Quantum State-to-State Dynamics of the H + LiH â H2 + Li Reaction

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The Journal of Physical Chemistry

Quantum State-to-State Dynamics of the H + LiH → H2 + Li Reaction Xiaohu He,†,‡,§ Hui Wu,‡ Peiyu Zhang, ‡ and Yan Zhang*‡ †

School of Chemical Engineering, Dalian University of Technology, Dalian 116023, China

‡

State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China §

University of Chinese Academy of Sciences, Beijing 100049, China

AUTHOR INFORMATION Corresponding author *E-mail: [email protected] (Y.Z.).

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ABSTRACT: State-to-state quantum dynamics calculations for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0)

→ H 2 + Li reactions are carried out based on an ab initio ground electronic state potential energy

surface (PES). Total and product state-resolved integral and differential cross sections and rate constants are calculated. The present total integral cross sections and rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction are found to be in agreement with previous literature results. Product

state-resolved integral cross sections and rate constants reveal that the H 2 products are preferred

to be formed in their ro-vibrational excited states. The differential cross sections show that the intensity of forward scattering for the H 2 products in their ro-vibrational excited states is stronger than other states. The mechanisms for the 𝑣𝑣 = 0 and 𝑣𝑣 = 1 reactions are found to be highly consistent with each other. Further, the influence of the stripping mechanism on the H + LiH

reaction is studied. It is found that the stripping mechanism could be responsible for the decrease of the reactivity, the product state distribution and scattering direction of the H 2 products. It is related to the “attractive” feature of the underlying PES.

KEYWORDS: H + LiH reaction, differential cross section, rate constants, stripping mechanism, attractive feature.


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1. Introduction The H + LiH → H 2 + Li reaction is a very typical reaction which is of highly astrophysical, physical, and chemical interests.1-7 It is argued that the LiH molecule is of importance in the evolution of the early universe,3,4,6-9 since it is proposed that LiH may have contributed to form the first condensed structure of the early universe after the recombination era.4,10 The LiH 2 system is also of interests for some physical and chemical concerns. The LiH 2 system has only five electrons, in which two of them are core electrons, and three are valence electrons, which are involved in the ground electronic state. Therefore, it is the second electronically simple neutral triatomic system after H 3 .6,11-13 The LiH 2 system is the simplest collisional system involving a metal atom.6,11,13 From the viewpoint of energy transformation, this reaction in its ground state is a typical barrier-less and exothermic reaction.6,7,11,12,14-18 Because of the astrophysical, physical, and chemical importance of the H + LiH reaction, great efforts have been made by many researchers to observe and understand its reactive dynamics and kinetics. The reverse of the title reaction (Li* + H 2 → LiH + H) has been studied experimentally and theoretically in different electronic states.1,2,5,19,20 These investigations have provided valuable knowledge about the formation of LiH. The direct experimental data for the title reaction in its ground state, H(2S) + LiH (X, 1Σ+) → H 2 (X, 1Σ+ g ) + Li (2S), is still missing,3,4,6,7,12 since it is difficult to prepare the reactant in its ground electronic state. Therefore, accurate quantum scattering dynamics study of this reaction is inevitable for the purpose of understanding the mechanism in detail. In order to obtain complete and exact reactive dynamic information of the H + LiH reaction, an accurate three-dimensional potential energy surface (PES) is a prerequisite. In the reactive PESs reported11,14-17,21 until now, the ones of Dunne et al. (hereafter DMJ PES),16 Prudente et al.


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(hereafter PMM PES),17 and Wernli et al. (hereafter WCBG PES)11 have been applied in various classical and quantum reactive dynamics studies.6-9,11-13,16-18,22-33 It is generally accepted that there is no energy barrier presenting along the reaction path for the H + LiH reaction,6,7,11,12,14-18 and the reaction is highly exothermic by ~ 2 eV.6,7,11,12,14,17-19,21 The WCBG PES supports an exothermicity of ~2.258 eV.6,7,11,18 The DMJ PES is semi-empirical, and it holds unphysical wells.6,17 These wells may eventually result in the very different dynamical results than the other two PESs.17 The PMM and WCBG PESs are based on the ab initio calculations of comparable level. The fitting procedure of the WCBG PES is considered to be better than that of the PMM PES.7 The root-mean-square (RMS) deviations of the fitting for the PMM and WCBG PESs are 64 and 2.2 meV, respectively.7,11,17 The accuracy of fitting procedure of the WCBG PES is fairly high.6,7,11,18 The WCBG PES is employed in the present calculations. Extensive theoretical works reported before 2012 have been reviewed by Roy and Mahapatra (see reference 6 and the references therein). Recently, there are still researchers contributing to the study of this reaction.7,18,28-33 The works of Padmanaban and Mahapatra23-27 and Defazio et al.22 indicate that the H-exchange channel dominates over the LiH depletion channel on the DMJ PES. The dynamic results based on the PMM and WCBG PESs have an entirely different structure.6,7,17,18,29,30 On these PESs, the LiH depletion channel dominates over the H-exchange channel. Integral cross-section (ICS) and thermal reaction rate constants of the H + LiH reaction have been studied using the classical and quantum methods on the PMM and WCBG PESs.6-9,1618,22-25

Differential cross section (DCS) or polarization-dependent differential cross section

(PDDCS) were only calculated by the quasi-classical trajectory (QCT) method in the convenient of the inexpensive computational cost.12,18,28,30,31 However, DCS is a crucial physical quantity which helps researchers to understand the reaction mechanism in detail. Full quantum DCS for


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the H + LiH reaction are still unavailable until now, which provides the primary motivation for this work. Quantum state-to-state dynamics study of the H + LiH reaction is numerically expensive in two ways. First, the number of total angular momentum included in the calculation is rather large in order to get converged results.6,7,33 Second, the significant Coriolis Coupling (CC) effect makes the computation to be quite time consuming. In this paper, we carry out quantum dynamics calculations for the H + LiH reaction based on the WCBG PES11 to provide detailed results and discussion about the DCS of this reaction. We also compute several typical state-tostate rate constants to understand the reaction. Besides, it is proposed by Gómez-Carrasco et al.7 that the H + LiH reaction is mainly dominated by the stripping mechanism. The accurate quantum study is expected to provide critical informations which are most concerned for the researchers. The paper is organized as follows. In section 2, the quantum method is outlined, and the key computational parameters are intoduced in this section. In section 3, all the results are exhibited and discussed in detail. We provide the main conclusions of this work in section 4.

2. Computational details In this work, we perform a series of full quantum calculations for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 =

0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗 ′ ) + Li reactions at the collision energies ranging from 0.05 to 0.6 eV. We use (𝑣𝑣, 𝑗𝑗) and (𝑣𝑣 ′ , 𝑗𝑗 ′ ) to denote the vibrational and rotational quantum numbers of the reactant and

product molecules, respectively. A recently developed graphics processing units (GPU) accelerated time dependent wave packet (TDWP) program34 is applied to our calculations. This program which is developed by Zhang and Han has been proved to be efficient and accurate.34,35 The TDWP method applied in this work has been described previously in detail (see references 34 and 35 and the references therein).


