+ HD - American Chemical Society

Article pubs.acs.org/JPCA

State-to-State Quantum Dynamics of Reactions O(3P) + HD (v = 0−1, j = 0) → OH+D and OD+H: Reaction Mechanism and Vibrational Excitation Jing Zhang,†,‡ Shou-Bao Gao,† Hui Wu,‡ and Qing-Tian Meng*,† †

School of Physics and Electronics, Shandong Normal University, Jinan 250014, China State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, 457 Zhongshan Road, Dlian 116023, China

Downloaded by GEORGETOWN UNIV on August 23, 2015 | http://pubs.acs.org Publication Date (Web): August 17, 2015 | doi: 10.1021/acs.jpca.5b04255

‡

ABSTRACT: Time-dependent quantum wave packet dynamics calculations have been performed in order to characterize the dynamics and mechanism of O(3P) + HD (v = 0−1, j = 0) → OH+D and OD+H reactive collisions using the adiabatic potential energy surface by Rogers et al. [J. Phys. Chem. A 2000, 104, 2308] Special attention has been paid to the calculations and discussion of the state resolved integral and differential cross sections and the product state distributions. In addition, the intramolecular isotopic branching ratio has been determined. The results revealed that the OD + H is the favored product channel and the product OH has the same quantum number v as the reactant HD. For low collision energy, the product angular distributions concentrate in the backward region being consistent with a rebounding mechanism. In the case of higher collision energy, the stripping collisions with larger impact parameters tend to produce sideways and forward scatterings, especially for the HD vibrationally excited state. The cross section and intramolecular isotopic branching ratio are in agreement with the previous theoretical results. A cartoon depiction collision model is built and works well for our calculation results.

1. INTRODUCTION The reaction O(3P) + H2 is of fundamental important in combustion processes,1 as well as in atmospheric2−4 and interstellar5 chemistry. Its relative simplicity and the fact that the reaction has an energy barrier of about 0.56 eV below which it occurs through an abstraction mechanism,6 make it amenable to accurate electronic structure and dynamics calculations. Over the last two decades, on the experiment side, the reaction rates and related quantities obtained by using different experimental techniques have been reported.7−15 On the theory side, a variety of potential energy surfaces (PESs) and dynamics calculations have been known for this reaction.6,16−31 In order to further expound the related dynamics, in this paper, we focus on the O(3P) + HD→ OH/OD + D/H reactions for investigating their reaction mechanisms, intramolecular isotopic branching ratio and the effects of the vibrational excitation of the reactant diatomic HD on them. In recent years, there have been several reports on the isotopic reaction O(3P) + HD.32,34−38 The early experiment by Robie et al.32 measured the branching ratio for the title reactions over the temperature range 339−500 K by using the laser-induced fluorescence under steady-state conditions. The results illustrated that the OH/OD ratio increases rapidly with decreasing temperature in qualitative agreement with theory, showing that the reaction is dominated by tunneling below 400 K. © XXXX American Chemical Society

To interpret the mechanisms of the title reactions, several groups at the forefront of the theoretical studies have paid attentions to the PES in recent years.6,16−20 Undoubtedly all of these PESs can give reasonable dynamics information, including the total reaction probabilities and rate constants. However, in terms of the state-to-state dynamics, not all of those PESs are sufficiently accurate,6 except for the one constructed by Rogers et al.6,33 On the basis of this PES, many groups, such as Chu et al.30 and Zhao et al.,29 have carried out dynamics investigations and achieved excellent results. The quantum dynamics studies of the title reactions and their isotopic variants have been considered in the previous work.21−38 However, there are few relevant calculations of the title reactions at the state-to-state level, and even no reports related with the calculations of their differential cross sections (DCSs). On the basis of the reduced dimensionality exact quantum and quasiclassical method, Bowman et al.34 calculated the reaction probabilities and rate constants for the O(3P) + HD (v = 0, 1) → OH + D and OD + H reactions on the ab initio collinear MODPOLCI surface. The results showed that for O + HD reaction the dominant product has the same quantum number as the reactant. Song et al.35 employed the Received: May 4, 2015 Revised: July 16, 2015

A

DOI: 10.1021/acs.jpca.5b04255 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article


