDCSs) of the product H2 are also calculated at different collision energies. The reaction mechanism is analyzed based on the stereodynamics properties. It is found that the abstraction mechanism is appropriate for the title reaction.

Stereodynamics in reaction O(1D) + CH4 → OH + CH3

A theoretical study of the stereodynamics for reaction O(1D) + CH4 → OH + CH3 has been carried out using the quasiclassical trajectory method (QCT) on a potential energy surface structured by Gonzalez et al. The integral cross sections (ICSs), differential cross sections (DCSs) and product rotational angular momentum polarization have been calculated. With the collision energy increasing, the ICS decreases. There is no threshold energy, because no barrier is found on the minimum energy path. The DCS results show that the backward and forward scatterings exist at the same time. With the collision energy increasing, the dominant rotation of the product changes from the right-handed direction to the left-handed direction in planes parallel to the scattering plane. In the isotopic effect study, the decrease of the mass factor weakens the polarization degree of the rotational angular momentum vectors of the products.

The dynamical study of O(1D) + HCl(v = 0, j = 0) reaction at hyperthermal collision energies

BackgroundsThe quasi-classical trajectory calculations for O(1D) + HCl → OH + Cl (R1) and O(1D) + HCl → ClO + H (R2) reactions have been performed at hyperthermal collision energies (60.0, 90.0, and 120.0 kal/mol) on the 1A' state. Reaction probabilities and integral cross sections are calculated. The product rotational distributions for the two channels, and the product rotational alignment parameters are investigated. Also, the alignment and the orientation of the products have been predicted through the angular distribution functions (concerning the initial/final velocity vector, and the product rotational angular momentum vector). To have a deeper understanding of the natures of the vector correlation between reagent and product relative velocities, a natural generalization of the differential cross section __PDDCS00, is calculated.ResultsThe OH + Cl channel is the main product channel and is observed to have essentially isotropic rotational distributions. The ClO + H channel is found to be clearly rotationally polarized.ConclusionsThe dynamical, especially the stereodynamical characters are quite different for the two channels of the title reaction. Most reactions occur directly, except for R2 reaction at the collision energies of 60.0 and 120.0 kcal/mol. The alignment and orientation effects are weak/strong for R1/R2 reaction. The well structure on the potential energy surface and hyperthermal collision energies might result in the dynamical effects.

Influence of early-staged energy barrier on stereodynamics of reaction of LiH(ν=0, j=0)+H→Li + H2

Theoretical studies of stereodynamics for reaction LiH(ν=0, j=0)+H→Li+H2 have been carried out with quasiclassical trajectory method on two potential energy surfaces(PESs) structured as W-PES and P-PES. The main difference of the two PESs is at fixed angle of Li-H-H from 110° to 180°. In this angle range, there is an early-staged energy barrier on the P-PES, but there is no barrier on the W-PES. Some studies have been done to explore the influence of the early-staged energy barrier on this exothermic reaction. Integral cross sections, differential cross sections and product rotational angular momentum of the reaction have been calculated. When Ec 0.48 eV, the dominant influence of barrier is to promote reacting. The angular distribution of the product H2 is extremely forward on both the PESs, because the lifetime of most complexes is short. Totally, the lifetime on the P-PES is longer than that on W-PES for the existence of the barrier. With the collision energy increasing, on the both PESs, the distribution of the direction of the product H2 angular momentum changed, and there is a trend that peak at (90°,270°) gets weaker and peak at (90°,90°) gets stronger. The energy barrier weakens the degree of the rotation alignment of the H2.

Quasi-classical trajectory study of the reaction H′ + HS on a new ab initio potential energy surface H2S (3A″)

Theoretical study on the dynamics of reactions H′ + HS(v = 0, j = 0)→H2 + S and H′ + HS(v = 0, j = 0)→H + H′S is performed with quasi-classical trajectory (QCT) method on a new ab initio potential energy surface for the lowest triplet state of H2S (3A″) constructed in 2012 by Lv et al. The QCT-calculated reaction integral cross-sections are in good agreement with previous quantum wave packet results over the collision energy range of 0–50 kcal/mol. Both the abstraction and exchange reactions are governed by direct reaction dynamics and the trajectories follow the minimum energy path. The rotational angular momentum vector j′ of products in the two reaction channels are not only aligned perpendicular to scattering plane but also oriented along the negative direction of the axis perpendicular to the scattering plane. With the increase in collision energy, the variation trends of product polarization in the two reaction channels are different and that may be attributed to the obviously different characteristic of the two channels on the potential energy surface. Alignment and orientation of the product rotational angular momentum vector j′ of the abstraction reaction H′ + HS(v = 0, j = 0)→H2 + S and the exchange reaction H′ + HS(v = 0, j = 0)→H + H′S.

INVESTIGATION OF THE EXCHANGE REACTIONH + H′S → HS + H′ON THE1A′STATE POTENTIAL ENERGY SURFACE

The quantum time dependent wave packet (TDWP) and quasiclassical trajectory (QCT) calculations were carried out to study the exchange reaction H(2S) + H′S(2Π) → HS(2Π) + H′(2S) on the1A′potential energy surface (PES). The integral cross sections of the H + H′S (v = j = 0) → HS + H′reaction calculated by the two methods were presented. The results reveal that the integral cross sections (ICS) decrease with the collision energy increasing. The result of the QCT calculations is reasonably consistent with the time-dependent wave packet. Moreover, the differential cross sections (DCS) were calculated by the QCT method at the four different collision energies, which display a forward–backward symmetry. A long-lifetime H2S intermediate complex of the exchange reaction was found according to the trajectories. In the stereodynamics investigation, the polar and dihedral angle distribution functions were calculated, which have the distinct oscillations. The oscillations could be attributed to the deep well on the1A′PES. However, based on the polar-angle and dihedral angle distribution functions, it could be predicted that the main product rotational angular momentum preferentially point to the positive or negative direction of y-axes.

QUASICLASSICAL TRAJECTORY STUDY OF STEREODYNAMICS FOR THE REACTIONSLi+HF/DF/TF

Stereodynamics of the reaction Li + HF (v = 0,j = 0) → LiF + H and its isotopic variants on the ground electronic state (12A′) potential energy surface (PES) are studied by employing the quasiclassical trajectory (QCT) method. At a collision energy of 2.2 kcal/mol, product rotational angular momentum distributions, P(θr) and P(ϕr), are calculated in the center-of-mass (CM) frame. The results demonstrate that the product rotational angular momentum j′is not only aligned along the direction perpendicular to the reagent relative velocity vector k, but also oriented along the negative y-axis. The four generalized polarization-dependent differential cross sections (PDDCSs) are also computed. The PDDCS00distribution shows a sideways scattering for the reaction Li + HF and a strongly backward scattering for the reaction Li + DF . However, it displays both the forward and backward scatterings for the reaction Li + TF . These features demonstrate that the Li + HF and Li + DF reactions proceed predominantly through the direct reaction mechanism. However, the Li + TF reaction undergoes both the direct and indirect reaction mechanisms. The PDDCS21-distribution indicates that the product angular distributions are anisotropic.