- Email: [email protected]
HCl product branching ratios for the Cl+HD reaction on BW2 potential energy surface
6 April 2001
Chemical Physics Letters 337 (2001) 349±354
www.elsevier.nl/locate/cplett
Quasi-classical trajectory study of the DCl/HCl product branching ratios for the Cl HD reaction on BW2 potential energy surface Mao-Du Chen, Bi-Yu Tang, Ke-Li Han *, Nan-Quan Lou State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China Received 23 November 2000; in ®nal form 30 January 2001
Abstract The dynamics of the Cl + HD reaction has been studied by means of quasi-classical trajectory calculations on BW2 potential energy surface. The integral cross-sections versus collision energy and the DCl/HCl product branching ratios calculated quasi-classically on BW2 potential energy surface predict a clear preference to the production of DCl over HCl. The computed results also show that the integral cross-sections and the DCl/HCl product branching ratios strongly depend on the initial rotational quantum numbers j and the vibrational quantum numbers v. The calculated results are in reasonable agreement with experimental data, and some other theoretical results as well. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction Cl H2 and its isotopic variants have played an important role in the development of gas-phase reaction dynamics. Because of their importance in atmospheric chemistry and photochemical air pollution, the reaction of a chlorine atom with molecular hydrogen and its isotopic variants have been paid considerable attention both experimentally and theoretically [1±15]. These reactions have been a prototypical threeatom reaction system in the ®eld of molecular reaction dynamics and have served as test cases for bimolecular reaction rate theory [16], particularly transition state theory [17] and the theory of iso*
Corresponding author. Fax: +86-411-467-5584. E-mail address: [email protected] (K.-L. Han).
tope eects [18]. The isotope eects in reaction dynamics are kinetically interesting for they provide dierent dynamic views on the same potential energy surface (PES). The decisive progress, both experimental and theoretical, is making this system a new benchmark in the ®eld of reaction dynamics. On the experimental side, the infrared frequency-modulation measurements of absolute rate constants for the Cl + HD reaction between 295 and 700 K have been reported by Taatjes et al. [12]. Liu and coworkers [19] have measured the eects of H2 rotational states and Cl spin±orbit states on the Cl H2 v 0 excitation function, and additionally report that the vast majority of HCl products are back scattered. Skouteris et al. [20] presented the results of van der Waals interaction in the Cl + HD reaction in a crossed molecular
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 1 9 - 6
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beam experiment. They found a strong preference for the production of DCl by measuring the reaction excitation function for each of both product channels. On the theoretical side, several potential energy surfaces for the Cl H2 system have been constructed and many dynamical calculations on these surfaces have been performed, employed all kinds of computational methods such as quasi-classical trajectory (QCT) theory, the hyperspherical coordinate reaction scattering methods and time-dependent (TD) quantum wave packet approach. Eyring and co-workers [17] suggested the ®rst potential energy surface for this system. In 1985 Truhlar's group compared 11 semiempirical surfaces for the Cl H2 system in rate-constant calculations and found that the GSW surface, a generalized-LEPS-type PES [21] produced in 1973 by Stern et al., gave the most accurate results. They also pointed out that the GSW surface was not satisfactory for the exchange reaction [5]. GQQ surfaces [5], which were based on the abovementioned GSW surface and some new ab initio data, were developed by Schwenke et al. In 1996, an improved PES called G3 was presented by Allison et al. [9], which was developed by modifying the GQQ bending potential in the Cl±H±H saddle point region. Various dynamics calculations, including quantum mechanical (QM) reactive scattering [10], VTST [9], and QCT calculations [8], were performed on the G3 surface, and the calculated results are in good agreement with experimental data. However, the recent molecular beam experiments of Lai and Liu [20] for Cl + HD at low collision energies gave HCl + D/DCl + H branching ratios in strong disagreement with exact quantum calculations performed by Skouteris and Manolopoulos [20] on the G3 potential energy surface. So Bian et al. [22] presented a new global three-dimensional PES named BW2 for the Cl H2 system which has been computed using the most accurate electronic structure methods and basis sets presently available. In contrast to the G3 PES, the exact QM reactive scattering calculations for this system on the BW2 PES predicted the large DCl/HCl branching ratios at low collision energies correctly and in better agreement with the recent