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Extensive calculations have been done to ensure the convergence of the present dynamics results. The optimal parameters (listed in Table 1) are thus determined and firstly applied to the calculation for total angular momentum 𝐽𝐽 = 0, then extended up to 𝐽𝐽 > 0. Inclusion of total angular momentum is extended up to 𝐽𝐽 = 60 in order to guarantee the convergence of the cross sections. The initial wave packet is firstly constructed in the space-fixed (SF) reactant Jacobi

coordinates. In our calculation, the preparation of the wave packet is done on the central processing unit (CPU), and then the whole propagation process is implemented on GPUs in the body-fixed (BF) product Jacobi coordinates.34 In Table 1, 𝑅𝑅 is the distance between Li and the

center-of-mass of the product molecule H 2 , and 𝑟𝑟 is the internuclear distance of H 2 . GómezCarrasco et al. have used a set of equations of mass factors which are written as36 𝑎𝑎 =

𝑚𝑚𝐴𝐴 ⁄(𝑚𝑚𝐴𝐴 + 𝑚𝑚𝐵𝐵 ) and 𝑐𝑐 = 𝑚𝑚𝐶𝐶 ⁄(𝑚𝑚𝐵𝐵 + 𝑚𝑚𝐶𝐶 ) . Gómez-Carrasco et al. concluded that if 𝑎𝑎 ≫ 𝑐𝑐 the reactant Jacobi coordinate is preferred, and it is convenient to use product Jacobi coordinates if 𝑎𝑎 ≪ 𝑐𝑐. For the H + LiH reaction 𝑎𝑎 and 𝑐𝑐 are ~ 0.5 and ~ 0.875, respectively. Therefore, the

product Jacobi coordinate is suitable for studying the H + LiH reaction. The usage of

approximations in the calculations is restrained for the purpose of obtaining exact state-to-state dynamic information. The Coriolis Coupling (CC) effect is treated accurately in this work (see section I in the supporting information). The state-to-state ICS can be calculated as34,35,37,38 𝜋𝜋

𝜎𝜎𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝐸𝐸𝑐𝑐 ) = 𝑘𝑘 2 𝐶𝐶𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝐸𝐸𝑐𝑐 )

(1)

𝑣𝑣𝑣𝑣

where 𝑘𝑘𝑣𝑣𝑣𝑣 is the modulus of the translational wave vector. 𝐸𝐸𝑐𝑐 is the collision energy. 𝐶𝐶𝑣𝑣𝑣𝑣→𝑣𝑣′𝑗𝑗′ (𝐸𝐸𝑐𝑐 ) is the state-to-state cumulative reactive probability, which is expressed as 𝑔𝑔

𝑠𝑠 ∑𝐾𝐾′ ∑𝐾𝐾 ∑𝐽𝐽(2𝐽𝐽 + 1) �𝑆𝑆𝑣𝑣𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ 𝐾𝐾′ � 𝐶𝐶𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝐸𝐸𝑐𝑐 ) = (2𝑗𝑗+1)

2

(2)

where 𝑆𝑆𝑣𝑣𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ 𝐾𝐾′ is the element of the scattering matrix.34 𝑔𝑔𝑠𝑠 is the post antisymmetrization ACS Paragon Plus Environment

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factor.37,38 Fermi-Dirac (FD) statistics requires that the spin states of the H 2 products should be considered. Subsequently, 𝑔𝑔𝑠𝑠 is taken as 3⁄2 and 1⁄2 for ortho and para H 2 molecules,

respectively. 𝑔𝑔𝑠𝑠 is equal to 1 if the Boltzmann statistics is included in the calculation. The state-to-state DCS is calculated as34,35 d𝜎𝜎𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝜃𝜃,𝐸𝐸𝑐𝑐 ) d𝛺𝛺

1

2

�𝑔𝑔

𝐽𝐽 = (2𝑗𝑗+1) ∑𝐾𝐾′ ∑𝐾𝐾 �2𝑖𝑖𝑘𝑘 𝑠𝑠 ∑𝐽𝐽(2𝐽𝐽 + 1)𝑑𝑑𝐾𝐾′ 𝐾𝐾 (𝜃𝜃)𝑆𝑆𝑣𝑣𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ 𝐾𝐾′ � 𝑣𝑣𝑣𝑣

(3) 𝐽𝐽

𝐾𝐾′ and 𝐾𝐾 are the product and reactant helicity quantum numbers, respectively. 𝑑𝑑𝐾𝐾′ 𝐾𝐾 (𝜃𝜃) is the reduced rotation matrix element. 𝜃𝜃 is the scattering angle.

The state-to-state rate constants are calculated by using the corresponding ICS results, which is

given as6,7 𝐾𝐾𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝑇𝑇) =

1

8 2 ∞ 𝐸𝐸𝑐𝑐 �𝜋𝜋𝜇𝜇 3 � ∫0 𝐴𝐴−𝐵𝐵𝐵𝐵 (𝑘𝑘𝐵𝐵 𝑇𝑇)

𝜎𝜎𝑣𝑣𝑣𝑣→𝑣𝑣′ 𝑗𝑗′ (𝐸𝐸𝑐𝑐 )𝑒𝑒 −𝐸𝐸𝑐𝑐⁄𝑘𝑘𝐵𝐵 𝑇𝑇 𝑑𝑑𝐸𝐸𝑐𝑐

(4)

where 𝑘𝑘𝐵𝐵 is the Boltzmann constant. The total ICS, DCS, and rate constant can be obtained by summing over the corresponding state-to-state results.

3. Results and discussion 3.1 Integral cross sections The total ICSs for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 + Li reactions are depicted in Figure

1. The present ICS for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction (ICS0) agrees well with the result of Gómez-Carrasco et al.,7 which included the CC effect. ICSs of Roy and Mahapatra6 show similar trend of variation to the present results but have a difference in magnitude. The difference can be attributed to the significant CC effect of the H + LiH reaction which was not included in the calculations of Roy and Mahapatra (see the discussion in section I in the supporting information).6,7 The theoretical results7,12,18,28-31,33 employing the PMM PES17 show a similar


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feature with our results (see section II in the supporting information). In contrast, the results6,16,17,22,23,25 based on the DMJ PES16 have an entirely different structure, and this difference has been discussed in reference 6. Observing the figure, it can be found that ICS0 monotonously decreases as 𝐸𝐸𝑐𝑐 increases. The decrease could be caused by more repulsive regions of the PES being available at higher 𝐸𝐸𝑐𝑐 .39 Moreover, the ICS for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 =

0) reaction (ICS1) is calculated in the present investigation. One can find that ICS1 is smaller than ICS0 within the whole range of 𝐸𝐸𝑐𝑐 . Obviously, the initial vibrational excitation has a remarkably negative effect on the reactivity. This phenomenon could also be induced by the excitation of LiH opening more repulsive regions of the PES, and therefore reducing the reactivity. The F + HBr → FH + Br reaction is a typical barrier-less reaction which does not support any potential wells. For the F + HBr reaction the initial vibrational excitation also reduce the reactivity40,41. However, for a barrier-less reaction with potential wells (eg. O(1D) + H 2 → OH + H42 and S(1D) + H 2 → SH + H43), the reactivity is not sensitive to the variation of the initial vibrational level. Therefore, that the reactivity is prohibited by reactant vibrational excitations is not a common character for all barrier-less reactions. In Figure 2, the present product vibrational state-resolved ICSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0)

→ H 2 (𝑣𝑣 ′ ) + Li reaction are compared with the corresponding results of Gómez-Carrasco et al.7

Two features can be found from this figure. First, the formation of the H 2 product in 𝑣𝑣′ = 1 and 2 states is favored. Second, the H 2 product in 𝑣𝑣′ ≤ 4 can be formed at low collision energies, but

the reactions for the formation of H 2 in 𝑣𝑣′ > 4 states have energy threshold. The present

calculated results are in reasonable agreement with the results of Gómez-Carrasco et al.7 Obviously, the reaction becomes endothermic if the H 2 products are formed in the vibrational states above 𝑣𝑣 ′ = 4. The formation of H 2 products in 𝑣𝑣 ′ = 5 state has an energy threshold at ~ ACS Paragon Plus Environment

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0.22 eV, and for the H 2 (𝑣𝑣 ′ = 6) products it is found to be ~ 0.6 eV. The product vibrational

state-resolved ICSs for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ ) + Li reaction is given in Figure

S6 in the supporting information. The energy threshold for the H 2 products in 𝑣𝑣 ′ = 5 state is ~ 0.07 eV, which is smaller than that for the 𝑣𝑣 = 0 reaction.