The Journal of Physical Chemistry A quasiclassical trajectory (QCT) method to study the intramolecular isotope effect for the O(3P) + HD (v = 0, j = 0) reaction over the energy range 0.65−6.5 eV (15−150 kcal/mol) and found that OD + H is the favored channel. Sultanov et al.36 also carried out the quantum scattering calculations of the O(3P) + HD and O(3P) + D2 reactions. The results revealed that the hydrogen atom transfer leading to the OH product dominates at low temperature for the O(3P) + HD reaction. Wu et al.37 carried out the QCT calculations of the title reactions at scattering energy on the range of 0.2−1.0 eV on the lowest electronic PES 13A″.6 The results showed that the production of nascent molecule OD prefers linear arrangement or interaction of O−D−H in the reaction of O(3P) + HD → OD + H. Wei et al.38 also used the QCT method to study the dynamics of the O(3P) + H2/HD (v = 0, j = 0) reactions. The calculated results indicated that the product polarization is very sensitive to the mass factor and the directions of scattering are strongly dependent on the choice of quantum state. As we all know, the zero-point energy and the tunneling effect are not taken into consideration in the QCT method, which may produce inaccurate results, especially nearby the threshold energy. Only the state-to-state quantum mechanical (QM) studies can provide a more detailed and rigorous knowledge of the chemical reaction process, especially from the DCS calculations. However, none of the earlier QM calculations have yielded state-resolved cross sections. Thus, in this paper, we employed the time-dependent quantum wave packet (TDQWP) method to investigate the state-to-state quantum scattering dynamics of the title reactions on the chemical accurate PES of Rogers et al.6 in collision energy range 0.2−1.0 eV. The remainder of this article is organized as follows. Section 2 briefly outlines the computational details of our quantum dynamical calculations. Section 3 presents, in turn, the total and selected state-to-state reactive integral cross sections (ICSs), product rotational distributions and the total DCSs for neutral and vibrationally excited HD molecule, as well as the intramolecular isotopic branching ratio. The analysis, together with the discussion of the calculation results and a comparison with previous theoretical results, is also unfolded in this section. Finally, section 4 summarizes the main conclusions of the work.

As indicated in ref 6, 951 geometries were used to the regular-accuracy MOLPRO calculations of the electronic energies for the lowest 3A″ state of the title reactions. A rotating Morse spline method and a generalized London− Eyring−Polanyi−Sato (LEPS) double-polynomial method were employed to fit the results. All the calculations were based on internally contracted configuration interaction method with a very large basis set (cc-pV5Z). The main features of this PES are shown in Figure 1. It can be clearly seen that the barrier

Figure 1. Minimum-energy path energies as a function of the distance along the minimum-energy reaction path.6

height of the O + HD reaction is about 0.56 eV. The title reactions are endothermic by 0.126 eV and the minimum energy path processes occur at the collinear configuration of the three nuclei. The details of the chemical accuracy of this new PES have been described in ref 6. B. TDQWP Method. The state-to-state QM studies can provide the most detailed information and profound insight of chemical reaction process. With the development of the modern computer technology, the atom−diatom reactive scattering problems have been mostly solved, including the simple direct reactions such as H + D2,40,41 H + HD,42 F + H2,43 and the challenging reactions with deep wells such as O + H2,30 or with multiple PESs such as Cl + H2.44 Here, we report converged state-resolved ICS and DCS for the title reactions in the collision energy range 0.2−1.0 eV with the TDQWP method. While the calculations of DCS have been reported for many triatomic reactions and two tetra-atomic systems up to now,45 theoretical calculations are still a great challenge of computational time consumption.46−52 In this paper, the TDQWP method is efficiently implemented on graphics processing units (GPUs). This new efficient GPUs version of TDQWP code is developed by Zhang and Han and has been proved to be more efficient than central processing units (CPUs) with the test calculations of the H + H2 and O(3P,1D) + H2 reactions.53 The Hamiltonian of the title reactions in body-fixed (BF) product Jacobi coordinates can be written as,54

2. THEORETICAL METHODS A. PES. The presence of the spin−orbit coupling in the oxygen atom and multiply degenerate PESs make the study of the title reactions more difficult.23 Recently, several authors23,28−30,39 reported that, when the collision energy is higher than 1.0 eV, the ICSs obtained from a full calculation with a complete model that include non-Born−Oppenheimer coupling between all PESs differ by at most 10% from independent single PES calculations. When the considered collision energy is below 1.0 eV, recent QCT studies21,23,30 of surface-hopping effects between O(3P) + H2 and O(1D) + H2 reactions have shown that the dynamics properties can be accurately described by single surface calculations on 3A′ and 3 A″ PESs. The above argument is further supported by the fact that the ICSs obtained from recent crossed molecular beam measurements11 are in a good agreement with the calculation results on the singlet PES 3A′ and 3A″.24 Thus, for the sake of simplicity, we carried out the state-to-state dynamics calculations of the title reactions on the single-surface 3A″ of Rogers et al.6