crossed molecule beam experiment measurement [20]. Time-dependent (TD) quantum wave packet dynamics studies have been performed by Yang et al. [23±25] on this new PES for the reaction Cl H2 and its isotopic variants and some interesting results are presented. It is our intention in this Letter to get more dynamics information for this system; QCT calculation has been performed for the reaction Cl + HD on BW2 PES. 2. Theory 2.1. Potential energy surface Bian et al. [22] chose the functional forms proposed by Aguado and Paniagua [26] for the analytical representation of the BW2 potential energy surface and the ®tting procedure used to create the BW2 PES has been described in detail. The BW2 potential energy surface diers qualitatively from the previous LEPS-type surface, such as the G3 surface. Firstly, in both the entrance and exit channels the BW2 surface has longrange van der Waals minima that are absent in the G3 surface. Secondly in the entrance channel, the BW2 surface is least repulsive for perpendicular (T-shaped) approach of Cl toward H2 while the G3 surface is most repulsive for the T-shaped structure. The saddle point of the BW2 surface is located earlier in the entrance channel than that of the G3 surface, whereas the barrier height of the BW2 surface (7.61 kcal/mol) is very close to that of the G3 surface (7.88 kcal/mol). By adding the zero point energies at the saddle point and the asymptotic channel of the BW2 surface the eective barrier height (4.03 kcal/mol) is very close to that of the G3 surface (4.36 kcal/mol). In addition, the BW2 imaginary frequency 1294 icm 1 corresponding to the asymmetric stretch is substantially lower than that 1520 icm 1 of the G3 surface. This implies that the reaction barrier of the BW2 surface is thicker than that of the G3 surface. 2.2. Quasi-classical trajectory calculations The general method for the calculation of quasi-classical trajectories is the same as the one
M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
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used previously [27±31]; the classical Hamilton's equations are integrated numerically for motion in three dimensions. In the present work, we have carried out calculations of the reaction cross-sections and the DCl/HCl product branching ratios with the variations in collision energy, initial rotational quantum number j and initial vibrational quantum number v. A batch of 50 000 trajectories was run for each of the Cl + HD reactions and the integration step size in the trajectories was chosen to be 0.1 fs, which guarantees the conservation of the total energy and total angular momentum. 3. Results and discussion Although the experimental results for measuring thermal rate coecients and product angular distributions performed for the reaction Cl H2 and its isotopic variants are sensitive to the shape of the potential energy surface in the transition state region, they are comparatively insensitive to the potential in the reactant valley. In order to provide a more sensitive test of the reactant valley region, Skouteris et al. [20] performed a crossed molecular beam experiment on the Cl + HD isotopomer of the reaction. At the same time, they also presented the exact quantum mechanical results of the DCl/HCl product branching ratios and excitation function for Cl HD v 0; 82% j 0 18% j 1 on BW2 PES [20], with the hyperspherical coordinate reaction scattering method. The QCT-computed reaction cross-sections are depicted in Fig. 1A for the Cl HD ! HCl D and Cl HD ! DCl H reaction, the corresponding DCl/HCl product branching ratios are shown in Fig. 1B. Clearly, the QCT-computed results of reaction cross-sections and the DCl/HCl product branching ratio are in reasonable agreement with the QM calculated results and experimental data. As can be seen from Fig. 1, QCT calculation on the new global potential energy surface revealed a dramatic preference for producing DCl for the reaction Cl + HD. One reason is probably the fact that the center of mass of the HD molecule is closer to the D atom implying a greater cone of acceptance for the attack of Cl to this end of the
2 ) and DCl/HCl Fig. 1. Integral reaction cross-sections (A product branching ratios for the Cl + HD v 0; 82% j 0 18% j 1 reaction. (A) Shows the integral reaction crosssections for DCl and HCl production as a function of the collision energy. (B) Shows the corresponding DCl/HCl product branching ratios. The solid line is for the present calculation, the dotted line is for the quantum mechanical calculation from [20], and the dash line is for the experimental results from [20]. All the experimental results are normalized to the corresponding QM results.
molecule, and thus reproducing the preference for the DCl product very well. The most important reason may arise from the features of the BW2 surface, since the BW2 surface is attractive at long
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distances and has a van der Waals minimum with a well depth of 0.5 kcal/mol at a T-shaped equilibrium geometry. As pointed out in [20], the van der Waals forces in its entrance valley de¯ect trajectories away from the collinear transition state saddle point, thereby inhibiting the reaction at low collision energies. Because the center of mass of HD is closer to the D atom, the H atom experiences the van der Waals forces at a larger Cl-toHD separation. This eect is more sensitive to the HCl product than to the DCl product. As a result, the reaction Cl + HD will be more likely to produce DCl. In order to compare our results with those of Skouteris et al. [20] and Yang et al. [25], the crosssections with the product channels HCl and DCl in [20] and in the present work are summed up to obtain the integral cross-sections for the reaction Cl + HD. Fig. 2 depicts the comparison of the QCT integral cross-sections with those from [20,25]. It is observed that there is a reasonable agreement among the QCT-computed results and TD quantum wave packet results as well as hyperspherical coordinate reaction scattering calculation. The cross-sections computed using the QCT method are lower than those of the QM theories (see Figs. 1 and 2). This is very reasonable,
2 ) as a function of the Fig. 2. Integral reaction cross-sections (A collision energy for the Cl HD v 0; 82% j 0 18% j 1 reaction. The dotted line indicates the present calculation, the dashed line is the quantum mechanical calculation taken from [20], and the solid line is the TD quantum wave packet calculation taken from [25].