Furthermore, we also calculate the state-to-state ICSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2

(𝑣𝑣 ′ , 𝑗𝑗′) + Li reaction at 𝐸𝐸𝑐𝑐 = 0.05, 0.1, 0.3, and 0.6 eV, which are shown in Figure 3. As can be seen, the range of rotational quantum number of the H 2 products is very broad for each

vibrational state. A great amount of the products distribute in rotational hot states. The ICS firstly increases with 𝑗𝑗′ to a maximum value, and then decreases to a small value. At each 𝐸𝐸𝑐𝑐 , the

highest 𝑗𝑗′ state decreases as 𝑣𝑣 ′ increases. Since the total energy is constant, the internal energy regularly shifts from rotation to vibration with increasing 𝑣𝑣 ′ level. The shapes of the ICSs for

each 𝑣𝑣 ′ state are found to resemble to each other. The ICSs vary with increasing 𝐸𝐸𝑐𝑐 in two

aspects. First, the range of 𝑗𝑗′ is expanded, although the increase is not very evident. Second, the H 2 products are increasingly inclined to distribute in rotational hot states at higher 𝐸𝐸𝑐𝑐 . For

example, the maximum value of the ICS for each 𝑣𝑣 ′ state is located at an intermediate 𝑗𝑗′ value at

𝐸𝐸𝑐𝑐 = 0.05 eV. At 𝐸𝐸𝑐𝑐 = 0.6 eV, the maximum value of the ICS for each 𝑣𝑣 ′ state is located at a large 𝑗𝑗′ value. Figure 3(d) also compared the product rotational distributions with and without FD statistics for the H 2 (𝑣𝑣′ = 0) products at 𝐸𝐸𝑐𝑐 = 0.6 eV. The result with FD statistics shows a

distinct saw-toothed shape, and the reactivity for the ortho H 2 products (odd 𝑗𝑗 ′ states) is larger

than that for the para H 2 products (even 𝑗𝑗 ′ states). In contrast, the distribution without FD statistics shows a unimodal character. Although it is reported that the effect of the nuclear spin

statistics is non-negligible when the theoretical results are compared with the experiments,37,38 the exclusion of the statistics will not influence the analysis of the reaction mechanism


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following. The corresponding state-to-state ICSs for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗′) +

Li reaction (see Figure S7 in the supporting information) are found to be similar to that for the 𝑣𝑣 = 0 reaction, indicating that their mechanisms are consistent to each other. 3.2 Initial state selected rate constant

Total and product vibrational state-resolved rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) →

H 2 (𝑣𝑣 ′ ) + Li reaction at temperatures ranging from 300 to 3000 K are calculated and shown in Figure 4. The total rate constant of this work is compared with literature results in Figure 4a. As

can be seen, the present result is in good agreement with the result of Gómez-Carrasco et al.7 It is unsurprising, since the ICSs agree with each other very well (see Figure 1). In addition to this agreement, the present result obviously deviates from other results which used different approximations in the calculations.6,8,10 The result of Stancil et al.10 shows the maximum difference from the present result: the present rate constant is about 1 × 10−9 cm3/s, which is

about two orders of magnitude larger than the result of Stancil et al.10 Figure 4b gives the product

vibrational state-resolved rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ ) + Li reaction.

It can be seen that the rate constants for the H 2 (𝑣𝑣 ′ = 1,2) products are the largest ones. The rate

constants for the H 2 (𝑣𝑣 ′ = 0,3,4) products are smaller. The rate constant for the H 2 (𝑣𝑣 ′ = 5)

products is about one order of magnitude smaller than the results for other vibrational states. The total and product vibrational state-resolved rate constants for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 + Li reaction (see Figure S8 in the supporting information) are found to be slightly smaller than

that for the 𝑣𝑣 = 0 reaction. The rate constants for the H 2 (𝑣𝑣 ′ = 1,2) products of the 𝑣𝑣 = 1

reaction are the largest ones, which is the same as that for the 𝑣𝑣 = 0 reaction.

Figure 5 displays a set of representative state-to-state rate constants for the H + LiH (𝑣𝑣 =

0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗′) + Li reaction at temperatures ranging from 300 to 3000 K. These results ACS Paragon Plus Environment

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are carefully selected via extensive observations: at each 𝑣𝑣 ′ , the rate constants for different 𝑗𝑗′ are compared, and the larger ones are selected. As a result, the rate constants for the H 2 products in the states of (𝑣𝑣 ′ = 0, 𝑗𝑗 ′ = 13) , (𝑣𝑣 ′ = 1, 𝑗𝑗 ′ = 11) , (𝑣𝑣 ′ = 2, 𝑗𝑗 ′ = 8,12) , (𝑣𝑣 ′ = 3, 𝑗𝑗 ′ = 7) , and

(𝑣𝑣 ′ = 4, 𝑗𝑗 ′ = 4) are shown. It is observed that the H 2 (𝑣𝑣 ′ = 2, 𝑗𝑗 ′ = 8,12) products are the most

probable products of the reaction. Besides, it is found that at temperatures smaller than 1500 K, the H 2 products in 𝑗𝑗′ around 8 play a major role in the reaction, while at temperatures larger than

1500 K, 𝑗𝑗′ around 12 are prevailing. Bovino et al.8 had reported a set of state-to-state rate constants for the H + LiH reaction calculated by a uniform 𝐽𝐽-shifting approach.44 They concluded

that the H 2 products in their ground ro-vibrational state are preferentially formed. Clearly, the present calculation gives a different description about the reaction: the products for the H + LiH reaction are preferentially formed in their excited ro-vibrational states, and the preferred final state varies with temperature. The state-to-state rate constants for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) →

H 2 + Li reaction are given in Figure S9 in the supporting information. The most probable final states for the H 2 products are found to be close to the outcomes from the 𝑣𝑣 = 0 reaction.

3.3 Differential cross sections

DCS describes the product angular distribution of a reaction.12,45,46 Figure 6 gives the total DCSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 + Li reaction at 𝐸𝐸𝑐𝑐 = 0.05, 0.1, 0.3, and 0.6 eV.

Apparently, the H 2 products are mainly forward scattered in all cases. In the meantime, the sideward and backward scatterings are quite weak. The DCSs or PDDCSs based on the PES of Prudente et al.12,13,17,18,28,30,31 have shown similar dynamics pattern (see section II in the supporting information). As 𝐸𝐸𝑐𝑐 increases, the scattering intensity in most of the scattering angles

decreases. This is consistent with the decrease of ICS0 shown in Figure 1. However, the decrease of the scattering intensity is anisotropic. The products retain more forward scattering than


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sideward and backward scatterings at high 𝐸𝐸𝑐𝑐 comparing with low 𝐸𝐸𝑐𝑐 . For instance, at 𝜃𝜃 = 0°,

the DCSs at 𝐸𝐸𝑐𝑐 = 0.05 and 0.6 eV are 19.8 and 12.5 Å2/sr, respectively, but at 𝜃𝜃 = 90°, they are 2.6 and 0.4 Å2/sr, respectively.

Figure 7 presents the product vibrational state-resolved DCSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0)

→ H 2 (𝑣𝑣′) + Li reaction at 𝐸𝐸𝑐𝑐 = 0.05, 0.1, 0.3, and 0.6 eV. It is known that the ICS for the H 2

(𝑣𝑣 ′ = 5) products at the 𝐸𝐸𝑐𝑐 less than 0.6 eV is very small. Therefore, at 𝐸𝐸𝑐𝑐 = 0.05, 0.1, and 0.3

eV, only the DCSs for the H 2 (𝑣𝑣 ′ = 0 − 4) products are shown. The 𝑣𝑣′-dependent ICSs indicate that the mechanism of the H + LiH reaction could be complicated regarding vibration.7

Generally, there are more translational energy can be conserved if the H 2 products are formed in their excited vibrational states ( 𝑣𝑣 ′ = 4 in this case), and less translational energy being conserved for the H 2 products formed in their ground vibrational state (𝑣𝑣 ′ = 0). The product

angular distribution of the H + LiH reaction is obviously the compromise of the above two

limiting cases. If more translational energy is conserved, the intensity of forward scattering would be strong. Figure 7 shows that the forward scattering for the H 2 products in 𝑣𝑣 ′ = 2,3,4 states is strong, and for the products in other states the forward scattering is weak. The angular

distribution for the H 2 products in 𝑣𝑣 ′ = 0 state is almost isotropic at 𝐸𝐸𝑐𝑐 = 0.05 and 0.1 eV, and at 𝐸𝐸𝑐𝑐 = 0.3 and 0.6 eV, the angular distribution inconspicuously peaks in the forward direction. The angular distribution for the H 2 (𝑣𝑣 ′ = 1) products peaks in the forward direction, and the

intensity increases with increasing 𝐸𝐸𝑐𝑐 . The DCS for the H 2 products in 𝑣𝑣 ′ = 5 state peaks in the

scattering angle range of 0º ~ 10º, but the intensity is weak since the reactivity is small.