2 (J ̂ − j ̂)2 ĵ ℏ2 ∂ 2 + + + V (R ⃗ , r ⃗ , θ ) Ĥ = − 2μR ∂R2 2μR R2 2μr r 2

+ h(̂ r ) B

(1) DOI: 10.1021/acs.jpca.5b04255 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 1. Parameters Used in the Time-Dependent Wave Packet Calculationsa grid/basis range and size:

initial wave packet absorption length in R and r absorption strength in R and r total propagation time time step


a

O + HD → OD + H

O + HD → OH + D

R ∈ [0.1, 20.0], Ntotal = 158, Nint R R = 149, total r ∈ [0.5, 12.5] Nr = 200, Nrb = 100, Nvb = 4, Jmax = 120 R0 = 8.5, δ = 0.28, E0 = 0.60 eV 4.0/4.0 0.03/0.03 25000 5

R ∈ [0.1, 20.0], Ntotal = 180, Nint R R = 169, total r ∈ [0.5, 14.5] Nr = 200, Nrb = 100, Nvb = 4, Jmax = 130 R0 = 8.5, δ = 0.19, E0 = 0.59 eV 4.0/4.0 0.03/0.03 30000 5

All parameters being given in a.u. unless stated otherwise.

where R and r are, respectively, the product atom−diatom (D− OH/H−OD) and diatomic (OH/OD) distances, μR the reduced mass between atom D(H) and diatom OH (OD), μr the reduced mass of OH(OD), J ̂ the total angular momentum operator, j ̂ the rotational angular momentum operator of OH(OD), and V(R⃗ , r,⃗ θ) the interaction potential excluding the diatomic OH(OD) reference potential. As the diatomic reference Hamiltonian, ĥ(r) is defined by 2

Sfi(E) =

00 0

00

μ R kαi α

2π

R αhl(2) (kαiR α)|G(R α) α (8)

μ R kβf

aβf (E) = ⟨φf |χf+ ⟩ =

β

2π

Rβhl(1) (kβf Rβ) β

(3)

|δ(Rβ − R ∞) (9)

Here, φi and φf are the initial and final free wave function, |χf⟩ = δ(Rβ − Rβ ∞)φvf jf(rβ)|JMjf lf⟩ represents the radial component of the product wave packet, Rβ ∞ is a fixed radial coordinate in the asymptotic region, h(1) and h(2) are the spherical Hankel functions of the first and second kind.56 Finally, the DCS and ICS can be obtained by a scattering matrix summing over all relevant total angular momentum quantum numbers J dσv ′ j ′ , v0j (θ , E) 0

dΩ

⎛ ⎞ ̂ Δ/2) exp⎜ −iĤ 0 Δ ⎟ψ JMp(R⃗ , r ⃗ , t ) exp( −iV Δ)exp( −iVrot ⎝ 2⎠

=

1 (2j0 + 1) 2

∑∑

(4)

K′

where

2 2 ĵ L̂ + 2μR R2 2μr r 2

i

(2)

⎛ Δ⎞ ̂ Δ/2) ψ JMp(R⃗ , r ⃗ , t + Δ) = exp⎜ −iĤ 0 ⎟ exp( −iVrot ⎝ 2⎠

̂ = Vrot

(7)

aαi(E) = ⟨φi|χi+ ⟩ =

where φv0j0(rα) presents the rovibrational eigenfunction of the diatomic molecule, |JMj0l0ε⟩ is the SF rotational basis, which describes the angular motion with M being the projection of the total angular momentum J, v0 and j0 present, respectively, the initial vibrational and rotational quantum number of the diatomic molecule. α and hereinafter the β is the label for the reactant and product channels, respectively. After the preparation of the initial wave packet on the CPU in SF reactant Jacobi coordinate, the initial wave function can be propagated in BF product Jacobi coordinates by a splitoperator scheme, entirely on GPU, defined as,53

ℏ2 ∂ 2 ℏ2 ∂ 2 · 2 − · + Vr(r ) Ĥ 0 = − 2μR ∂R 2μr ∂r 2

dt exp(iEt /ℏ)⟨χβf |

and the coefficients are given by

The initial wave function of the reactant is prepared in a space-fixed (SF) reactant Jacobi coordinates system using the Gaussian wave packet in the R direction and can be expressed as |χi ⟩ = ψαυJMjεl = G(R α)φυ j (rα)|JMj0 l0ε⟩

