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

Methodology and computational details

where b_max denotes the maximum value of the impact parameter b.

The associated uncertainties with the ICS can be calculated according to Δσ = [(N_tot − N_r)/(N_tot · N_r)]^1/2σ.

The angular brackets 〈⋯〉 in Eq. (14) represent the average over all angles.

The initial ro-vibrational quantum numbers of the HCl reactant are set as v = 0, and j = 0. 1,000,000 trajectories are used on the ¹A' electronic states at the collision energies of 60.0, 90.0 and 120.0 kcal/mol. The time integral step size is 10^-4 ps. The maximum values of impact parameter b_max are 2.80/1.15 (60.0 kcal/mol), 2.81/1.55 (90.0 kcal/mol), and 2.86/1.05 (120.0 kcal/mol) for R1/R2 reaction and the unit is in Angstrom.

The PES we used is constructed by Bittererová et al.[12]. The title reaction proceeds without a barrier to either set of products, but via two complex regions, HOCl and HClO. For R1 (R2) reaction, according to Ref. [12], ¹A' state has a deep well in bent geometry corresponding to stable HOCl (HClO) molecule and the well depth is -102.16 (-48.20) kcal/mol. The schematic of the energetics of the O(¹D) + HCl ab initio global potential is exhibited in Figure 1.

For the A + BC → AB + C reaction, in the impulse model [27], the product rotational angular momentum j' could be described with the reagent orbital and rotational angular momenta, l and j, i.e.$\mathit{j}\text{'}=\mathit{l}{sin}^{\mathbf{2}}\beta +\mathit{j}{cos}^{\mathbf{2}}\beta +{\mathit{J}}_{\mathbf{1}}\frac{m_B}{m_{\mathit{AB}}}$, where ${\mathit{J}}_1=\sqrt{{\mu }_{\mathit{BC}}R}\left({\mathbf{r}}_{\mathit{AB}}\times {\mathbf{r}}_{\mathit{CB}}\right)$ and ${cos}^2\beta =\frac{m_A{m}_C}{\left(m_A+m_B\right)\left(m_B+m_C\right)}$. μ _BC is the reduced mass of the BC molecule, R, the repulsive energy, and r _AB , r_CB, the unit vectors where B points to A and where B points to C, respectively, β is known as the skew angle. For R1 (R2) reaction, β ≈ 17° (β ≈ 85°), which is a pretty small (large) angle. Larger polarization properties are expected for the products with the smaller value of cos²β ( i.e. R2 reaction) according to the kinematic limit, which could be observed via the alignment parameters. l sin  ² β + j cos  ² β is symmetric, which leads to the symmetric distribution of P(θ _r ) in Figure 2. However, $\frac{{\mathit{J}}_{\mathit{1}}{m}_B}{m_{\mathit{AB}}}$ shows a preferred direction due to the repulsive energy and results in the biased orientation of the products as shown in P(φ _r ) distributions.

RPs and ICSs

Figures 2 and 3 show the results of RPs and ICSs at the collision energies of 60.0, 90.0, and 120.0 kcal/mol. The OH products shown in Figure 2(a) and Figure 3(a) are apparently favoured over the ClO products shown in Figure 2(b) and Figure 3(b), which agrees well with the quantum results at low collision energies [12]. With the increase of the collision energy, both RP and ICS obviously decrease except for ICS at the collision energy of 90.0 kcal/mol for R1 reaction. The title reaction proceeds without a potential barrier and typically by complex formation, which can be displayed through the quantum RPs [12]. This oscillating structure might cause the translational excitation to impede the reaction. Also, the quantum ICSs [12] show the inverse dependence on the initial relative kinetic energy, and the OH product is favoured over the ClO product. The statistical errors for RPs are ± 0.00042/ ± 0.000086, ± 0.00042/ ± 0.000055, ± 0.00041/ ± 0.000017 for R1/R2 reaction at E_col = 60.0, 90.0 and 120.0 kcal/mol, respectively.

The branching ratios $\frac{{\sigma }_{\mathit{ClO}}}{{\sigma }_{\mathit{OH}}}$ are about 0.0056(± 0.000075), 0.0042(± 0.000084) and 0.0002(± 0.000011) at the collision energies of 60.0, 90.0 and 120.0 kcal/mol in due order. It is obvious that the branching ratio rapidly decreases with the increase in the collision energy. The branching ratios are much smaller than those at the lower collision energies [2, 3, 12, 14].

The product rotational distributions (PRDs)

Figure 4 shows the PRDs of R1 (as shown in Panel (a)) and R2 (as shown in Panel (b)) reactions. Obviously, the products for R1 and R2 reactions are rotationally hot. The peak shifts towards larger rotational quantum numbers except for R2 reaction at the collision energy of 120.0 kcal/mol. The PRDs of R2 reaction show much broader ranges than those of R1 reaction due to larger polarization properties for R2 as mentioned above. For the Li + HF → Li + F reaction (which also belongs to Heavy heavy-Light (HHL) scheme), LiF product is also produced in highly excited states [35, 36].

As mentioned in Refs. [35–37], vector correlation of angular momentum orientation and alignment in chemical reactions can provide rich information on the reaction dynamics. By analyzing the alignment parameters, two angular distributions (P(θ _r ) and P(φ _r )), and PDDCS₀₀, we can get a view of the stereodynamical information of the title reaction.

The product rotational alignment

For R1 reaction as shown in Figure 5(a), P₂ slightly increases with the increase of the collision energy. The value of P₂ becomes less negative (-0.073, 0.001, and 0.018 for E_col = 60.0, 90.0 and 120.0 kcal/mol, respectively) and the product rotational angular momentum tends to have a less anisotropic distribution. With the increase of the collision energy, the degree of alignment is almost invariant (only slightly increases) which could be ascribed to the Heavy Light-heavy (HLH) mass combination [6]: much angular momentum transfers from the reagent orbit to the product orbit, l-l', and little to rotation. Therefore, large variations in the direction of j' are needed for compensating even small variations in l'.