Observing the figure, it can be found that the DCSs have abundant fluctuation structures, which suggests the existence of interactions among different parts of the partial waves. In many cases, especially at high 𝐸𝐸𝑐𝑐 , the strong forward scatterings are usually accompanied by one or more ACS Paragon Plus Environment

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secondary peaks in the forward direction. For example, at 𝐸𝐸𝑐𝑐 = 0.3 eV, the DCS for the H 2

(𝑣𝑣 ′ = 2) products has a secondary peak located at 𝜃𝜃 = 17°. The fluctuations do not change the dynamics significantly, and most of them disappear in the total DCS because of the averaging over different partial waves. It is speculated that these fluctuations might be quantum effects, and we anticipate that they could be examined in future experimental or theoretical studies. The quasi-classical trajectory (QCT) calculations may not be capable to reproduce them. The fluctuations of a QCT DCS (e.g., Figures 3 and 4 in reference 12) has strong correlation with the total sample number and the fitting procedure.46-48 Detailed study of these structures with nearside-farside theory49 and glory theory50 is expected to provide more insightful analysis about the reaction mechanism. State-to-state DCS can describe a chemical reaction in detail.45 We select a set of representative state-to-state DCSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ = 0,2,4, 𝑗𝑗′) + Li

reaction at 𝐸𝐸𝑐𝑐 = 0.05, 0.3, and 0.6 eV, and show them in Figure 8. The angular distribution for

the H 2 (𝑣𝑣 ′ = 0) products at 𝐸𝐸𝑐𝑐 = 0.05 eV is almost isotropic (see Figure 7a). However, extra mechanism can be revealed if the product rotational state is distinguishable. In Figure 8a1, the H 2 products are roughly distributed in two regions. A part of the H 2 are in the interval of 0 ≤ 𝑗𝑗′ ≤ 10 and 0° < 𝜃𝜃 < 30°. The angular distribution of the rest of the H 2 clearly has a strong

correlation with 𝑗𝑗′: as 𝑗𝑗′ increases, the peak shifts from the backward direction (𝜃𝜃 ~ 180°) to the

forward direction (𝜃𝜃 ~ 45° in this case). Figure 8a2 shows that there are several peaks in the forward direction (𝜃𝜃 ~ 0°) in the interval of 0 ≤ 𝑗𝑗′ ≤ 8, and in the meantime there are several

smaller peaks distributed in other directions. In Figure 8a3, only the peaks in the forward direction are noticeable. At 𝐸𝐸𝑐𝑐 = 0.05 eV, the products are mainly forward scattered, and they are

mainly distributed at cold 𝑗𝑗′ states considering the available 𝑗𝑗′ range in each 𝑣𝑣 ′ state. Meanwhile, ACS Paragon Plus Environment

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the sideward and backward scatterings are small but evident. At a higher 𝐸𝐸𝑐𝑐 , there are much less

H 2 products scattered in the sideward and backward directions. The peaks in the forward direction tend to distribute at hot 𝑗𝑗′ states. In Figure 8b1, the angular distribution for the H 2

products peaks at 𝜃𝜃 = 0°, 𝑗𝑗 ′ = 15 and 𝜃𝜃 = 30°, 𝑗𝑗 ′ = 16. Also, the angular distribution of the

products in the directions 𝜃𝜃 > 45° varies with 𝑗𝑗′, which is similar with the distribution shown in Figure 8a1. In Figure 8b2, the peaks in the forward direction are also located at hot 𝑗𝑗 ′ states. In

Figure 8b3, a broad peak in the forward direction appears in the interval of 2 ≤ 𝑗𝑗′ ≤ 6. As shown

in Figures 8c1-8c3, at 𝐸𝐸𝑐𝑐 = 0.6 eV, the H 2 products are more focused in the forward direction,

and the products scattered in other directions are further declined. Overall, the H 2 products in

their ro-vibrational excited states prefer to distribute in the forward direction, and this preference is enhanced with increasing 𝐸𝐸𝑐𝑐 . The peaks in the forward direction in all cases are distributed in a narrow scattering angle range, i.e., 0° < 𝜃𝜃 < 30°. The secondary peaks appeared in the 𝑣𝑣 ′ -

resolved DCSs (see, Figures 7c and 7d) can be further understood in the state-to-state DCSs. The mechanism of the peaks in the forward direction is consistent with the accompanied secondary peaks. The total and product state-resolve DCSs for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗′) + Li

reaction are given in Figures S10, S11, and S12 in the supporting information. It is observed that the DCSs for the 𝑣𝑣 = 0 and 𝑣𝑣 = 1 reactions are quite similar to each other, further indicating that the mechanisms are consistent. 3.4 Reaction mechanism There are two possible mechanisms in the H + LiH reaction. One is a stripping mechanism corresponding to large 𝐽𝐽 values or large impact parameter collisions which lead to forward scattering. The other is a rebound mechanism. The H + LiH reaction is proposed to be dominated


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by the stripping mechanism in all cases.7 The stripping mechanism also tends to produce rotationally excited H 2 products, which obviously supports the preference of a 𝐽𝐽 → 𝑗𝑗′ angular momentum transfer. In this work, we make an attempt to elaborate the influence of the stripping mechanism to the reaction in detail. Figure 9 gathers the relevant data which will be discussed subsequently. The stripping mechanism in an exothermic reaction, A + BC → AB + C, described such a collision process: the atom A approaches to the BC molecule and takes B away from C, while C is recoiled in the opposite direction with little translational energy like a “spectator”.51,52 Such a description strongly implies that the energy release occurs before A encounters BC. Therefore, the stripping mechanism can be related to the “attractive” feature of the underlying PES.35,53,54 This description also reveals that the stripping mechanism is corresponding to high 𝐽𝐽 values or large impact parameter collisions, because the reaction for small impact parameter or small 𝐽𝐽

values mainly occurs in the repulsive regions of the PES where the rebound mechanism dominates the reaction.35,39,51,54 The PES employed in this work is highly attractive,6,11 suggesting that the stripping mechanism may play a decisive role in the reaction. To elaborate the features of the PES, we provide a plot of it in section IV in the supporting information. Figure 9a depicts the contributions of different part of the partial waves to the total ICSs for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 + Li reactions. We stipulate that 𝐽𝐽 ∈ [0, 13] are low 𝐽𝐽

values and 𝐽𝐽 ∈ [14, 60] are high 𝐽𝐽 values. Accordingly, ICS0 and ICS1 are divided into two parts.

It can be found that at 𝐸𝐸𝑐𝑐 greater than 0.065 eV the ICS is dominated by high 𝐽𝐽 values, and the trend is opposite at lower 𝐸𝐸𝑐𝑐 . This phenomenon is probably due to that the collisions for low 𝐽𝐽

values at higher and lower 𝐸𝐸𝑐𝑐 are of rebound and stripping types, respectively. In this circumstance, the rebound type collision would probably avoid the reaction by rebounding the


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reactants back to the reaction channel. One can also find that the vibrational excitation of the reactants has a remarkably negative effect on the reactivity. A closer observation reveals that ICS11 and ICS12 are smaller than ICS01 and ICS02, respectively. It indicates that at 𝑣𝑣 = 1 the reactivity of each 𝐽𝐽 partial wave is universally suppressed. Figure 9b gives the cumulative reactive probabilities for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) reactions at 𝐸𝐸𝑐𝑐 = 0.05, 0.3, and 0.6 eV.

The distributions show that on the side of high 𝐽𝐽 values the “slope” of the curve is more abrupt

than the other side. The peaks tend to be close to the side of high 𝐽𝐽 values, and this tendency is more obvious at high 𝐸𝐸𝑐𝑐 . These features explicitly show that in all cases the reaction is dominated by high 𝐽𝐽 values.