+∞

∫−∞

exp(iHt̂ /ℏ)|χαi ⟩

2

ℏ ∂ h(̂ r ) = − + Vr(r ) 2μr ∂r 2

1 2πaαi(E)aβ*f (E)

K0

σv ′ j ′ , v0j =

(5)

0

1 2ik v0j

0

∑ (2J +

1)dKJ ′ K 0(θ )SvJ′ j ′ K ′ , v0j K 0 0

(10)

J

1 (2j0 + 1)k v0j 2 0

∑ ∑ ∑ (2J + 1)|SvJ′ j ′ K′ ,v j K |2 00

K′

K0

0

J

(11)

Here, θ is the scattering angle between the incoming reactants and the scattered products, kv0j0 the initial wave vector for the reactant, dJK′K0(θ) the reduced rotation matrix with K0 and K′ being the projection of the initial and final total angular momentum J, SJv′j′K′,v0j0K0 the S-matrix for transitions from initial vibrotational level v0, j0 of reactants HD to final levels v′, j′ of the products OH(OD) at an incident energy E.

(6)

with L̂ = J ̂ − j.̂ Vr(r) is the diatomic potential energy of OH(OD). The use of GPU and product Jacobi coordinates reduces the computational time largely, without losing accuracy of state-to-sate information. In the BF product Jacobi coordinates, the scattering matrix element can be obtained as,53,55 C


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The Journal of Physical Chemistry A

Table 2. Convergence Test of the Total Reaction Probabilities as a Function of K (with Ecol = 0.92 eV, J = 20, 30, and 40) Ecol = 0.92 eV

K

O + HD (v0 = 0, j0 = 0) → OD + H

O + HD (v0 = 0, j0 = 0) → OH + D

J = 20

10 15 20 10 15 20 10 15 20

0.3288391 0.3236948 0.3259136 0.1330797 0.1284388 0.1289408 0.0003496 0.0003020 0.0003029

0.0745058 0.0745063 0.0745066 0.0522313 0.0522313 0.0522313 0.0209243 0.0209240 0.0209237

J = 30


J = 40

3. RESULTS AND DISCUSSION A. Numerical Aspects. Here we perform the state-to-state calculations to obtain the DCS of the title reactions for the collision energies up to 1.0 eV. In order to get the converged results, many tests have been carried out for v = 0, J = 0 to determine the optimal numerical parameters, which are summarized in Table 1. In this work, one of the key convergence parameters is denoted by K, which sets an upper limit on the helicity quantum number. The convergence tests are shown in Table 2. It can be seen that the number of K for selected J and higher collision energy Ecol = 0.92 eV, given by K = min (20, J + 1), is sufficient to yield converged results. In this paper, we only focus on the vibrational sates v = 0 and v = 1 of the reactant HD, and for v = 1, the helicity limit is K = min (25, J + 1). B. Total Reaction Probability and ICS. We first focus on the total reaction probabilities for several partial waves in Figure 2. As shown in this figure for J = 0, because of the contribution of tunneling, the onset of reactivity occurs at a collision energy of ∼0.4 eV(∼0.35 eV) for the OD + H (OH + D) product channel, which is lower than the zero point corrected barrier (∼0.56 eV). We also observe that as J increases, the reaction threshold shifts to the higher collision energy, due to an increasingly large centrifugal barrier. The threshold energy of the J = 40 partial wave for the OD + H product channel is approximately 1.0 eV. This demonstrates that the convergence of the J values is equal to 40 at this present collision energy range for the calculation of the ICSs. While for the OH + D product channel, the convergence of the J values is equal to 53, being larger than OD + H product channel. Above cases indicate that the convergence of the OD + H product channel for J is faster than that of the OH + D product channel. Figure 3 displays the initial state resolved reaction cross sections as a function of the collision energy by using the timedependent wave packet code for the state-to-state scattering processes. Because of the existence of the potential barrier, the ICSs are zero until the collision energy is greater than certain threshold energy, after which they increase monotonically with the collision energy. As can be seen from the comparison of these two product channels, because of the lighter H atom leading to more tunneling, the reactions involving H exchange have threshold energies considerably lower than the ones for D exchange. For the O + HD reactive system, since the interaction between the O atom and both H and D is repulsive, if O approaches the molecule obliquely, OD + H is the favored product channel in our collision energy range. In the QCT calculation by Song et al.,35 they showed that the major factor is the torque which O exerts on HD in most orientations. The results also show that there is little or no dependence on angle if O approaches anywhere at the D end of the molecule, but if

Figure 2. Total reaction probabilities as a function of the collision energy for the O(3P) + HD (v = 0, j = 0) reaction at several J values. Key: (a) the OD + H product channel; (b) the OH + D product channel.

