SCIENCE CHINA Chemistry

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*Corresponding author (email: qtmeng@sdnu.edu.cn)

• ARTICLES • April 2010 Vol.53 No.4: 927–932

doi: 10.1007/s11426-010-0043-x

Quasi-classical trajectory approach to the stereo-dynamics of the reaction F + HO→HF + O

ZHAO Juan1, XU Yan1, ZHAO Xian2 & MENG QingTian1*

1 College of Physics and Electronics, Shandong Normal University, Jinan 250014, China; 2 State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, China

Received June 20, 2009; accepted September 16, 2009

Quasi-classical trajectory (QCT) calculations are employed for the reaction F + HO(0,0)→HF + O based on the adiabatic po-tential energy surface (PES) of the ground 3A″triplet state. The average rotational alignment factor P2(j′·k) as a function of collision energy and the four polarization dependent generalized differential cross sections have been calculated in the cen-ter-of-mass (CM) frame, separately. The distribution P(r) of the angle between k and j′, the distribution P(r) of dihedral an-gle denoting k k′ j′ correlation, and the angular distribution P(r, r) of product rotational vectors in the form of polar plots are calculated as well. The effect of Heavy-Light-Heavy (HLH) mass combination and atom F’s relatively strong absorbability to charges on the alignment and the orientation of product molecule HF rotational angular momentum vectors j′ is revealed.

product polarization, F + HO reaction, quasi-classical trajectory, vector correlations

1 Introduction

In recent years, the reactions of hydrogen halides with oxy-gen atoms have attracted more attention due to their impor-tance in catalytic destruction cycle, and the halogenated compounds, which have large abundance in nature, are most widely studied [1–8]. As one of the model systems for open shell reactions on account of the relatively simple electronic structure, HOF system is often chosen as the objective of the investigation. Moreover, the HOF reactive system has accurate potential energy surfaces (PESs), which are given by Gómez-Carrasco et al. [1–4, 6, 7]. Based on these PESs, many dynamic studies have been carried out. Furthermore, Gómez-Carrasco et al. have simulated the OHF photode-tachment in 3A″ PES [1] and studied the reaction F(2P) +

OH(2) O(3P) + HF(1+) on the global three- dimensional adiabatic PESs for the excited 23A″ and 13A′ triplet states of OHF system [2]. Later, they calculated the cross sections of

F(2P) + OH(2) reaction for the adiabatic singlet states [3], and the reaction O(1D) + HF OH + F based on one ground 1A′ state has also been studied [4]. What they have used so far in the calculations for F(2P) + OH(2) O(3P) + HF(1+) reactive collision on the 3A″ground electronic state are the wave packet method and the quasi-classical trajectory (QCT) theory [6, 7]. The comparison of these two calculations showed that the corresponding results had a good agreement with each other [6, 7].

The previous work for F(2P) + OH(2) O(3P) + HF(1+) reaction on the ground 3A″ PES has dealt with the scalar properties such as reaction probability, reactive cross sec-tions, thermal rate coefficient and rovibrational energy dis-tribution of the HF molecule [6, 7]. In order to understand the dynamics of the F + HO reaction completely, it is nec-essary to study its vector properties, which can provide more information about chemical reaction stereo-dynamics [9–19]. By comprehending the scalar and vector properties together, the full picture of the scattering dynamics can be presented [14, 15]. For this reason, we studied the influ-ences of collision energy and rotational excitation of re-

928 ZHAO Juan, et al. Sci China Chem April (2010) Vol.53 No.4

agents on product polarization for the reaction H + FO

OH + F, and the results indicate that both the orientation and the alignment of the rotational angular moment were im-pacted by collision energies [20, 21]. In addition, we have studied the isotope effect of the stereo-dynamics for the reactions F + H(D)O H(D)F + O, and the evident influ-ence of isotope substitution on the product polarization was revealed [22]. Recently, we have also investigated the axial polarization of product molecules for reaction H + FO HF

+ O [23] and the effect of the reagent vibration on stereo- dynamics of the reaction O(1D)+HF

O(1D) + HF F + OH [24]. In the present paper, in order to understand the stereo-dynamics of the reaction better, we carry out the QCT calculations for F(2P) + OH(2) O(3P)

+ HF(1+) reaction on a global PES of the ground 3A″ adia-batic electronic state.

