Considerable attention has been devoted to the O(^{1}D) + HCl reaction [1–22], due in part, to its significant role in stratospheric chemistry. Using *ab initio* self consistant field (SCF) and configuration interaction (CI) methods, Bruna *et al*. [1] reported potential curves for the ground and various valence and Rydberg excited states of HOCl and HClO. The angular and velocity distributions of ClO product from the reaction of O(^{1}D) + HCl at 12.2 kcal/mol collision energy were calculated in a crossed-molecular-beam study in Ref. [2]. Experimentally, the reactions of O(^{1}D) + HCl → OH + Cl and OCl + H were studied at an average collision energy of 7.6, 7.7, and 8.8 kcal/mol through the resonance-enhanced multiphoton ionization technique [3]. Nascent state-resolved ClO (X^{2}П) radicals produced in reaction of O(^{1}D) with HCl were measured by employing the technique of vacuum-ultraviolet laser-induced fluorescence [4]. Hernandez *et al*. [5] calculated the potential energy surface (PES) of the O(^{1}D) + HCl reaction and performed a quasi-classical trajectory (QCT) study on this PES. Cross sections over the collision energy range of 0.0-20.0 kcal/mol were presented and product angular distributions were given at the collision energies of 7.6 and 12.2 kcal/mol. Alvariño *et al*. [6] studied the dependence of calculated product rotational polarization on the scattering angle for the title reaction using QCT method. An accurate *ab initio* HOCl PES was constructed by Skokov *et al*. [7] in 1998. Through a QCT calculation [8], the product angular distribution and dihedral angle distribution for the ClO forming process are performed together with product vibrational distribution for the OH forming process. The quantum and QCT reaction probabilities (RPs) [9] were presented over the collision energy range of 2.3-18.4 kcal/mol by Christoffel *et al*.. At the collision energy of 12.2 kcal/mol, integral cross sections (ICSs) for vibrational states summed over rotational states for the ClO and OH products, and translational energy distributions of the ClO product were also performed [9]. Based on Ref. [7], a global PES was constructed for the X^{1}A' electronic ground state of HOCl including the accurate HClO isomer [10]. Vibrational energy levels and intensities were computed for both HOCl and HClO up to the OH + Cl dissociation limit and above the isomerization barrier using the PES of Ref. [10]. Bittererová *et al*. [11] performed a wave-packet calculation to study the effect of reactant rotation and alignment on product branching in the O(^{1}D) + HCl → ClO + H, OH + Cl reactions using the PES of Ref. [10]. A new fit to extensive *ab initio* calculations of a global potential [10] and the quantum wave packet calculations of the O(^{1}D) + HCl → ClO + H, OH + Cl reactions were reported by Bittererová *et al*. [12]. Accurate time-dependent wavepacket calculation for the O(^{1}D) + HCl reaction was carried out by Lin *et al*. [13]. Recently, we have studied the effects of the collision energy and reagent vibrational excitation on the reaction of O(^{1}D) + HCl → OH + Cl [22].

However, most of these studies were focused on the case of low collision energies. As well known, hyperthermal collisions act a part in the chemistry of extreme environments, such as those encountered in plasma, rocket plumes, and space vehicles in low-earth orbit. The hyperthermal O + HCl chemistry plays an important role in the reacting flows coming from the interaction of a jet and the rarefied atmosphere [23], and we need the data of accurate reaction cross sections and branching ratios at high collision energies to assess its importance. The dynamics of high-energy collisions remains mostly unexplored, and there are only a few studies concerned with the O(^{3}P) + HCl reaction [24, 25].

The title reaction is especially demanding, and interesting, due to the presence of two product channels,

O\left({}^{1}D\right)+\mathit{HCl}\left({}^{1}{\mathrm{\Sigma}}^{+}\right)\to \mathit{OH}\left({}^{2}\u041f\right)+\mathit{Cl}\left({}^{2}P\right)

(R1)

\to \mathit{ClO}\left({}^{2}\u041f\right)+H\left({}^{2}S\right)

(R2)

As noted in Ref. [12], when the collision energy is below 0.55 eV (12.68 kcal/mol), the quantum integral cross sections (ICSs) display an inverse dependence on the collision energy, and the OH product is favoured over the ClO product. But what will happen when the collision energy is hyperthermal?

In this paper, based on the recent-developed ^{1}A' PES [12], a quasi-classical trajectory (QCT) calculation is performed on the O(^{1}D) + HCl(v = 0, j = 0) reaction so as to study the dynamical, especially the stereodynamical characteristics at hyperthermal collision energies. To evaluate the importance of the hyperthermal O + HCl chemistry, RPs, cross sections and branching ratios at high collision energies are investigated. Also, our investigation can provide necessary data to the hyperthermal O + HCl chemistry. The products for R1 and R2 reactions have hot rotational populations. Alignment and orientation effects are shown through two angular distribution functions. The scattering directions of the products are also studied through the PDDCS_{00} results. The statistical errors are marked as error bars in the Figures.

### Methodology and computational details

In the framework of quasi-classical trajectory (QCT) approach [21, 22, 26–34], the center-of-mass (CM) frame is used. The reagent relative velocity vector *k* is chosen to be parallel to the *z* axis, and the scattering plane contains the initial and final velocity vectors (noted as *k* and *k*', respectively). In the CM frame, *θ*_{
r
} and *φ*_{
r
} are the corresponding polar and azimuthal angles of the product rotational momentum *j*', respectively. The scattering angle between *k* and *k*' is marked as *θ*_{
t
}, namely

cos{\theta}_{t}=\frac{\left(\mathit{k}\xb7\mathit{k}\text{'}\right)}{\left(\left|\mathit{k}\right|\xb7\left|\mathit{k}\text{'}\right|\right)}.