because for the QCT method we do not consider the quantum eect that is very pronounced for a reaction at low collision energy. The most signi®cant dierences between QCT and QM results found in Fig. 1B show that the QM calculated DCl/HCl product branching ratios change slowly while the collision energy increases, but the QCT results alter more sharply. From Figs. 3A and 4A, one can ®nd that the integral cross-sections rise rapidly as j or v increases. Both vibrational and rotational excitations have a positive eect on the reactivity which probably arises from the characteristic of nonlinear equilibrium geometry of the BW2 surface. Another reason is probably that the BW2 surface has a Cl±HD van der Waals well, and the van der Waals interactions are not con®ned to the well region but persist for some distance into the side of the reaction barrier. When HD is in a state of low rotational excitation or vibrational excitation, the van der Waals interactions de¯ect trajectories away from the collinear transition state saddle point. When HD is in high rotational states or vibrational states, the trajectories with more rapid HD rotation or vibration are not de¯ected so strongly by the weak van der Waals forces. Fig. 3A shows that the variation of integral cross-sections with the change of rotational quantum number j computed from the QCT calculation agrees qualitatively with that of TD wave packet calculation on the BW2 surface. However at low rotational excitation, the TD wave packet calculated values of integral cross-sections are larger than the QCT results. The enhancement of the quantum tunneling eect as j increases may account for these discrepancies. The classical translational energy threshold increases substantially with initial j, but the QM one remains unchanged. In contrast to our QCT results, the QCT and QM calculations on the G3 surface [14,25] show that the rotational excitation on the reaction cross-sections has a negative eect, and the QCT results are larger than the QM values because of ignoring the zero-point energy at the transition state. Fig. 3B shows that the DCl/HCl product branching ratios for the Cl HD ! HCl D and Cl HD ! DCl H reactions decrease as j increases. The QCT results in the present
M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
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2 ) and DCl/HCl Fig. 4. Integral reaction cross-sections (A product branching ratios for the Cl HD j 0 reaction. (A) The integral reaction cross-sections as a function of the vibrational quantum numbers at the ®xed collision energy 8.0 kcal/ mol. (B) The corresponding DCl/HCl product branching ratios.
2
Fig. 3. Integral reaction cross-sections (A ) and DCl/HCl product branching ratios for the Cl HD v 0 reaction. (A) The integral reaction cross-sections as a function of the rotational quantum numbers at the ®xed collision energy 8.0 kcal/ mol. The square is for the TD quantum wave packet calculation taken from [25]. (B) The corresponding DCl/HCl product branching ratios.
work are in qualitative agreement with the experimental data [32] and theoretical results using the hyperspherical coordinate reaction scattering method [20]. As mentioned above, the reason is that the trajectories with more rapid HD rotation are not de¯ected so strongly by the van der Waals forces. Thus the DCl/HCl product branching ratios with the HD molecule in high-
ly-excited rotational states are determined almost entirely by the shape of the potential in the transition state region. As depicted in Fig. 4B, the DCl/HCl product branching ratios also decrease with an increase in vibrational quantum number v. The van der Waals minimum existing in the reactant valley on the BW2 surface probably contributes to this phenomenon as well. When HD is in ground states, most of the trajectories that form the product HCl on the G3 PES are de¯ected by the torque toward perpendicular geometries in the reactant valley of the BW2 PES. However, the eect of the van der Waals forces on the reactive trajectories is probably weak since the barrier height relative to the HD reagent in vibrationally excited states is lowered.
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M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
4. Conclusions We have carried out the quasi-classical trajectory calculation for the Cl + HD reaction on a new global ab initio potential energy surface, named BW2 surface. The integral cross-sections and the DCl/HCl product branching ratios increase with increasing collision energy. The most important reason arises from the features of the BW2 potential energy surface. That is, the BW2 surface is attractive at long distances and has a van der Waals minimum with a well depth of 0.5 kcal/mol at a T-shaped equilibrium geometry. The QCT calculations also show that the integral cross-sections increase as the initial rotational quantum number j and the vibrational quantum number v increase, but the DCl/HCl product branching ratios decrease rapidly. All of our QCT calculated results are in reasonable agreement with experimental data and other theoretical results. Acknowledgements This work is supported by KBRSF and the National Science Foundation of China (Grant No. 29953001 and 29825107).