We also paid some attention to the DCS to understand the mechanism more deeply.34,46 The

contributions of different parts of the partial waves to the DCSs for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 =

0) → H 2 (𝑣𝑣 ′ = 2) + Li reactions are portrayed in Figure 9c. The H 2 products are mainly

scattered in the forward direction. This phenomenon is rather straightforward, since the reaction is governed by the stripping mechanism. Therefore, a small proportion of the reaction exothermicity is deposited into the translational energy of the H 2 product moving it along its

original direction of motion.52 In order to understand the forward scattering, the DCS is divided into two parts corresponding to low and high 𝐽𝐽 values, respectively. Since the interference

between the two sets of partial waves is very small, this separation55 is acceptable (see section V in the supporting information). It can be found that for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction the forward scattering mainly originates from the partial waves of large 𝐽𝐽 values (DCS02). The H 2

products for the partial waves of small 𝐽𝐽 values are mainly backward scattered, and the reactivity represented by DCS01 is small. The features of DCS01 reveal that the collisions at this

circumstance (Figure 9c) are of rebound type, and the rebound type collisions would probably


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avoid the reaction by rebounding the reactants to the reaction channel. The DCSs for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) reaction have similar trend of variation, except the reactivity is lower. Figure 9c

shows that the forward scattering could be an expression of the stripping mechanism in the H + LiH reaction. For a reaction on an “attractive” PES, a great proportion of the energy release would turn into the product vibration.53 To exhibit that, the proportions of the translational, vibrational, and rotational energies in the total available energy as functions of 𝐸𝐸𝑐𝑐 for the H + LiH (𝑣𝑣 = 0 −

1, 𝑗𝑗 = 0) reactions are calculated and shown in Figure 9d. It can be seen that the proportion of

the vibrational energy is the largest one, ranging from ~ 48% (at 𝐸𝐸𝑐𝑐 = 0.05 eV) to ~ 45% (at

𝐸𝐸𝑐𝑐 = 0.6 eV). Obviously, the “attractive” feature dominates the reaction in the whole energy scope.53 As 𝐸𝐸𝑐𝑐 increases, the proportion of rotational energy increases. This change may be due

to that more 𝐽𝐽 partial waves should be included at higher 𝐸𝐸𝑐𝑐 , and 𝐽𝐽 tends to turn to 𝑗𝑗′. The energy distributions for the 𝑣𝑣 = 0 and 𝑣𝑣 = 1 reactions are almost the same, which further implies that the mechanisms are consistent.

Elementary chemical reaction processes are normally idealized by various reaction mechanisms in the theoretical research. These mechanisms can be attributed to specific features of the corresponding PES, such as potential energy barrier or well.56-61 Generally, barrier or well is considered to be responsible for the direct or indirect mechanism, respectively. As one of the direct

mechanisms,

the

stripping

mechanism

has

been

concerned

in

different

literatures.35,39,51,52,54,60 Conventionally, the stripping mechanism is regarded to be more common in ion-molecule reactions, or some bimolecular reactions at relatively high 𝐸𝐸𝑐𝑐 .35,51,52,54,60

Nevertheless, to our knowledge, the previous literatures did not provide a distinct description of the relation between the stripping mechanism and the feature of the underlying PES. Under the


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conditions of high 𝐸𝐸𝑐𝑐 or ion-molecule reactants, the reaction may proceed on multiple PESs.

Therefore, it is unlikely to solely relate the stripping mechanism to specific features of one PES. The H + LiH reaction has no barriers or wells along its reaction path, therefore the stripping mechanism can be solely related to the “attractive” feature of the underlying PES. The increasing of the 𝐸𝐸𝑐𝑐 and 𝑣𝑣 level have negative effects on the reactivity, and forward scattering is

predominant in all cases. In a word, the dynamics character of the stripping mechanism is fairly explicit. The present system could be a prototype to understand the stripping mechanism and provide useful information for the study of other relevant reactions, since the “attractive” feature is quite ubiquitous in many reaction systems.

4. Conclusions In the present study, a series of accurate quantum scattering dynamics calculations have been performed for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 + Li reactions at the collision energies

ranging from 0.05 to 0.6 eV on the WCBG PES.11 In these calculations, we applied a recently developed graphic processing units accelerated time dependent wave packet program,34 which has been proved to be efficient and accurate.34,35 Total and state-to-state integral cross sections, rate constants and differential cross sections are presented. The total integral cross section and rate constant for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction agree well with the recent work, in particular reference 7.

The total integral cross section for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) reaction is smaller than that for

the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction. It indicates that the vibrational excitation of the reactant can

decrease the reactivity of the H + LiH reaction. Product vibrational state-resolved and state-tostate integral cross sections for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reactions reveal that the reaction tends to produce H 2 molecule in its ro-vibrational excited states, and this tendency becomes


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more prominent at high collision energies. The results for the 𝑣𝑣 = 1 reaction have similar trend of variation, but the reactivity is slightly lower.

We also calculated the product vibrational state-resolved and state-to-state rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ ) + Li reaction. Among the vibrational state-resolved rate

constants, the ones of the H 2 (𝑣𝑣 ′ = 1,2) products are largest. The state-to-state rate constants

reveal that the H 2 products in (𝑣𝑣 ′ = 2, 𝑗𝑗 ′ = 8 − 12) states are the most probable products of the

reaction. The results also confirm that the H 2 products are preferred to be formed in their ro-

vibrational excited states. It is different from the result of Bovino et al.8 in which the H 2 products are preferentially formed in their ground ro-vibrational state. The preferred state of the H 2 products varies with temperature. At temperatures less than 1500 K, the H 2 products in 𝑗𝑗′ around

8 are prevailing, while at temperatures greater than 1500 K, the H 2 products in 𝑗𝑗′ around 12 are predominant. For the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) reaction, the rate constant is lower than that for the 𝑣𝑣 = 0 reaction, and the preferred final states are slightly different.

Moreover, the present investigation gives the total and state-to-state differential cross sections

for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) reaction. The results indicate that the H 2 products are mainly

scattered in the forward direction. The intensity of forward scattering for the H 2 products in their vibrational excited states (𝑣𝑣 ′ = 2 − 4) is stronger than other states. Abundant fluctuations appear

in the angular distributions for those products, especially in the forward directions. The state-tostate differential cross sections show that the H 2 products in their ro-vibrational excited states tend to be scattered in the forward direction. The angular distributions for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) reaction are found to be similar with that for the 𝑣𝑣 = 0 reaction.

The influence of the stripping mechanism on the H + LiH reaction is studied and elaborated in

detail. The stripping mechanism is considered to be responsible to the decrease of the integral


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cross sections with increasing collision energy or initial vibrational level. Moreover, it could also be attributed to the stripping mechanism that most of the H 2 products are formed in their rovibrational excited states and scattered in the forward direction. The product energy distribution in different freedom of motion (translation, vibration, and rotation) reveals that the stripping mechanism can be related to the “attractive” feature of the underlying PES. It seems that the present reaction system can be a prototype to study the stripping mechanism and provide useful information for the study of other relevant reactions, since the “attractive” feature is quite ubiquitous in many reaction systems. The present results should be examined by an accurate experimental study, especially an experiment which can designate initial and final quantum states. We anticipate that the present study could stimulate future accurate experiments and quantum dynamics work for this reaction.


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ASSOCIATED CONTENT Supporting Information A part of the quantum calculation details, comparison results on the PMM and WCBG PESs, a set of dynamics results for the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 + Li reaction on the WCBG PES

(including integral and differential cross sections and rate constants), and a plot of the potential energy surface. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (Y.Z.) Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This research was supported by the National Natural Science Foundation of China No.21103167.