O starts at the H end there is a torque pushing H away from the O atom. The net effect when the O atom approaches the D end of HD is rotating the molecule into a more linear O−D−H configuration. On the contrary, when the O atom approaches the H end of HD the repulsive forces cause the HD to rotate away from the linear O−H−D arrangement. However, if the O atom is not within these reaction cones (within ±30° of collinear) at either end of HD, then there is a strong torque on the molecule which rotates the H atom away from the O atom and facilitates the formation of OD. A similar phenomenon was also found for the F + HD reactive system.57 In addition, the fact that the center of mass is closer to the deuterium atom determines a wider cone of acceptance for the attack of the O atom on this side of the molecule than for collisions where the incoming atom approaches the H side of the reactant molecule. And because of the asymmetric location of the center of mass D


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Figure 3. Total ICSs and product vibrational state distributions as a function of collision energy for the O(3P) + HD (v = 0, j = 0) reaction. Key: (a) the OD + H product channel; (b) the OH + D product channel, along with the results of Wu et al.37

Figure 4. 2J + 1 weighted opacity functions for the O(3P) + HD (v = 0, j = 0) reaction at selected collision energies of 0.4, 0.6, 0.8, and 1.0 eV as a function of total angular momentum J. Key: (a) the OD + H product channel; (b) the OH + D product channel.

within the diatomic molecular axis, collisions with the H atom will be related to lower O−HD distances. For a given collision energy, the range of attack angle leading to reaction will be more restricted for the H than for the D end of the molecule HD and the reaction integral cross sections for the product OH + D will be smaller. This, in principle, also favors the formation of OD. In addition, it should be pointed out that because of the differences in the PES and calculation methods used, our ICSs are a little larger than the existing results of Wu et al.37 In order to shed light on the J dependence of the total reaction probabilities, we plot the total reaction probability, P(J), as a function of the total angular momentum quantum number, J, for both channels of the O(3P) + HD (v = 0, j = 0) reaction at four different collision energies, shown in Figure 4. Notice that the total reaction probability values, P(J), have been multiplied by 2J + 1 such that the integral of each curve is proportional to the respective ICS. As can be seen from Figure 4, the reaction takes place at relatively small J values at low collision energies. The distribution of J, being arch-shaped approximately, increases with J, reaches a maximum at an certain J and then decreases to zero before reaching the last available value of J. With the increase of collision energy, a marked shift of the probability maximum occurs to larger J values. As we all know, the J dependence of the total reaction probability is an analogue of classical opacity function P(b), i.e., the reaction probability as a function of the impact parameter b. Thus, different J dependence means different impact parameter dependence. According to the above description, for the O(3P) + HD → OD/OH + H/D abstraction process, two reaction

mechanisms have been proposed: a rebound mechanism and a stripping mechanism. The rebound collisions can associate with small impact parameter collisions and lead to a backward scattering, while the striping scatterings correspond to the relatively large impact parameter collisions and tend to produce the forward and sideways scattering.58 Hereafter, the forward direction is always along the incoming O atom. On the basis of the above descriptions, we can expect that at low collision energy, the backward scattering is predominated, while with collision energy increases, the sideways and forward scatterings may be prevailing. Comparing the two product channels with the same reagents, we find that the total reaction probability of forming OD is larger than that of OH except for at lower collision energy 0.4 eV. The detail of the reaction probability for collision energy 0.4 eV is shown in the inset of the Figure 4. This phenomenon can be attributed to the following reasons. At lower collision energy, the tunneling effect on the reactivity is important. Meanwhile when the collision occurs on the H side of the molecule HD, comparing with the O atom approaching the deuterium atom, the distances to the center of mass involved in the process are larger, and the centrifugal barrier for collisions at a given value of J is lower, which certainly favors the formation of OH. However, for higher collision energy, the width of the cone of acceptance is the main factor when it comes to determining the reactivity, and therefore the reaction probability for OD channel is larger. It should be also remarked that the range of J values necessary to the convergence of the E


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Figure 5. Product rotational state distributions for the O(3P) + HD (v = 0, j = 0) reaction at four different collision energies. Key: (a−d) the OD + H product channel; (e−h) the OH + D product channel.