[9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
References [1] D.L. Thompson, H.H. Suzukava Jr., L.M. Ra, J. Chem. Phys. 62 (1975) 4727. [2] J.C. Miller, R.T. Gordon, J. Chem. Phys. 78 (1983) 3713. [3] S.C. Tucker, D.G. Truhlar, B.C. Garrett, A.D. Isaacson, J. Chem. Phys. 82 (1985) 4102. [4] D.W. Schwenks, S.C. Tucker, R. Steckler, F.B. Brown, G.C. Lynch, D.G. Truhlar, B.C. Garrett, J. Chem. Phys. 90 (1989) 3110. [5] W.L. Hase, Science 266 (1994) 998. [6] M. Alagia, N. Balucani, P. Casavecchia, D. Stranges, G.G. Volpi, J. Chem. Soc. Faraday Trans. 91 (1995) 575. [7] F.J. Aoiz, L. Baares, Chem. Phys. Lett. 247 (1995) 232. [8] M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, E.H. van Kleef, G.G. Volpi, F.J. Aoiz, L. Baares, D.W.
[25] [26] [27] [28] [29] [30] [31] [32]
Schwenke, T.C. Allison, S.L. Mielke, D.G. Truhlar, Science 273 (1996) 1519. T.C. Allison, G.C. Lynch, D.G. Truhlar, M.S. Gordon, J. Phys. Chem. 100 (1996) 13575. S.L. Mielke, T.C. Allison, D.G. Truhlar, D.W. Schwenke, J. Phys. Chem. 100 (1996) 13588. P. Casavecchia, N. Balucani, G.G. Volpi, Annu. Rev. Phys. Chem. 50 (1999) 347. C.A. Taatjes, Chem. Phys. Lett. 306 (1999) 33. U. Manthe, W. Bian, H.-J. Werner, Chem. Phys. Lett. 313 (1999) 647. M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, G.G. Volpi, F.J. Aoiz, L. Baares, T.C. Allison, S.L. Mielke, D.G. Truhlar, Phys. Chem. Chem. Phys. 2 (2000) 599. S.A. Kandel, A.J. Alexander, Z.H. Kim, R.N. Zare, F.J. Aoiz, L. Ba~ nsares, J.F. Castillo, V. Saez Rabanos, J. Chem. Phys. 112 (2000) 670. R.E. Weston Jr., J. Phys. Chem. 83 (1979) 61. A. Wheeler, B. Topley, H.J. Eyring, J. Chem. Phys. 4 (1936) 178. J. Bigeleisen, F.S. Klein, R.E. Weston, M. Wolfsberg, J. Chem. Phys. 30 (1959) 1340. S.H. Lee, L.H. Lai, K. Liu, J. Chem. Phys. 110 (1999) 8229. D. Skouteris, D.E. Manolopoulos, W. Bian, H.-J. Werner, L.H. Lai, K. Liu, Science 286 (1999) 1713. M.J. Stern, A. Persky, F.S. Klein, Chem. Phys. Lett. 121 (1985) 475. W. Bian, H.-J. Werner, J. Chem. Phys. 112 (2000) 220. B.H. Yang, B.Y. Tang, H.M. Yin, K.L. Han, J.Z.H. Zhang, J. Chem. Phys. 113 (2000) 7182. B.H. Yang, H.T. Gao, K.L. Han, J.Z.H. Zhang, J. Chem. Phys. 113 (2000) 1434. B.H. Yang, M.H. Yin, K.L. Han, J.Z.H. Zhang, J. Phys. Chem. A. 104 (2000) 10517. A. Aguado, M. Paniagua, J. Chem. Phys. 96 (1992) 1265. M.D. Chen, M.L. Wang, K.L. Han, S.L. Ding, Chem. Phys. Lett. 301 (1999) 303. L. Zhang, M.D. Chen, M.L. Wang, K.L. Han, J. Chem. Phys. 112 (2000) 3710. M.Q. Cai, L. Zhang, B.Y. Tang, M.D. Chen, G.W. Yang, K.L. Han, Chem. Phys. 255 (2000) 283. M.L. Wang, K.L. Han, G.Z. He, J. Chem. Phys. 109 (1998) 5446. K.L. Han, G.Z. He, N.Q. Lou, J. Chem. Phys. 105 (1996) 8699. Y. BarYaakov, A. Persky, F.S. Klein, J. Chem. Phys. 59 (1973) 2415.