2 Theory

In the calculations, the used adiabatic ground 3A″ PES was provided by Gómez-Carrasco et al. [6, 7], who obtained it by fitting 8069 ab initio points to two- and three-body polynomial expansion in modified Rydberg coordinates [25]. The detailed function form and deduction process of the PES can be referred to in ref. [7].

The calculation method of QCT is the same as the one used in refs. [14, 16–24, 26–30]. The classical Hamilton’s equations are numerically integrated in three dimensions. In the present work, we have carried out calculations of the product rotational polarization with initial vibrational quan-tum number v = 0 and initial rotational number j = 0. A batch of 10000 trajectories is run for the energy of each title reac-tion and these trajectories were initiated with an F-HO in-ter-nuclear separation of 1 nm. The integration step size in the trajectories is chosen to be 0.1 fs, which guarantees the conservation of the total energy and total angular momen-tum. The maximum value of the impact parameter, bmax, was computed by calculating 10000 trajectories at fixed values of the impact parameter, b, and systematically in-creasing the value of b until no reactive trajectories were obtained, and the calculated range of impact parameters was 0.048–0.310 nm. The reaction cross section is defined as r

= b2max(Nr/N), where Nr/N is the ratio of the number of reac-

tive trajectories to the total number of trajectories. The

sampling error is defined as r r( ) / 100%,N N NN

and the reaction cross section error in our calculation is de-fined as r= r.

The general theory of the product rotational polarization is standard [16–24, 26–39], and here we only summarize the details relevant to the present work. In the center-of-mass (CM) frame shown in Figure 1, the reagent relative velocity vector k is parallel to the z axis and the xz plane is the scattering plane containing the initial and final relative ve-

Figure 1 The center-of-mass coordinate system used to describe the k, k′ and j′ distribution.

locity vectors, k and k′. The angle t is the so-called scat-tering angle between the reagent relative velocity and the product relative velocity. r and r are the polar and azi-muthal angles of the final rotational angular momentum j′.

The most common vector correlation is that of k j′ and the polar angle distribution function P( r) can be expanded in a series of Legendre polynomials, and the expanding co-efficients are called orientation ( k is odd) and alignment ( k is even) parameter. Because the rotational alignment of the product has been measured in most experiments [14], we calculated the average rotational alignment factor P2(j′·k) in this work.

The dihedral angle distribution function P( r) describing k k′ j′ correlation can be expanded in Fourier series. Us-ing angles r and r, the direction of j′ can be defined, and the space distribution of the product’s rotation angular mo-mentum can be written as P( r, r). In this calculation, P( r), P( r), and P( r, r) are expanded up to k = 18, n = 24, and k = 7, respectively, which is sufficient for good conver-gence.

The full three-dimensional angular distribution associ-ated with k k′ j′ can be represented by a set of general-ized polarization dependent differential cross sections ( PDDCSs ) in the CM frame like Figure 1. The fully corre-lated CM angular distribution is written as the sum [13]

*t r t r

t

d[ ] 1( , ) ( , )

4 dkq

kqkq

kP C

(1)

where [k] = 2k + 1, (1/)(dkq/dt) is a generalized PDDCS,

and t r t r( , ) 4 (2 1) ( , )kq kqC k Y is the modified

spherical harmonic function. In the present work, (2/)(d00/d t), (2/)(d20/d t), (2/)(d22/d t) and (2/)(d21 /d t) are calculated with the computational method developed by Han and coworkers [11, 14, 16–19, 30], and these PDDCSs are expanded up to k = 7 for good convergence.

ZHAO Juan, et al. Sci China Chem April (2010) Vol.53 No.4 929

3 Results and discussion

Figure 2 shows the dependence of the product rotational alignment on collision energies. It can be seen from the fig-ure that the P2(j′·k) values slightly decrease when the col-lision energies are below 0.3 eV and evidently increase above 0.3 eV, which indicates that the product rotational alignment becomes weaker as the collision energy increases.