calculations showed a vibrational inversion population at high collision energy. This discrepancy may result from the limitation of the calculation method and the inaccuracy PES had used by Bowman et al. Figure 5 shows the product rotational state distributions of the two product channels for the title reactions at several selected collision energies as a function of the product rotational quantum numbers j′. Compared with the product vibrational distributions, the rotational states of the OD (OH) product are inverted in all vibrational levels for considered energies. In Figure 5, for the OD + H product channel, similar features have been found at all collision energies. The peak of the distribution is somewhere between j′ = 0 and the maxima j′ value allowed by energy, and bell-shaped curves are visible. We also find that the negative correlation exists between rotational and vibrational excitations, i.e., the values of the most populated rotational level diminish with the increase of the product vibrational number v′. This tendency is the expected one in triatomic reactions. At the certain collision energy, for example Ecol = 0.6 eV of the OD + H product channel, for v′ = 0, the distribution is broad and rotational levels 0−16 are significantly

integral cross section calculations is larger for the OH + D product channel in the energy range investigated. This phenomenon is in correspondence with the fact that the center of mass of the reactant molecule is closer to the deuterium atom. Thus, we can also predict that the sideways and forward scatterings may be more obvious in the OH + D product channel than in the other one at high collision energy region. C. Product State Distributions. The calculated product OD/OH vibrational distributions for the title reactions on the 3 A″ state are also shown in Figure 3, which are obtained by summing all available rotational state populations in each vibrational channel. In the energy range considered, v′ = 0, v′ = 1, and v′ = 2 vibrational levels of the OH/OD molecule are open. It can be readily seen that the OH product molecule is formed predominantly in the v′ = 0 level and the OD product is found to be predominantly in v′ = 0 and v′ = 1 states. We can expect that there are more rotational states in low-lying vibrational states. The earlier reduced dimensionality exact quantum calculations by Bowman et al.34 have shown the same product state distributions law for the OH + D product channel, while for the OD + H product channel their F


Article

The Journal of Physical Chemistry A populated, while for v′ = 1, the distribution is narrow and it peaks at j′ = 3−5 and rotational levels j′ ≥ 12 are not populated. This is due to that the smaller kinetic energy in the higher vibrational channel restricts the number of rotational levels populated. Despite the similarity at different collision energies, some discrepancies arise with increasing the collision energy. The ICS maximum shifts to higher j′ values and the amplitude of the maximum increases as collision energy increases. The increase of the amplitude of the maximum with collision energy means more rotational channels of products effectively open at higher collision energies. The inspection of the product rotational state distributions for those collisions where OH is formed leads to similar conclusions, although these processes exhibit a higher degree of vibrational adiabaticity than their OD counterparts, especially at the lower collision energy. D. DCS. The total DCSs, which are summed over all energetically accessible product vibrational and rotational states, at the four collision energies are shown in Figure 6. The relative Downloaded by GEORGETOWN UNIV on August 23, 2015 | http://pubs.acs.org Publication Date (Web): August 17, 2015 | doi: 10.1021/acs.jpca.5b04255

participation of larger impact parameter collisions, which is consistent with our expectation from Figure 4a. In addition, we can find that the DCSs of the OH channel exhibit a little different behavior. At 0.4 eV, all products are predominantly backward scattered. With the increase of collision energy, the trends of shifting to the smaller scattering angles and of peaking away from backward regions are apparent. This different behavior between the two product channels is consistent with our expectation from Figure 4. Similar behaviors were found for the reactions Cl + CD4/CH459and F + HD60 previously. On the basis of the above statement, we come to a conclusion that at lower collision energies, the title reactions are predominated by the rebound reaction mechanism, while for the higher collision energies both stripping and rebound mechanisms exist. For the purpose of extracting the information on the reaction mechanism, we also show a reaction model by a cartoon in Figure 7 to analyze the energy dependence of the above

Figure 7. Cartoon depicting head-on (upper panel) and glancing (lower panel) collisions between an oxygen atom and a deuterium−hydrogen molecule for the OD + H product channel.