Chemical Physics Letters 337 (2001) 349±354
www.elsevier.nl/locate/cplett
Quasi-classical trajectory study of the DCl/HCl product branching ratios for the Cl HD reaction on BW2 potential energy surface Mao-Du Chen, Bi-Yu Tang, Ke-Li Han *, Nan-Quan Lou State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China Received 23 November 2000; in ®nal form 30 January 2001
Abstract The dynamics of the Cl + HD reaction has been studied by means of quasi-classical trajectory calculations on BW2 potential energy surface. The integral cross-sections versus collision energy and the DCl/HCl product branching ratios calculated quasi-classically on BW2 potential energy surface predict a clear preference to the production of DCl over HCl. The computed results also show that the integral cross-sections and the DCl/HCl product branching ratios strongly depend on the initial rotational quantum numbers j and the vibrational quantum numbers v. The calculated results are in reasonable agreement with experimental data, and some other theoretical results as well. Ó 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction Cl H2 and its isotopic variants have played an important role in the development of gas-phase reaction dynamics. Because of their importance in atmospheric chemistry and photochemical air pollution, the reaction of a chlorine atom with molecular hydrogen and its isotopic variants have been paid considerable attention both experimentally and theoretically [1±15]. These reactions have been a prototypical threeatom reaction system in the ®eld of molecular reaction dynamics and have served as test cases for bimolecular reaction rate theory [16], particularly transition state theory [17] and the theory of iso*
Corresponding author. Fax: +86-411-467-5584. E-mail address: [email protected] (K.-L. Han).
tope eects [18]. The isotope eects in reaction dynamics are kinetically interesting for they provide dierent dynamic views on the same potential energy surface (PES). The decisive progress, both experimental and theoretical, is making this system a new benchmark in the ®eld of reaction dynamics. On the experimental side, the infrared frequency-modulation measurements of absolute rate constants for the Cl + HD reaction between 295 and 700 K have been reported by Taatjes et al. [12]. Liu and coworkers [19] have measured the eects of H2 rotational states and Cl spin±orbit states on the Cl H2 v 0 excitation function, and additionally report that the vast majority of HCl products are back scattered. Skouteris et al. [20] presented the results of van der Waals interaction in the Cl + HD reaction in a crossed molecular
0009-2614/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 1 ) 0 0 2 1 9 - 6
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M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
beam experiment. They found a strong preference for the production of DCl by measuring the reaction excitation function for each of both product channels. On the theoretical side, several potential energy surfaces for the Cl H2 system have been constructed and many dynamical calculations on these surfaces have been performed, employed all kinds of computational methods such as quasi-classical trajectory (QCT) theory, the hyperspherical coordinate reaction scattering methods and time-dependent (TD) quantum wave packet approach. Eyring and co-workers [17] suggested the ®rst potential energy surface for this system. In 1985 Truhlar's group compared 11 semiempirical surfaces for the Cl H2 system in rate-constant calculations and found that the GSW surface, a generalized-LEPS-type PES [21] produced in 1973 by Stern et al., gave the most accurate results. They also pointed out that the GSW surface was not satisfactory for the exchange reaction [5]. GQQ surfaces [5], which were based on the abovementioned GSW surface and some new ab initio data, were developed by Schwenke et al. In 1996, an improved PES called G3 was presented by Allison et al. [9], which was developed by modifying the GQQ bending potential in the Cl±H±H saddle point region. Various dynamics calculations, including quantum mechanical (QM) reactive scattering [10], VTST [9], and QCT calculations [8], were performed on the G3 surface, and the calculated results are in good agreement with experimental data. However, the recent molecular beam experiments of Lai and Liu [20] for Cl + HD at low collision energies gave HCl + D/DCl + H branching ratios in strong disagreement with exact quantum calculations performed by Skouteris and Manolopoulos [20] on the G3 potential energy surface. So Bian et al. [22] presented a new global three-dimensional PES named BW2 for the Cl H2 system which has been computed using the most accurate electronic structure methods and basis sets presently available. In contrast to the G3 PES, the exact QM reactive scattering calculations for this system on the BW2 PES predicted the large DCl/HCl branching ratios at low collision energies correctly and in better agreement with the recent