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References (1) Bililign, S.; Hattaway, B. C.; Robinson, T. L.; Jeung, G. H. Far-Wing Scattering Studies on the Reaction Li∗(2p, 3p) + H 2 → LiH(vʺ=1, 2, Jʺ) + H. J. Chem. Phys. 2001, 114, 7052-7058. (2) Chen, J. J.; Hung, Y. M.; Liu, D. K.; Fung, H. S.; Lin, K. C. Reaction Pathway, Energy Barrier, and Rotational State Distribution for Li(22P J ) + H 2 → LiH(X1S+) + H. J. Chem. Phys. 2001, 114, 9395-9401. (3) Lepp, S.; Stancil, P. C.; Dalgarno, A. Atomic and Molecular Processes in the Early Universe. J. Phys. B-At. Mol. Opt. Phys. 2002, 35, R57-R80. (4) Bodo, E.; Gianturco, F. A.; Martinazzo, R. The Gas-Phase Lithium Chemistry in the Early Universe: Elementary Processes, Interaction Forces and Quantum Dynamics. Phys. Rep. 2003, 384, 85-119. (5) Chen, J. J.; Lin, K. C. Influence of Vibrational Excitation on the Reaction Li(22P J ) + H 2 (v=1) → LiH(X1S+) + H. J. Chem. Phys. 2003, 119, 8785-8789. (6) Roy, T.; Mahapatra, S. Quantum Dynamics of H + LiH Reaction and Its Isotopic Variants. J Chem. Phys. 2012, 136, 174313. (7) Gómez-Carrasco, S.; González-Sánchez, L.; Bulut, N.; Roncero, O.; Bañares, L.; Castillo, J. F. State-to-State Quantum Wave Packet Dynamics of the LiH + H Reaction on two Ab Initio Ptential Energy Surfaces. Astrophys. J. 2014, 784, 55. (8) Bovino, S.; Wernli, M.; Gianturco, F. A. Fast LiH Destruction in Reaction with H: Quantum Calculations and Astrophysical Consequences. Astrophys. J. 2009, 699, 383-387. (9) Bovino, S.; Tacconi, M.; Gianturco, F. A.; Galli, D.; Palla, F. On the Relative Abundanceof LiH and LiH+ Molecules in the Early Universe: New Results from Quantum Reactions. Astrophys. J. 2011, 731, 107.


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(10) Stancil, P. C.; Lepp, S.; Dalgarno, A. The Lithium Chemistry of the Early Universe. Astrophys. J. 1996, 458, 401-406. (11) Wernli, M.; Caruso, D.; Bodo, E.; Gianturco, F. A. Computing a Three-Dimensional Electronic Energy Manifold for the LiH + H Φ Li + H 2 Chemical Reaction. J. Phys. Chem. A 2009, 113, 1121-1128. (12) Liu, Y. F.; He, X. H.; Shi, D. H.; Sun, J. F. Theoretical Study of the Dynamics for the H + LiH (v=0, j=0) → H 2 + Li Reaction and Its Isotopic Variants. Eur. Phys. J. D 2011, 61, 349-353. (13) Liu, Y. F.; He, X. H.; Shi, D. H.; Sun, J. F. Stereodynamics of the Reaction H + LiH (v=0, j=0) → H 2 + Li and Its Isotopic Variants. Comput. Theor. Chem. 2011, 965, 107-113. (14) Clarke, N. J.; Sironi, M.; Raimondi, M.; Kumar, S.; Gianturco, F. A.; Buonomo, E.; Cooper, D. L. Classical and Quantum Dynamics on the Collinear Potential Energy Surface for the Reaction of Li with H 2 . Chem. Phys. 1998, 233, 9-27. (15) Bodo, E.; Gianturco, F. A.; Martinazzo, R.; Raimondi, M. Computed Orientational Anisotropy and Vibrational Couplings for the LiH + H Interaction Potential. Eur. Phys. J. D 2001, 15, 321-329. (16) Dunne, L. J.; Murrell, J. N.; Jemmer, P. Analytical Potential Energy Surface and Quasiclassical Dynamics for the Reaction LiH(X,1Σ+) + H(2S) → Li(2S) + H 2 (X,1Σ+ g ). Chem. Phys. Lett. 2001, 336, 1-6. (17) Prudente, F. V.; Marques, J. M. C.; Maniero, A. M. Time-Dependent Wave Packet Calculation of the LiH + H Reactive Scattering on a New Potential Energy Surface. Chem. Phys. Lett. 2009, 474, 18-22. (18) Sha, G. Y.; Yuan, J. C.; Meng, C. G.; Chen, M. D. Influence of Early-Staged Energy Barrier on Stereodynamics of Reaction of LiH(v=0, j=0) + H → Li + H 2 . Chem. Res. Chin. Univ.


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Chem. 2006, 5, 871-885.

(28) Jiang, Z. J.; Wang, M. S.; Yang, C. L.; He, D. Influence of Collision Energy and Reagent


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Vibrational Excitation on the Stereodynamics of the Reaction H + LiH → H 2 + Li. Chem. Phys. 2013, 415, 8-13. (29) Jiang, Z. J.; Wang, M. S.; Yang, C. L.; He, D. The Effects of Collision Energy and Reagent Vibrational Excitation on the Reactivity of the Reaction H + LiH: A Quasiclassical Trajectory Study. Comput. Theor. Chem. 2013, 1006, 31-36. (30) Li, D.; Wang, Y. L.; Wang, J.; Zhao, Y. T. Influence of Collision Energy and Reagent Vibrational Excitation on the Dynamics of the Reaction H + LiH. Int. J. Quantum Chem. 2013, 113, 2379-2384. (31) Wang, Y. L.; Zhang, J. C.; Jiang, Y. L.; Wang, K.; Zhou, M. Y.; Liang, X. R. Investigation of Stereo-dynamic Properties for the Reaction H + HLi by Quasi-classical Trajectory Approach. Bull. Korean Chem. Soc. 2012, 33, 2873-2877. (32) Wang, Y. L.; Zhang, J. C.; Tian, B. G.; Wang, K.; Liang, X. R.; Zhou, M. Y. QuasiClassical Trajectory Study of the Reaction Probability and Cross Section of the Reaction LiH + H. J. Theor. Comput. Chem. 2013, 12, 1250093. (33) Zhai, H. S.; Li, W. L.; Liu, Y. F. Coriolis Coupling Influence on the H + LiH Reaction. Bull. Korean Chem. Soc. 2014, 35, 151-157. (34) Zhang, P. Y.; Han, K. L. Adiabatic/Nonadiabatic State-to-State Reactive Scattering Dynamics Implemented on Graphics Processing Units. J. Phys. Chem. A 2013, 117, 8512-8518. (35) Yao, C. X.; Zhang, P. Y.; Duan, Z. X.; Zhao, G. J. Influence of Collision Energy on the Dynamics of the Reaction H (2S) + NH (X3Σ−) → N (4S) + H 2 (X1Σ g +) by the State-to-State Quantum Mechanical Study. Theor. Chem. Acc. 2014, 133, 1489. (36) Gómez-Carrasco, S.; Roncero, O. Coordinate Transformation Methods to Calculate Stateto-State Reaction Probabilities With Wave Packet Treatments. J. Chem. Phys. 2006, 125, 054102.


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(37) Chao, S. D.; Harich, S. A.; Dai, D. X.; Wang, C. C.; Yang, X.; Skodje. R. T. A Fully State- and Angle-Resolved Study of the H + HD → D + H 2 Reaction: Comparison of a Molecular Beam Experiment to ab initio Quantum Reaction Dynamics. J. Chem. Phys. 2002, 117, 8341-8361. (38) De Fazio. D. The H + HeH+ → He + H 2 + Reaction From the Ultra-Cold Regime to the Three-Body Breakup: Exact Quantum Mechanical Integral Cross Sections and Rate Constants. Phys. Chem. Chem. Phys. 2014, 16, 11662-11672. (39) Duan, Z. X.; Li, W. L.; Xu, W. W.; Lv, S. J. Quasiclassical Dynamics for the H + HS Abstraction and Exchange Reactions on the 3A" and the 3A' States. J. Chem. Phys. 2013, 139, 094307. (40) Kornweitz, H.; Persky. A. Quasiclassical Trajectory Calculations for the Reactions F + HCl, F + HBr, and F + HI. J. Phys. Chem. A 2004, 108, 140-145. (41) Quan, W. l.; Tang, P. Y.; Tang, B. Y.; Han. K. L. Quantum Wave Packet Studies on F + HBr Reaction. Chem. Res. Chin. Univ. 2007, 23, 96-100. (42) Pradhan, G. B.; Balakrishnan, N.; Kendrick. B. K. Ultracold Collisions of O(1D) and H 2 : the Effects of H 2 Vibrational Excitation on the Production of Vibrationally and Rotationally Excited OH. J. Chem. Phys. 2013, 138, 164310. (43) Jambrina, P. G.; Lara, M.; Menendez, M.; Launay, J. M.; Aoiz. F. J. Rate Coefficients From Quantum and Quasi-classical Cumulative Reaction Probabilities for the S(1D) + H 2 Reaction. J. Chem. Phys. 2012, 137, 164314. (44) Zhang, D. H.; Zhang, J. Z. H. Uniform J-shifting Approach for Calculating Reaction Rate Constant. J. Chem. Phys. 1999, 110, 7622-7626. (45) Aoiz, F. J.; Verdasco, E.; Sáez Rábanos, V.; Loesch, H. J.; Menéndez, M.; Stienkemeier, F.