calculation results for the OD + H product channel. From the conservation of total angular momentum,61 a smaller-impactparameter collision leads to rotationally cold products, which usually corresponds with the backward scattering. Similarly, the large-impact-parameter collision between O and HD molecule usually leads to rotationally excited products, which are associated with sideways and forward scattering (θ ∼ 0° not shown in Figure 7.). In the present study, we find two different reactive pathways for the title reactions. The first one, the headon collisions, the O atom attacks the HD molecule normally along the minimum energy path in O−D−H near linear configuration. This collision is correlated with a smaller-impactparameter collision and tends to produce backward scattering. The other one is the glancing collision. This collision usually leads to sideways and forward scattering and supplies products of a high internal excitation by large-impact-parameter collisions. The title reactions are governed by the rebound mechanism, and the product OD (OH) is predominantly formed by small-impact-parameter collisions and scattered in the backward region, showing the relatively rotational cold OD (OH) products at lower collision energy. With the collision energy increasing, the spatial preferences of the reaction tend to the sideways scattering region, which is related with the largerimpact-parameter, thus result in a broader product rotational distributions. On the basis of the above description, we find the increasing contribution of glancing collisions with the collision

Figure 6. Total DCSs for the O(3P) + HD (v = 0, j = 0) reaction at four different collision energies. (a) the OD + H product channel; (b) the OH + D product channel.

magnitude of the DCSs is the reflection of the values of the reaction probabilities, as discussed in connection with Figure 4. The ICSs at four collision energies are 0.0008, 0.1666, 0.6150, and 1.1044 Å2 for OD and 0.0023, 0.0643, 0.1893, and 0.3421 Å2 for OH. The angular distribution of the OD product is mainly concentrated in the backward region at the lower collision energies, as a consequence of a dominating rebound mechanism. However, as the collision energy increases, the consequence of the stripping mechanism makes the sideways scatterings appear and increase. This behavior is due to the G


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changes, especially for the OD + H product channel. For both channels, the collisions become less vibrationally adiabatic. This change manifests itself more intensely for the O(3P) + HD (v = 1) collisions, where the v′ = 1 OD + H products and the v′ = 0 OH + D products only predominate for the largest values of j′. Moreover, the value of the most populated j′ shows a marked shift toward higher j′ values and the amplitude of the maximum increases faster with the increase of the collision energy for the same product vibrational state in comparison with v = 0. For the initial vibrational state v = 1, more internal energy makes it available to excite rotational degrees of freedom of the product OD(OH) molecule, which will result in broader rotational distributions shifted to higher rotational states. In addition, great changes have taken place in the shape, and a few small peaks have been found at higher collision energy. Thus, based on the above description and the previous depiction unfolded in section 3D, we predict that the forward and sideways scatterings are more obvious for the vibrationally excited state. From Figure 10, we can see that the vibrational excitation of the reactant HD can cause significant changes in the shape of the DCS curves in comparison with Figure 6. For the OD + H product channel, the shape of the DCS curve is almost independent of the initial vibrational state, and the products spread over the whole range of the scattering angles. The features of the curves can be described as follows. For the OD + H product channel, the maximum of the DCS amplitude locates at the backward region, and then the DCS decreases monotonically to the forward region, where a small peak becomes apparent. With the increase of collision energy, especially in the higher collision energy 1.0 eV, the DCS maximum shifts to the sideways region and the values in the backward region began to decrease. This decrease results from the depression of reactivity by collision energy and can be explained by the mechanism proposed by Zhang et al.62 At low collision energy, the reaction is mainly governed by the head-on collisions and thus results in the backward scattering, while at the high collision energy, the oblique collisions become more popular, in which the centrifugal potential plays an important role. The large centrifugal potential enhances the forward and sideways scattering and meantime inhibits the backward scattering. For the OH + D product channel, the values of the DCS become near to four constants similar to Figure 6b, in the backward region, while in the forward and sideways scattering region, some peaks appear, especially in the higher collision energy. This latter case is different from Figure 6b, in which the DCS decreased monotonically until to zero with no contribution from the forward scattering. It is clear from the depiction unfolded in this paragraph that, except in the backward region, the OH + D channel exhibits a larger sensitivity to the initial vibrational state of the reactants than its OD + H counterpart. On the basis of the above description and the analysis unfolded in section 3D, we conclude that both the rebound and stripping mechanism exist in the whole considered collision energies. F. Branching Ratio. Figure 11 shows the intramolecular isotopic branching ratios between the OD and OH products as a function of the collision energy along with the theoretical results of Song et al.35 It can be seen that the branching ratios are less than 1 until the collision energy is greater than a certain energy, after which they increase largely, followed by a slight increase, and finally nearly tend to be a constant with further increasing of the collision energy. The changing trend of the branching ratio near the threshold energy can be attributed to


energy can explain the energy dependence of the total DCSs. The backward bias persists at all the collision energies considered. Thus, we come to the conclusion that, in the case of high collision energies, both rebound and stripping mechanisms exist. The above analysis is also suitable for the OH + D product channel. E. Vibrational Excitation. For the sake of investigating the effect of the vibrational excitation of the reactant diatomic molecule HD on the dynamics properties and the reaction mechanism of the title reactions, we have calculated the ICS, product rotational state distribution and DCS with HD in the v = 1 state, as shown in Figures 8, 9 and 10.