crossed molecule beam experiment measurement [20]. Time-dependent (TD) quantum wave packet dynamics studies have been performed by Yang et al. [23±25] on this new PES for the reaction Cl H2 and its isotopic variants and some interesting results are presented. It is our intention in this Letter to get more dynamics information for this system; QCT calculation has been performed for the reaction Cl + HD on BW2 PES. 2. Theory 2.1. Potential energy surface Bian et al. [22] chose the functional forms proposed by Aguado and Paniagua [26] for the analytical representation of the BW2 potential energy surface and the ®tting procedure used to create the BW2 PES has been described in detail. The BW2 potential energy surface diers qualitatively from the previous LEPS-type surface, such as the G3 surface. Firstly, in both the entrance and exit channels the BW2 surface has longrange van der Waals minima that are absent in the G3 surface. Secondly in the entrance channel, the BW2 surface is least repulsive for perpendicular (T-shaped) approach of Cl toward H2 while the G3 surface is most repulsive for the T-shaped structure. The saddle point of the BW2 surface is located earlier in the entrance channel than that of the G3 surface, whereas the barrier height of the BW2 surface (7.61 kcal/mol) is very close to that of the G3 surface (7.88 kcal/mol). By adding the zero point energies at the saddle point and the asymptotic channel of the BW2 surface the eective barrier height (4.03 kcal/mol) is very close to that of the G3 surface (4.36 kcal/mol). In addition, the BW2 imaginary frequency 1294 icm 1 corresponding to the asymmetric stretch is substantially lower than that 1520 icm 1 of the G3 surface. This implies that the reaction barrier of the BW2 surface is thicker than that of the G3 surface. 2.2. Quasi-classical trajectory calculations The general method for the calculation of quasi-classical trajectories is the same as the one
M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
351
used previously [27±31]; the classical Hamilton's equations are integrated numerically for motion in three dimensions. In the present work, we have carried out calculations of the reaction cross-sections and the DCl/HCl product branching ratios with the variations in collision energy, initial rotational quantum number j and initial vibrational quantum number v. A batch of 50 000 trajectories was run for each of the Cl + HD reactions and the integration step size in the trajectories was chosen to be 0.1 fs, which guarantees the conservation of the total energy and total angular momentum. 3. Results and discussion Although the experimental results for measuring thermal rate coecients and product angular distributions performed for the reaction Cl H2 and its isotopic variants are sensitive to the shape of the potential energy surface in the transition state region, they are comparatively insensitive to the potential in the reactant valley. In order to provide a more sensitive test of the reactant valley region, Skouteris et al. [20] performed a crossed molecular beam experiment on the Cl + HD isotopomer of the reaction. At the same time, they also presented the exact quantum mechanical results of the DCl/HCl product branching ratios and excitation function for Cl HD v 0; 82% j 0 18% j 1 on BW2 PES [20], with the hyperspherical coordinate reaction scattering method. The QCT-computed reaction cross-sections are depicted in Fig. 1A for the Cl HD ! HCl D and Cl HD ! DCl H reaction, the corresponding DCl/HCl product branching ratios are shown in Fig. 1B. Clearly, the QCT-computed results of reaction cross-sections and the DCl/HCl product branching ratio are in reasonable agreement with the QM calculated results and experimental data. As can be seen from Fig. 1, QCT calculation on the new global potential energy surface revealed a dramatic preference for producing DCl for the reaction Cl + HD. One reason is probably the fact that the center of mass of the HD molecule is closer to the D atom implying a greater cone of acceptance for the attack of Cl to this end of the
2 ) and DCl/HCl Fig. 1. Integral reaction cross-sections (A product branching ratios for the Cl + HD v 0; 82% j 0 18% j 1 reaction. (A) Shows the integral reaction crosssections for DCl and HCl production as a function of the collision energy. (B) Shows the corresponding DCl/HCl product branching ratios. The solid line is for the present calculation, the dotted line is for the quantum mechanical calculation from [20], and the dash line is for the experimental results from [20]. All the experimental results are normalized to the corresponding QM results.
molecule, and thus reproducing the preference for the DCl product very well. The most important reason may arise from the features of the BW2 surface, since the BW2 surface is attractive at long
352
M.-D. Chen et al. / Chemical Physics Letters 337 (2001) 349±354
distances and has a van der Waals minimum with a well depth of 0.5 kcal/mol at a T-shaped equilibrium geometry. As pointed out in [20], the van der Waals forces in its entrance valley de¯ect trajectories away from the collinear transition state saddle point, thereby inhibiting the reaction at low collision energies. Because the center of mass of HD is closer to the D atom, the H atom experiences the van der Waals forces at a larger Cl-toHD separation. This eect is more sensitive to the HCl product than to the DCl product. As a result, the reaction Cl + HD will be more likely to produce DCl. In order to compare our results with those of Skouteris et al. [20] and Yang et al. [25], the crosssections with the product channels HCl and DCl in [20] and in the present work are summed up to obtain the integral cross-sections for the reaction Cl + HD. Fig. 2 depicts the comparison of the QCT integral cross-sections with those from [20,25]. It is observed that there is a reasonable agreement among the QCT-computed results and TD quantum wave packet results as well as hyperspherical coordinate reaction scattering calculation. The cross-sections computed using the QCT method are lower than those of the QM theories (see Figs. 1 and 2). This is very reasonable,
2 ) as a function of the Fig. 2. Integral reaction cross-sections (A collision energy for the Cl HD v 0; 82% j 0 18% j 1 reaction. The dotted line indicates the present calculation, the dashed line is the quantum mechanical calculation taken from [20], and the solid line is the TD quantum wave packet calculation taken from [25].