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Experimental and Theoretical Study of the Li + HF (v = 1) → LiF + H Reaction. Phys. Chem. Chem. Phys. 2000, 2, 541-548. (46) Zhang, J. Z. H.; Miller, W. H. Quantum Reactive Scattering via the S-matrix Version of the Kohn Variational Principle: Differential and Integral Cross Sections for D + H 2 → HD + H. J.Chem. Phys. 1989, 91, 1528-1547. (47) Budenholzer, F. E.; Hu, S. C.; Jeng, D. C.; Gislason, E. A. The Expansion of Product Probability Distributions from Trajectory Calculations in Two-Dimensional Fourier Series. J. Chem. Phys. 1988, 89, 1958-1965. (48) Aoiz, F. J.; Herrero, V. J.; Sáez Rábanos, V. Quasi-Classical State to State Reaction Cross Sections for D + H 2 (v = 0, j = 0) → HD (v', j') + H. Formation and Characteristics of ShortLived Collision Complexes. J. Chem. Phys. 1992, 97, 7423-7436. (49) Sokolovski, D.; De Fazio, D.; Cavalli, S.; Aquilanti. V. On the Origin of the Forward Peak and Backward Oscillations in the F + H 2 (v = 0) → HF (v' = 2) + H Reaction. Phys. Chem. Chem. Phys. 2007, 9, 5664-5671. (50) Connor. J. N. L. Theory of Forward Glory Scattering for Chemical Reactions. Phys. Chem. Chem. Phys. 2004, 6, 377-390. (51) Levine, R. D. Molecular Reaction Dynamics; Oxford University Press, New York., 2005. (52) Smith, G. P. K.; Saunders, M.; Cross Jr., R. J. Crossed Beam Studies of Ion-Molecule Reactions in Methane and Ammonia. J. Am. Chem. Soc. 1976, 98, 1324-1330. (53) Kuntz, P. J.; Nemeth, E. M.; Polanyi, J. C.; Rosner, S. D.; Young, C. E. Energy Distribution Among Products of Exothermic Reactions. II. Repulsive, Mixed, and Attractive Energy Release. J. Chem. Phys. 1966, 44, 1168-1184. (54) Song, H.; Lee, S. Y.; Sun, Z.; Lu, Y. Time-Dependent Wave Packet State-to-State


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Dynamics of H/D + HCl/DCl Reactions. J. Chem. Phys. 2013, 138, 054305. (55) Panda, A. N.; Herráez-Aguilar, D.; Jambrina, P. G.; Aldegunde, J.; Althorpe, S. C.; Aoiz, F. J. A State-to-State Dynamical Study of the Br + H 2 Reaction: Comparison of Quantum and Classical Trajectory Results. Phys. Chem. Chem. Phys. 2012, 14, 13067-13075. (56) He, X.; Chao, V. W. K.; Han, K.; Hao, C.; Zhang, Y. Mechanism of the Collision Energy and Reagent Vibration’s Effects on the Collision Time for the Reaction Ca + HCl. Comput. Theor. Chem. 2015, 1056, 1-10. (57) Martı́nez, T.; Hernández, M. L.; Alvariño, J. M.; Aoiz, F. J.; Sáez Rábanos, V. A Detailed Study of the Dynamics of the O(1D) + HCl → OH + Cl, ClO + H Reactions. J. Chem. Phys. 2003, 119, 7871-7886. (58) Wang, X.; Dong, W.; Qiu, M.; Ren, Z.; Che, L.; Dai, D.; Wang, X.; Yang, X.; Sun, Z.; Fu, B.; et al. HF(v' = 3) Forward Scattering in the F + H 2 Reaction: Shape Resonance and SlowDown Mechanism. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 6227-6231. (59) Yang, T.; Chen, J.; Huang, L.; Wang, T.; Xiao, C.; Sun, Z.; Dai, D.; Yang, X.; Zhang, D. H. Extremely Short-Lived Reaction Resonances in Cl + HD (v = 1) → DCl + H due to Chemical Bond Softening. Science 2015, 347, 60-63. (60) Polanyi, J. C. Some Concepts in Reaction Dynamics. Acc. Chem. Res. 1972, 5, 161-168. (61) Proctor, D. L.; Davis, H. F. Vibrational vs. Translational Energy in Promoting a Prototype Metal-Hydrocarbon Insertion Reaction. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12673.


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Table 1. Numerical grid/basis parameters for the H + LiH (𝑣𝑣 = 0 − 1) → H 2 + Li reactions. Atomic units are used unless otherwise specified.

Coordinate range/number of grid points

𝑅𝑅 ∈ [0.002,18.0], 𝑁𝑁𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 144, 𝑁𝑁𝑅𝑅𝐼𝐼𝐼𝐼𝐼𝐼 = 104 𝑟𝑟 ∈ [0.5,21.0], 𝑁𝑁𝑟𝑟𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 = 112, 𝑁𝑁𝑟𝑟𝐼𝐼𝐼𝐼𝐼𝐼 = 12

Initial wave-packet

𝑗𝑗𝑚𝑚𝑚𝑚𝑚𝑚 = 80(86)a

Analysis line

13.5

Number of angular basis functions

𝑅𝑅0 = 14.0, 𝐸𝐸0 = 0.31 (eV), 𝛿𝛿 = 0.41

Absorption location in 𝑅𝑅/𝑟𝑟

14.0/17.0b

Propagation time/time step size

50 000/5

Absorption strength in 𝑅𝑅/𝑟𝑟

0.12/0.12b

86 is used to the calculation of the H + LiH (𝑣𝑣 = 1, 𝑗𝑗 = 0) → H 2 + Li reaction. The absorption function takes the form exp(−𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 ∆𝑡𝑡((𝑅𝑅 − 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 )⁄(𝑅𝑅𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 ))2 ) , 𝑅𝑅 ≥ 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 𝑓𝑓(𝑅𝑅) = � , 1 , 𝑅𝑅 < 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 where 𝐶𝐶𝑎𝑎𝑎𝑎𝑎𝑎 is the absorption strength, and 𝑅𝑅𝑎𝑎𝑎𝑎𝑎𝑎 is the absorption location. a b


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Page 30 of 41

Figure Captions Figure 1. Total integral cross sections (ICSs) for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 + Li

reactions. ICS0 and ICS1 are from the present work. The results of Gómez-Carrasco et al. and Roy and Mahapatra are from references 7 and 6, respectively. The three sets of results are all based on the WCBG PES. Figure 2. Product vibrational state-resolved ICSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣′) + Li reaction.

Figure 3. State-to-state ICSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗′) + Li reaction at 𝐸𝐸𝑐𝑐 =

0.05 (a), 0.1 (b), 0.3 (c), and 0.6 (d) eV. In panel (d) the open squares denote the ICS with FermiDirac statistics for the H 2 (𝑣𝑣′ = 0) products.

Figure 4. (a) Total reaction rate constant for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 + Li reaction. The result of this work is shown by a solid line. The result of Gómez-Carrasco et al.7 is shown by a

dashed line. The result of Bovino et al.8 is shown by a dotted line. The result of Roy et al.6 is shown by a dashed-dotted line. The estimated result of Stancil et al.10 is shown by a dasheddotted-dotted line. (b) Product vibrational state-resolved reaction rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ ) + Li reaction.

Figure 5. Several representative state-to-state reaction rate constants for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ , 𝑗𝑗′) + Li reaction.

Figure 6. Total differential cross sections (DCSs) for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 + Li reaction at 𝐸𝐸𝑐𝑐 = 0.05, 0.1, 0.3, and 0.6 eV.

Figure 7. Product vibrational state-resolved DCSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣′) + Li reaction at 𝐸𝐸𝑐𝑐 = 0.05 (a), 0.1 (b), 0.3 (c), and 0.6 eV (d).