(1)

The numbers of reactive trajectory and total trajectory are marked as *N*_{
r
} and *N*_{
tot
} in due order. The RP can be expressed as

P=\frac{{N}_{r}}{{N}_{\mathit{tot}}}.

(2)

The ICS *σ* can be defined as

\sigma =\pi {b}_{max}^{2}\frac{{N}_{r}}{{N}_{\mathit{tot}}},

(3)

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})]^{1/2}*σ*.

The differential cross section (DCS) is given by

\frac{\mathrm{d}\sigma}{\mathrm{d}\left(cos{\theta}_{t}\right)}=\frac{{N}_{r}\left({\theta}_{t}\right)\xb7\pi {b}_{max}^{2}}{2\pi sin{\theta}_{t}\xb7{N}_{\mathit{tot}}}.

(4)

During reactive encounter, the total angular momentum is conserved [26]

\mathit{j}+\mathit{l}=\mathit{j}\text{'}+\mathit{l}\text{'},

(5)

here *l* and *l*' are the reagent and product orbital momenta, respectively. When *j* is small (as is common), the rotation of the product can only result from *l*. The distribution of *j*' is described by *P*(*θ*_{
r
}), which can be expanded by a set of Legendre polynomials

P\left({\theta}_{r}\right)=\frac{1}{2}{\displaystyle \sum _{k}\left(2k+1\right){a}_{0}}\left(k\right){P}_{k}\left(cos{\theta}_{r}\right).

(6)

Here the polarization parameter *a*_{0}(*k*) can be expressed as

\begin{array}{l}{a}_{0}\left(k\right)={\displaystyle {\int}_{0}^{\pi}P\left({\theta}_{r}\right)}{P}_{k}\left(cos{\theta}_{r}\right)sin{\theta}_{r}d{\theta}_{r}\\ \phantom{\rule{2.5em}{0ex}}=\u3008{P}_{k}\left(cos{\theta}_{r}\right)\u3009.\end{array}

(7)

*a*_{0}(2) indicates the product rotational alignment

{a}_{0}\left(2\right)=\u3008{P}_{2}\left(cos{\theta}_{r}\right)\u3009=\frac{1}{2}\u30083{\mathrm{cos}}^{2}{\theta}_{r}\u20121\u3009.

(8)

*P*(*φ*_{
r
}) denotes the dihedral angle distribution, which can be expanded in the Fourier series

P\left({\phi}_{r}\right)=\frac{1}{2\pi}\left[1+{\displaystyle \sum _{\mathit{even},n\ge 2}{a}_{n}}\mathrm{cos}\left(n{\phi}_{r}\right)+{\displaystyle \sum _{\mathit{odd},n\ge 1}{b}_{n}\mathrm{sin}\left(n{\phi}_{r}\right)}\right].

(9)

The expansion coefficients *a*_{
n
} and *b*_{
n
} are given by

{a}_{n}=2\u3008cosn{\phi}_{r}\u3009,

(10)

{b}_{n}=2\u3008sinn{\phi}_{r}\u3009.

(11)

The full three-dimensional angular distribution associated with *k* **-** *k*'**-** *j*' correlation can be expressed as

P\left({\omega}_{t},{\omega}_{r}\right)={\displaystyle \sum _{\mathit{kq}}\frac{2k+1}{4\pi}\frac{1}{\sigma}\frac{\mathrm{d}{\sigma}_{\mathit{kq}}}{\mathrm{d}{\omega}_{t}}}{C}_{\mathit{kq}}{\left({\theta}_{r},{\phi}_{r}\right)}^{\ast},

(12)

where *C*_{
kq
}(*θ*_{
r
}, *φ*_{
r
}) are the modified spherical harmonics and the angles *ω*_{
t
} = *θ*_{
t
}, *φ*_{
t
} and *ω*_{
r
} = *θ*_{
r
}, *φ*_{
r
} refer to the coordinates of the unit vectors *k*' and *j*' along the directions of the product relative velocity and rotational angular momentum vectors, respectively. \frac{1}{\sigma}\frac{\mathrm{d}{\sigma}_{\mathit{kq}}}{\mathrm{d}{\omega}_{t}} is a generalized polarization-dependent differential cross section (PDDCS), and it can be written as

\frac{1}{\sigma}\frac{\mathrm{d}{{\sigma}_{\mathit{kq}}}_{\pm}}{\mathrm{d}{\omega}_{t}}={\displaystyle \sum _{{k}_{1}}\frac{2{k}_{1}+1}{4\pi}}{S}_{\mathit{kq}\pm}^{{k}_{1}}{C}_{{k}_{1}-q}\left({\theta}_{t},0\right).

(13)

Here the expectation value {S}_{\mathit{kq}\pm}^{{k}_{1}} is given by

{S}_{\mathit{kq}\pm}^{{k}_{1}}=\u3008{C}_{{k}_{1}q}\left({\theta}_{t},0\right){C}_{\mathit{kq}}\left({\theta}_{r},0\right)\left[{\left(-1\right)}^{q}{\mathrm{e}}^{\mathit{iq}{\phi}_{r}}\pm {\mathrm{e}}^{-\mathit{iq}{\phi}_{r}}\right]\u3009.

(14)

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 ^{1}A' 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], ^{1}A' 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(^{1}D) + 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 cos^{2}*β* ( *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.