because for the QCT method we do not consider the quantum eect that is very pronounced for a reaction at low collision energy. The most signi®cant dierences between QCT and QM results found in Fig. 1B show that the QM calculated DCl/HCl product branching ratios change slowly while the collision energy increases, but the QCT results alter more sharply. From Figs. 3A and 4A, one can ®nd that the integral cross-sections rise rapidly as j or v increases. Both vibrational and rotational excitations have a positive eect on the reactivity which probably arises from the characteristic of nonlinear equilibrium geometry of the BW2 surface. Another reason is probably that the BW2 surface has a Cl±HD van der Waals well, and the van der Waals interactions are not con®ned to the well region but persist for some distance into the side of the reaction barrier. When HD is in a state of low rotational excitation or vibrational excitation, the van der Waals interactions de¯ect trajectories away from the collinear transition state saddle point. When HD is in high rotational states or vibrational states, the trajectories with more rapid HD rotation or vibration are not de¯ected so strongly by the weak van der Waals forces. Fig. 3A shows that the variation of integral cross-sections with the change of rotational quantum number j computed from the QCT calculation agrees qualitatively with that of TD wave packet calculation on the BW2 surface. However at low rotational excitation, the TD wave packet calculated values of integral cross-sections are larger than the QCT results. The enhancement of the quantum tunneling eect as j increases may account for these discrepancies. The classical translational energy threshold increases substantially with initial j, but the QM one remains unchanged. In contrast to our QCT results, the QCT and QM calculations on the G3 surface [14,25] show that the rotational excitation on the reaction cross-sections has a negative eect, and the QCT results are larger than the QM values because of ignoring the zero-point energy at the transition state. Fig. 3B shows that the DCl/HCl product branching ratios for the Cl HD ! HCl D and Cl HD ! DCl H reactions decrease as j increases. The QCT results in the present
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2 ) and DCl/HCl Fig. 4. Integral reaction cross-sections (A product branching ratios for the Cl HD j 0 reaction. (A) The integral reaction cross-sections as a function of the vibrational quantum numbers at the ®xed collision energy 8.0 kcal/ mol. (B) The corresponding DCl/HCl product branching ratios.
2
Fig. 3. Integral reaction cross-sections (A ) and DCl/HCl product branching ratios for the Cl HD v 0 reaction. (A) The integral reaction cross-sections as a function of the rotational quantum numbers at the ®xed collision energy 8.0 kcal/ mol. The square is for the TD quantum wave packet calculation taken from [25]. (B) The corresponding DCl/HCl product branching ratios.
work are in qualitative agreement with the experimental data [32] and theoretical results using the hyperspherical coordinate reaction scattering method [20]. As mentioned above, the reason is that the trajectories with more rapid HD rotation are not de¯ected so strongly by the van der Waals forces. Thus the DCl/HCl product branching ratios with the HD molecule in high-
ly-excited rotational states are determined almost entirely by the shape of the potential in the transition state region. As depicted in Fig. 4B, the DCl/HCl product branching ratios also decrease with an increase in vibrational quantum number v. The van der Waals minimum existing in the reactant valley on the BW2 surface probably contributes to this phenomenon as well. When HD is in ground states, most of the trajectories that form the product HCl on the G3 PES are de¯ected by the torque toward perpendicular geometries in the reactant valley of the BW2 PES. However, the eect of the van der Waals forces on the reactive trajectories is probably weak since the barrier height relative to the HD reagent in vibrationally excited states is lowered.
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4. Conclusions We have carried out the quasi-classical trajectory calculation for the Cl + HD reaction on a new global ab initio potential energy surface, named BW2 surface. The integral cross-sections and the DCl/HCl product branching ratios increase with increasing collision energy. The most important reason arises from the features of the BW2 potential energy surface. That is, the BW2 surface is attractive at long distances and has a van der Waals minimum with a well depth of 0.5 kcal/mol at a T-shaped equilibrium geometry. The QCT calculations also show that the integral cross-sections increase as the initial rotational quantum number j and the vibrational quantum number v increase, but the DCl/HCl product branching ratios decrease rapidly. All of our QCT calculated results are in reasonable agreement with experimental data and other theoretical results. Acknowledgements This work is supported by KBRSF and the National Science Foundation of China (Grant No. 29953001 and 29825107).