Figure 8. State-to-state DCSs for the H + LiH (𝑣𝑣 = 0, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ = 0,2,4, 𝑗𝑗′) + Li ACS Paragon Plus Environment

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


reaction. The collision energies are 0.05 (a1-a3), 0.3 (b1-b3), and 0.6 (c1-c3) eV. Panels in one row share the scale bar on the right side. The DCSs are represented by logarithmic coordinate. Figure 9. (a) Total ICSs for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 + Li reactions. The 𝐽𝐽 partial

waves are divided into two sets, 𝐽𝐽 ∈ [0, 13] and 𝐽𝐽 ∈ [14, 60]. (b) Cumulative reaction probability for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) reactions at 𝐸𝐸𝑐𝑐 = 0.05, 0.3, and 0.6 eV. (c) DCSs for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) → H 2 (𝑣𝑣 ′ = 2) + Li reactions at 𝐸𝐸𝑐𝑐 = 0.3 eV. (d) Percentages of the

translational, vibrational, and rotational energies of the product molecules in the total available energy for the H + LiH (𝑣𝑣 = 0 − 1, 𝑗𝑗 = 0) reactions.


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50

Integral cross section (Å2)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 41

40 30

H + LiH (v, j = 0) ® H2 + Li v = 0, ICS0 v = 1, ICS1 v = 0, Gómez-Carrasco et al. v = 0, Roy and Mahapatra v = 1, Roy and Mahapatra

20 10 0 0.1

0.2

0.3 Ec (eV)

0.4

Figure 1.


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0.5

0.6

Page 33 of 41

20 15

(a)

H + LiH (v = 0, j = 0) ® H2 (v') + Li

v' = 0, Gómez-Carrasco et al. v' = 1, Gómez-Carrasco et al. v' = 0, this work v' = 1, this work

10 5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0 0.1

0.2

0.3

0.4

0.5

0.6

20 15

(b)

v' = 2, Gómez-Carrasco et al. v' = 3, Gómez-Carrasco et al. v' = 2, this work v' = 3, this work

10 5 0 0.1

0.2

0.3

0.4

0.5

0.6

10 8

(c)

v' = 4, Gómez-Carrasco et al. v' = 4, this work v' = 5, this work

6 4 2 0 0.1

0.2

0.3

0.4

0.5

Ec (eV)

Figure 2.


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0.6



2.0

2.0 H + LiH (v = 0, j = 0) ® H2 (v', j') + Li

1.5

(a) Ec = 0.05 eV

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4

1.0 0.5

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4

(b) Ec = 0.1 eV

1.5 1.0 0.5

0.0

0.0 0

1.0


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 41

5 v' = 0 v' = 1 v' = 2 v' = 3 v' = 4 v' = 5

0.8 0.6 0.4

10

15

20

0

5

10

15

20

1.0 (c) Ec = 0.3 eV

v' = 0 (FD) v' = 0 v' = 1 v' = 2 v' = 3 v' = 4 v' = 5

0.8 0.6 0.4

0.2

(d) Ec = 0.6 eV

0.2

0.0

0.0 0

5

10

15

20

0

j'

5

10 j'

Figure 3.


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15

20

Page 35 of 41

Rate coefficient (cm3/s)

1E-8 H + LiH (v = 0, j = 0) ® H2 + Li

(a) 1E-9

This work Gómez-Carrasco et al. Bovino et al. Roy and Mahapatra Stancil et al.

1E-10

1E-11 500

1000

1500

2000

2500

3000

1E-9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1E-10 H + LiH (v = 0, j = 0) ® H2 (v') + Li v' = 0 v' = 1 (b) v' = 2 v' = 3 v' = 4 v' = 5

1E-11

1E-12 500

1000

1500

2000

2500

Temperature (K)

Figure 4.


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3000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



1E-10

Page 36 of 41

H + LiH (v = 0, j = 0) ® H2 (v', j') + Li v' = 0, j' = 13 v' = 1, j' = 11 v' = 2, j' = 8 v' = 2, j' = 12 v' = 3, j' = 7 v' = 4, j' = 4

1E-11 500

1000

1500

2000

2500

Temperature (K)

Figure 5.


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3000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Differential cross section (Å 2/sr)

Page 37 of 41

20

H + LiH (v = 0, j = 0) ® H2 + Li Ec = 0.05 eV

15

Ec = 0.1 eV Ec = 0.3 eV

10

Ec = 0.6 eV 5

0 0

30

60

90

120

150

θ (deg) Figure 6.


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180


10

10 H + LiH (v = 0, j = 0) ® H2 (v') + Li

8


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(a) Ec = 0.05 eV

6 4 2 0

0

30

60

90

8

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4

(b) Ec = 0.1 eV

6 4 2

120 150 180

5

0

0

30

60

90

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4 120 150 180

5

4

(c) Ec = 0.3 eV

3 2 1 0

Page 38 of 41

0

30

60

90

4

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4

(d) Ec = 0.6 eV

3 2 1

120 150 180

0

0

30

60

90

θ (deg)

θ (deg)

Figure 7.


38 / 41

v' = 0 v' = 1 v' = 2 v' = 3 v' = 4 v' = 5 120 150 180

Page 39 of 41

j'

(a1) Ec = 0.05 eV, v' = 0

(b1) Ec = 0.3 eV, v' = 0

(c1) Ec = 0.6 eV, v' = 0

20

20

20

15

15

15

10

10

10

5

5

5 0

0

0 0

60

120

0

180

60

120

0

180

(b2) Ec = 0.3 eV, v' = 2

(a2) Ec = 0.05 eV, v' = 2

60

120

180

(c2) Ec = 0.6 eV, v' = 2

15

15

10

10

10

5

5

5

j'

15

0

0

0 0

60

120

0

180

60

120

0

180

(b3) Ec = 0.1 eV, v' = 4

(a3) Ec = 0.05 eV, v' = 4

60

120

180

(c3) Ec = 0.6 eV, v' = 4

12

12

12

8

8

8

4

4

4

j'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0

0

0 0

60

θ (deg)

120

180

0

60

120

180

0

60

θ (deg)

Figure 8.


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θ (deg)

120

180

1.0E-05 2.8E-05 8.0E-05 2.2E-04 6.3E-04 0.0018 0.0050 0.014 0.040 0.11 0.32 1.0E-04 2.7E-04 7.2E-04 0.0020 0.0053 0.014 0.038 0.10 0.28 0.74 2.0 1.0E-04 2.6E-04 6.8E-04 0.0018 0.0047 0.012 0.032 0.084 0.22 0.57 1.5


50 H + LiH (v, j = 0) ® H2 + Li

(a)

40

v = 0, Total ICS0 v = 0, ICS01 (J Î [0, 13]) v = 0, ICS02 (J Î [14, 60]) v = 1, Total ICS1 v = 1, ICS11 (J Î [0, 13]) v = 1, ICS12 (J Î [14, 60])

30 20 10 0 0.1

0.2

0.3

0.4

0.5

0.6

30

H + LiH (v, j = 0) ® H2 + Li

v = 0, Ec = 0.05 eV

(b)

v = 0, Ec = 0.3 eV v = 0, Ec = 0.6 eV v = 1, Ec = 0.6 eV

20

10

0 0

10

20

30

H + LiH (v, j = 0) ® H2 + Li

80

H + LiH (v, j = 0) ® H2 (v' = 2) + Li v = 0, Total DCS0 v = 0, DCS01 (J∈[0, 13]) v = 0, DCS02 (J∈[14, 60]) v = 1, Total DCS1 v = 1, DCS11 (J∈[0, 13]) v = 1, DCS12 (J∈[14, 60])

0.1

40

50

60

J

100 Ec = 0.3 eV

v = 1, Ec = 0.05 eV v = 1, Ec = 0.3 eV

(c)

1

Page 40 of 41

40

Ec (eV)

Percentage


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Cumulative reaction probability


(d)

60

v = 0, translational energy v = 0, vibrational energy v = 0, rotational energy v = 1, translational energy v = 1, vibrational energy v = 1, rotational energy

40 20

0.01

0 1

10

100

0.1

θ (deg)

0.2

0.3

Ec (eV)

Figure 9.


40 / 41

0.4

0.5

0.6

Page 41 of 41

Table of contents (TOC) image

Stripping Mechanism

0 Energy

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


+

Forward Scattering

Reaction Coordinate


41 / 41

Quantum State-to-State Dynamics of the H + LiH â H2 + Li Reaction

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Quantum State-to-State Dynamics of the H + LiH â H2 + Li Reaction