Figure 8. Total ICSs and product vibrational state distributions as a function of collision energy for the O(3P) + HD (v = 1, j = 0) reaction. Key: (a) the OD + H product channel; (b) the OH + D product channel.

Figure 8 shows the total and vibrationally resolved reaction ICS as a function of the collision energy for both channels of the reaction O(3P) + HD (v = 1, j = 0). Comparing with Figure 3, we can find a significant change, i.e., the vibrational excitation can enhance the reactivity of the title reactions. For the OD + H product channel, more vibrational channels effectively open for the considered energy range. It is interesting in Figure 8 that the product OD is formed preferentially vibrationally excited relative to the initial vibrational state of the reactant HD, i.e., OD (v′ = 2) is formed preferentially from HD (v = 1). While for the OH + D, as shown in Figure 8(b), the dominant product has the same quantum number as the reactant HD. This behavior is in agreement with the results of Bowman et al.34 When the vibrational level increases up to v = 1, as shown in Figure 9, the product rotational distributions display significant H


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Figure 9. Product rotational state distributions for the O(3P) + HD(v = 1,j = 0) reaction at four different collision energies. Key: (a−d) the OD + H product channel; (e−h) the OH + D product channel.

significant changes for the cross section branching ratio in the numerical value aspect. The maximum of the intramolecular isotopic branching ratio for vibrational excitation is less than for ground vibrational state, when making the comparison between v = 1 and v = 0. This behavior can be explained from the comparison between Figure 3 and Figure 8. It is found that, for the OD + H product channel with more effective product vibrational state, the integral cross sections present a decreasing trend in the higher collision energy for the whole product vibrational state for the vibrationally excited state. However, for the OH + D product channel, there is an opposite trend. That is to say that in promoting the reactivity, the vibrational excitation is more effective for the OH + D channel than for the OD + H channel in the case of high collision energy. For the lower collision energy, owing to the reduction of the threshold energy for the higher vibrational state of the HD, the behavior shown in Figure 11 appears.

that the tunneling effect of the OH is greater than that of OD, which is also consistent with the experiment results of Robie et al.32 As the collision energy increases, the tunneling effect should diminish and the other factor will dominate; i.e., the repulsive forces between O and HD will induce the molecule to rotate in such a way that in most orientation the H atom rotates away from the O atom. This, in principle, favors the formation of OD and leads to a branching ratio greater than 1. From Figure 11 we also can see that the present results are comparable with the theoretical results of Song et al.,35 and the difference between them can be attributed to the differences in the PES and the calculation methods. The barrier height of the PES employed by Song et al.35 is 0.542 eV, which is lower than 0.565 eV used in our work. For the QCT method, as pointed before, the zero-point energy and the tunneling effect are not taken into consideration, which may produce inaccurate results, especially nearby the threshold energy. And the shape of the branching ratio curve is almost independent of the initial vibrational state and is spread over a larger range of collision energy. Obviously, the values of the vibrational excitation cause I


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OH + D channel, the peak of the DCS at higher collision energy appears in the sideway scattering region. The backward bias persists at all the collision energies considered, which means that both the rebound and stripping mechanisms exist for two product channels in the case of higher energy. For v = 1, the vibrationally excited state product OD is usually formed preferentially relative to the initial vibrational state of the reactant HD. Although the corresponding angular distributions are still predominated by backward scattering, they become wider and spread over the whole range of scattering angle values, including a small contribution in the forward region. For the OH product channel, however, the values of the DCS become near four constants in the backward region, and then followed by some peaks in the forward and sideways scattering region, especially in the higher collision energy. Certainly, the above conclusions need further support from related experiments.

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AUTHOR INFORMATION

Corresponding Author

*(Q.-T.M.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Natural Science Foundation of Shandong province, China (Grant No. ZR2014AM022). The authors also thank Prof. K. L. Han for providing the computational codes.

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Figure 10. Total DCSs for the O(3P) + HD (v = 1, j = 0) reaction at four different collision energies. Key: (a) the OD + H product channel; (b) the OH + D product channel.

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Figure 11. Cross-section branching ratio σOD/σOH as a function of the collision energy. Also shown are the theoretical results of Song et al.35

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+ HD - American Chemical Society

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