For R2 reaction, the P₂ values at the three collision energies are approaching to -0.5, which indicates that the product rotation strongly aligned perpendicular to the reagents’ relative velocity k. This is a typical feature of the HHL system [6, 26, 35, 36]. A significant feature of this kind of reaction is the kinematic limit, i.e., the initial orbital angular momentum l completely goes into the product rotational angular momentum j', which leads to the alignment character. This is consistent with the alignment of Li + HF → LiF + H [35, 36]. The significant disposal of angular momentum in the product orbital motion, l → j' + l' declines the product rotational alignment, particularly at lower collision energies, so the calculated P₂ values deviate slightly from -0.5, which could also be supported by the P(θ _r ) results.

According to the results of H⁺+D₂(v = 0, j = 0) → HD(v’ , j’) + D⁺ reaction [37], the alignment of rotational angular momentum of HD products is nearly always close to zero due to the long-lived resonances. However, H⁺+D₂(v = 0, j = 0) → HD(v’ , j’) + D⁺ reaction belongs to Light light-light (LLL) scheme, and in the reference [37] the alignment is state-resolved, however, our results are the sum of all states. So there are different results for the alignment parameters. And through the observation of three internuclear distances with the propagation of collision time, we can find that the reactions proceed directly except for the collision energies of 60.0 and 120.0 kcal/mol for R2 reaction.

P(θ _r ) distributions

P(θ _r ) is the distribution function reflecting the k-j ' correlation, which is sensitive to two factors: the characters of PES and the mass factor. Obviously, there is a discrepancy between P(θ _r ) distributions of the two reactions due to the different mass factors of the two reactions. For R1 and R2 reactions, at all the collision energies, the P(θ _r ) distribution functions are symmetric with respect to θ _r  = 90° as analyzed above. The alignment effects are obscure /obvious for R1/R2 reaction, which is supported by P(φ _r ) distributions in Figure 7.

For R1 reaction shown in Panel (a), the largest peak appears at θ _r  = 90° at E_col = 60.0 kcal/mol. At the collision energy of 90.0 kcal/mol, the largest peaks are around θ _r  = 90°, 20° and 160°. Around θ _r  = 26° and 154°, there are the largest two peaks at E_col = 120.0 kcal/mol.

For R2 reaction shown in Panel (b), it is a HHL system, with the mass factor – ${cos}^2\beta =\frac{m_O{m}_H}{\left(m_O+m_{\mathit{Cl}}\right)\left(m_{\mathit{Cl}}+m_H\right)}\approx 0.0086$ approaching to zero, which manifests that the product rotational alignment is strong with regard to the initial velocity vector k[26], which could be also observed through the alignment parameter in Figure 5(b) and P(φ _r ) distributions in Figure 7(b).

P(φ _r ) distributions

P(φ _r ) describes the k-k'-j' correlation, which reflects the polarization of product rotational angular momentum j'. The P(φ _r ) distribution is asymmetric with respect to the k-k' scattering plane (i.e. at about φ _r  = 180°), which could be explained by the impulse model [27] as mentioned above.

For R1 reaction in Figure 7(a), there are only several small peaks, implying that the orientation effects are not obvious at the three different collision energies, which agrees well with the alignment parameter in Figure 5(a) and P(θ _r ) distributions in Figure 6(a).

For R2 reaction in Figure 7(b), the largest peaks appear around φ _r  = 0° (or 360°)/ φ _r  = 180°, implying that the ClO molecular axis vector orients along x/–x axis.

PDDCS₀₀

PDDCS₀₀ is proportional to DCS, which can be used to describe the k-k' correlation. Through PDDCS₀₀, we can study the scattering direction of the product.

For OH + Cl products (R1 reaction), obvious forward scattering is exhibited in Figure 8(a). The distribution is asymmetric with respect to θ _t  = 90°, and the peaks are found around θ _t  = 0°, which indicates that the impact time is short and that direct reaction dominates. Usually, the deep well results in a long-lived reaction intermediate. However, according to the PDDCS₀₀ results, direct reaction dominates at high collision energies. The internuclear distances of OH, HCl and ClO (labeled as R_OH, R_HCl, and R_ClO, respectively) as a function of propagation time are shown in Figure 9(a), which gives a proof of the direct reaction. For R1 reaction, the reaction times are short at the three collision energies.

For ClO + H products (R2 reaction), as shown in Figure 8(b), the distribution is observed to be almost backward-forward symmetric with backward scattering being slightly favoured, except for the case of E_col = 90.0 kcal/mol. We can deduce that part of the reaction occurs via a long-lived complex and part via direct abstraction of Cl atom, which is also a remarkable conclusion of Ref. [2, 5]. Moreover, the peaks locate close to θ _t  = 90°. H atom (with very slight mass) is one of the products, so the reduced mass of the products is also very small, which causes the products orbital angular momentum l' to be smaller than the products rotational angular momentum j' and the final relative velocity vector k' no longer to be remained in the xz plane. Of course, the scattering of the products is still cylindrically symmetric around z axis (k). So, the separation of H atom and ClO molecule is almost along the direction that perpendicular to the incoming direction of O atom (i.e. the direction of k). This results in the dominant population of the products along θ _t  = 90°. In Figure 9(b), the oscillating structures at the collision energies of 60.0 and 120.0 kcal/mol show that the complexes have long lifetimes compared with the reaction period. Also obviously, the direct reaction occurs at the collision energy of 90.0 kcal/mol.