[9] [10] [11] [12] [13] [14]
[15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
References [1] D.L. Thompson, H.H. Suzukava Jr., L.M. Ra, J. Chem. Phys. 62 (1975) 4727. [2] J.C. Miller, R.T. Gordon, J. Chem. Phys. 78 (1983) 3713. [3] S.C. Tucker, D.G. Truhlar, B.C. Garrett, A.D. Isaacson, J. Chem. Phys. 82 (1985) 4102. [4] D.W. Schwenks, S.C. Tucker, R. Steckler, F.B. Brown, G.C. Lynch, D.G. Truhlar, B.C. Garrett, J. Chem. Phys. 90 (1989) 3110. [5] W.L. Hase, Science 266 (1994) 998. [6] M. Alagia, N. Balucani, P. Casavecchia, D. Stranges, G.G. Volpi, J. Chem. Soc. Faraday Trans. 91 (1995) 575. [7] F.J. Aoiz, L. Baares, Chem. Phys. Lett. 247 (1995) 232. [8] M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, E.H. van Kleef, G.G. Volpi, F.J. Aoiz, L. Baares, D.W.
[25] [26] [27] [28] [29] [30] [31] [32]
Schwenke, T.C. Allison, S.L. Mielke, D.G. Truhlar, Science 273 (1996) 1519. T.C. Allison, G.C. Lynch, D.G. Truhlar, M.S. Gordon, J. Phys. Chem. 100 (1996) 13575. S.L. Mielke, T.C. Allison, D.G. Truhlar, D.W. Schwenke, J. Phys. Chem. 100 (1996) 13588. P. Casavecchia, N. Balucani, G.G. Volpi, Annu. Rev. Phys. Chem. 50 (1999) 347. C.A. Taatjes, Chem. Phys. Lett. 306 (1999) 33. U. Manthe, W. Bian, H.-J. Werner, Chem. Phys. Lett. 313 (1999) 647. M. Alagia, N. Balucani, L. Cartechini, P. Casavecchia, G.G. Volpi, F.J. Aoiz, L. Baares, T.C. Allison, S.L. Mielke, D.G. Truhlar, Phys. Chem. Chem. Phys. 2 (2000) 599. S.A. Kandel, A.J. Alexander, Z.H. Kim, R.N. Zare, F.J. Aoiz, L. Ba~ nsares, J.F. Castillo, V. Saez Rabanos, J. Chem. Phys. 112 (2000) 670. R.E. Weston Jr., J. Phys. Chem. 83 (1979) 61. A. Wheeler, B. Topley, H.J. Eyring, J. Chem. Phys. 4 (1936) 178. J. Bigeleisen, F.S. Klein, R.E. Weston, M. Wolfsberg, J. Chem. Phys. 30 (1959) 1340. S.H. Lee, L.H. Lai, K. Liu, J. Chem. Phys. 110 (1999) 8229. D. Skouteris, D.E. Manolopoulos, W. Bian, H.-J. Werner, L.H. Lai, K. Liu, Science 286 (1999) 1713. M.J. Stern, A. Persky, F.S. Klein, Chem. Phys. Lett. 121 (1985) 475. W. Bian, H.-J. Werner, J. Chem. Phys. 112 (2000) 220. B.H. Yang, B.Y. Tang, H.M. Yin, K.L. Han, J.Z.H. Zhang, J. Chem. Phys. 113 (2000) 7182. B.H. Yang, H.T. Gao, K.L. Han, J.Z.H. Zhang, J. Chem. Phys. 113 (2000) 1434. B.H. Yang, M.H. Yin, K.L. Han, J.Z.H. Zhang, J. Phys. Chem. A. 104 (2000) 10517. A. Aguado, M. Paniagua, J. Chem. Phys. 96 (1992) 1265. M.D. Chen, M.L. Wang, K.L. Han, S.L. Ding, Chem. Phys. Lett. 301 (1999) 303. L. Zhang, M.D. Chen, M.L. Wang, K.L. Han, J. Chem. Phys. 112 (2000) 3710. M.Q. Cai, L. Zhang, B.Y. Tang, M.D. Chen, G.W. Yang, K.L. Han, Chem. Phys. 255 (2000) 283. M.L. Wang, K.L. Han, G.Z. He, J. Chem. Phys. 109 (1998) 5446. K.L. Han, G.Z. He, N.Q. Lou, J. Chem. Phys. 105 (1996) 8699. Y. BarYaakov, A. Persky, F.S. Klein, J. Chem. Phys. 59 (1973) 2415.