The PDDCS describes the k k′ j′ correlation and the scattering direction of the product molecule HF. The calcu-lation of the PDDCSs for the title reaction on the ground

Figure 2 The product rotational alignment P2(j′·k) for F + HO(0,0)

HF + O as a function of collision energy.

3A″ PES is shown in Figures 3 (a)–(f) with the correspond-ing collision energies 0.1–0.6 eV, respectively. The PDDCS (2/)(d 00/d t) is simply the (k, k′) differential cross sec-tion (DCS). It can be seen that HF product molecules are backward scattered at collision energy of 0.1 eV and side scattered at collision energy of 0.2 eV. It is also obvious that the degree of forward scattering increases with collision energies EC≥0.3 eV, which is consistent with the fact that this reaction is mainly dominated by direct mechanism stated in ref. [7]. The PDDCS (2/)(d 20/d t) is simply called the expectation value of the second Legendre moment P2(cos r), and the trend of it is indistinctively opposite to that of (2/)(d 00/d t) in Figure 3 indicating that the prod-uct rotational alignment is weakly perpendicular to k.

It can also be seen in Figure 3 that the PDDCSs with q 0 are zero at the extremities of forward and backward scatter-ing. At these limiting scattering angles, the k k′ scattering plane is not determined and the value of these PDDCSs with q 0 must be zero [13]. The behavior of PDDCSs with q 0 at the scattering away from extreme forward and backward direction is more attractive [13]. It provides information on the r dihedral angel distribution, and the fact that the val-ues are nonzero at scattering angles away from t = 0 and 180° indicates the P(r, r) distribution is not isotropic for the scattering products. In Figure 3, it can be seen that the values of (2/)(d 22+/d t) are negative for all scattering angles, which indicates the remarkable preference of prod-uct alignment along the y-axis. It is very interesting to notice

Figure 3 The polarization dependent generalized differential cross section of the title reaction for six different collision energies. (a) EC = 0.1 eV, (b) EC =

0.2 eV, (c) EC = 0.3 eV, (d) EC = 0.4 eV, (e) EC = 0.5 eV, (f) EC = 0.6 eV.

930 ZHAO Juan, et al. Sci China Chem April (2010) Vol.53 No.4

that the product displays a stronger polarization at about 40° for the four collision energies 0.3–0.6 eV, and the degree of polarization becomes stronger when the collision energy increases.

The distribution of (2/)(d 21/d t) is related to sin2 r cos r. From Figures 3 (a) and (b) we can find that the values of it are negative but almost zero for the collision energies of 0.1 and 0.2 eV, indicating the product alignment is very slightly along the direction of vector x + z, while the collision energy is 0.3–0.6 eV, indicating the product is slightly aligned along the direction of vector xz at the scat-tering angles about 20°.

In order to better describe the k j′ correlation, we plot the P( r) distribution of the product HF in Figures 4 (a) and (b). It can be seen in the figure that the P( r) distribution is a relatively broad and symmetric distribution with a peak at r = 90°, which shows that the product rotational angular momentum vector prefers to align along the direction at the right angle to the relative velocity direction. In addition, it is clear in Figure 4(a) that the product alignment becomes stronger when the collision energy increases from 0.1 to 0.3 eV, while it becomes weaker when the collision energy in-creases from 0.4 to 0.6 eV as shown in Figure 4(b), which is well consistent with the curve shown in Figure 2.

The PDDCSs shown in Figure 3 contain rich information about the angular momentum polarization. To get a better graphical representation of the polarization of the HF prod- ucts from the title reaction, we have plotted the P( r) dis- tributions in Figures 5(a) and (b). The dihedral angle distri- butions P( r) describe k k′ j′ correlations. P( r) tends to be asymmetric with respect to the k k′ scattering plane (or about r = 180°), directly reflecting the polarization of an-

gular momentum for six different collision energies. As is seen in the figure, there are two peaks of P( r), respectively at 90° and 270°, which shows that the rotational angular momentum vector of HF is mainly aligned along the y-axis in the CM frame for the six different collision energies. The peak at r = 270° is apparently stronger than that at r = 90°, indicating the product rotational angular momentum vector is not only aligned, but also oriented along the negative y-axis for each collision energy. The narrower and larger distribution at r = 270° for collision energy indicates that the reaction is mainly dominated by in-plane mechanism, and the product molecule prefers clockwise rotating in a plane parallel to the scattering plane [39].

In Figure 5(a), it can be seen that the difference of peaks of P( r) at r = 90° and r = 270° becomes more significant when the collision energy increases from 0.1 to 0.3 eV, which indicates the trend of the product rotational angular momentum vector j′ being oriented along the negative y-axis is becoming stronger with increasing collision energy. However, the contrary is indeed true, i.e., j′ becomes more weakly oriented along the negative y-axis for the collision energy increasing from 0.4 to 0.6 eV in Figure 5(b).

In order to validate more information of the angular mo- mentum polarization, we also plot it in the form of polar plots r and r averaged over all scattering angles. As can be seen from Figure 6, the distribution of P( r, r) is in good accordance with the distribution of P( r) and P( r) of the HF products for six collision energies. The distribution of P( r, r) indicates that the products are strongly polarized perpendicu- lar to the scattering plane and the products of reaction are mainly rotating in planes parallel to the scattering plane.

Generally speaking, the higher the collision energy, the

Figure 4 The distribution of P( r), reflecting k j′ correlation at six collision energies. (a)EC = 0.1, 0.2, 0.3 eV; (b) EC = 0.4, 0.5, 0.6 eV.

ZHAO Juan, et al. Sci China Chem April (2010) Vol.53 No.4 931

stronger the product rotational alignment, which is pre- sented at the collision energy below 0.3 eV. However, it is contrary when the collision energy is greater than 0.4eV. As is reported in refs. [14, 16, 18], for a reactive system of Heavy-Light-Heavy (HLH) mass combination, the reactant orbital angular momentum L mostly transfer into the prod-uct orbital alignment, and j′ is almost independent of L. In view of F + HO(0,0) HF + O reaction studied in the pre-sent work, our calculation results can be explained using

HLH mass combination. In addition, F atom has relatively strong absorbability to charges. At higher collision energies, F atom rapidly and easily grips H atom away from HO molecule, and the overwhelming amount of collision energy transfers into the translational energy of the product, and the contribution to the product rotation angular momentum is little. Therefore, the alignment and orientation of product molecular rotational angular momentum are both weak when the collision energy is relatively high.

Figure 5 The dihedral angle distribution of P( r) with respect to the k k′ plane. (a) EC = 0.1 eV, 0.2 eV, 0.3 eV; (b) EC = 0.4 eV, 0.5 eV, 0.6 eV.

Figure 6 Polar plots of P( r, r) distribution for six different collision energies averaged over all scattering angles. (a) EC = 0.1 eV, (b) EC = 0.2 eV, (c) EC =

0.3 eV, (d) EC = 0.4 eV, (e) EC = 0.5 eV, (f) EC = 0.6 eV.

932 ZHAO Juan, et al. Sci China Chem April (2010) Vol.53 No.4

4 Conclusions

Here we presented a quasi-classical trajectory study of the product polarization for the reaction F(2P) + OH(2) O(3P)

+ HF(1+) at different collision energies. That the values of P2(j′·k) become larger indicates the product rotational alignment becomes weaker with the increase of collision energy. The four PDDCSs show that the products vary from backward scattering to forward when the collision energy increases. As the result of the HLH mass combination and atom F’s relatively strong absorbability to charges, the product rotational angular momentum vector j′ at higher collision energies is more weakly aligned and oriented.

The authors thank Prof. Susana Gómez-Carrasco for providing the poten-tial energy surface and Prof. Keli Han for providing Stereo-dynamics QCT program. This work is supported by the National Natural Science Founda-tion of China (Grant No. 10574083) and the Natural Science Foundation of Shandong Province of China (Grant No. Y2006A23). Partial financial support from the National Basic Research Program of China is also grate-fully acknowledged (Grant No. 2006CB806000).

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