SVRT模型在H+CD_4→HD+CD_3 反应散射中的应用
|
摘要
分子反应动力学是化学反应动力学的一个分支。用量子理论的方法来研究化学反应的动力学规律是其重要课题之一。当前，人们已经能够对四原子以内的反应体系进行全量子的严格计算。作为进一步的发展，人们将对四原子以上的反应体系进行研究。但由于原子数目和自由度的增加，会使计算量急剧上升，造成计算很难进行。最近提出的半刚性振转靶(Semirigid Vibrating Rotor Target)模型能够将反应体系的自由度减少，从而大幅度减少了计算量。利用这个模型，我们对6原子反应体系H+CD_4→HD+CD_3进行了量子计算。
半刚性振转靶(SVRT)模型把参加反应的多原子分子处理为两个基本的刚体，这两个刚性部分能沿通过它们质心的直线做一维振动，另外它还象一个刚性转子一样在3维空间中运动。实际上，就是把多原子分子处理为了准双原子分子，因而减少了体系的自由度，使得实际计算能够进行。这个模型适用于参加反应的多原子分子中有一个键较弱，且反应结束后可分为两部分的多原子分子。对一般的多原子-多原子分子反应体系，它用7个自由度来描述，对单原子-多原子分子反应体系仅仅需要4个自由度来描述，1999年SVRT模型成功地应用于H+H_2O和H+D_2O等4原子反应体系上，2000年应用SVRT模型对H+CH_4反应体系进行的量子计算又取得了比较好的结果。
我们把SVRT模型应用于H+CD_4→HD+CD_3反应体系上，把分子CD_4处理为D和CD_3两个刚性部分，建立了6原子反应体系的SVRT模型，并用4个自由度来描述此反应体系。然后在从头计算法得到的解析势能面(Jordan and Gilbert)上，采用含时波包法进行了量子计算。对CD_4分子在基态(v=O，j=0，m=0)和4个转动激发态(v=O，j=1，m=0)，(v=0，j=1，m=1)，(v=0，j=2，m=0)，(v=0，j=2，m=1)时分别计算出了体系的反应几率，总散射截面和速率常数。
本文中详细给出了H+CD_4→HD+CD_3反应体系的计算结果。通过分析和比较计算结果，我们得到如下结论。第一，体系的能量-反应几率变化曲线说明量子隧道效应显著。第二，能量-反应几率变化曲线呈现明显的振动结构。第三，转动
SVgr模型在H＋CD4—HD＋CD3反应散射中的应用 中文摘要
激发态时体系的反应几率随转动量子数j的增大有很大幅度的提高。表明在本体
系中，高的转动激发态对CD。分子中的C0键断裂有很大的贡献。这一点在选键
化学中有很重要的应用。另外在积分散射截面中，由于对各个分波求和，能量－
几率曲线的振动结构消失了。在相同入射能的情况下，总散射截面随转动量子数
j的增大而显著增大，随量子数m的增加而减小。最后比较各个量子态的速率常
数，我们也看出随量子数j的增加，速率常数升高，随量子数m的增加速率常数
降低，这些曲线在我们的图中都呈现相似的下降趋势，这和散射截面的规律是吻
合的。
总之，我们的结果是当前本体系全量子计算最精确的结果之一，它揭示了本
体系中某些重要的动力学微观物理机制，它为燃烧化学提供了有价值的数据。同
时也说明在研究多原子参与的化学反应中，SVRT模型是一种实际可行的方法，
值得应用到更一般的多原子分子反应体系中去。
Molecular reaction dynamics is a branch of chemical reaction dynamics. It is an important topic of molecular reaction dynamics to study the chemical reaction with the method of the quantum theories. At present, rigorous quantum dynamics calculations are limited only to systems involving not more than four atoms. For the further development, one will carry out quantitatively accurate quantum dynamic study for the systems including more than four atoms. But with decreasing of atomic number, the quantity of calculation will go up tremendously. In order to solve that. recently, the Semirigid Vibrating Rotor Target (SVRT) model has been proposed as a general theoretical model for practical dynamic polyatomic molecules. Reliable quantum dynamics calculation can be carried out for the system of more than four atoms using the SVRT method. Now the SVRT model is applied to study the reaction of H+CD4→HD+CD3 in four mathematical dimensions.
In the SVRT model, the target molecule is treated as a simirigid rotor composed of two rigid parts. The two rigid parts can exercise only one dimensional relative motion along the coordinate connecting the center-of-mass of the two parts. Their spatial motion is considered as a general asymmetric rotor. Practically, the SVRT model for the atom-polyatom reaction is a natural generalization of the exact atom-diatom reaction. So the quantity of calculation is reduced effectively. This model can be applied to the polyatomic molecule in that there is a weakly bond, and after the reaction the molecule can be split into two parts. In the study, the model permits realistic quantum dynamics calculation for a general atom-polyatom reaction with just four mathematical dimensions. Using the SVRT model, excellent quantum results have been obtained for the H+H2O, H+D2O and H+CH4 reactions.
In this paper, the SVRT model is applied to study the reaction of H+CD4→HD+CD3. In the reaction, the target molecule is treated as two parts of D and CD3, and the whole system is described with four dimensions. Our dynamic calculation is carried out on a recent ab initio potential energy surface (PES) of Jordan and Gilbert. The TDWP method also is employed as a computational tool. Reaction probability, cross section and rate constant are calculated for the title reaction from the ground state (v=0, j=0, m=0) and from the four rotational excited states (v=0, j=1,
m=0), (v=0, j=1, m=1), (v=0, j=2, m=0)and (v=0, j=2, m=1) of the molecule CD4.
Numerical results including reaction probability, cross section and rate constant are discussed in this article. By analysis and comparison of the results, we draw the conclusion as follows: Firstly, the quantum tunneling effect is quite pronounced. Second, the reaction probability shows resonance-like oscillatory structures in its dependence on collision energy. Thirdly, the probability goes up obviously with the rising of the rotational quantum number j. This indicates that the ascension of the rotational excited state is propitious of the split of the C-D bond in the molecule CD4. This feature plays a very important role in the field of the bond-selected chemist. Fourthly, the resonance structure disappears in the energy dependence of integral cross-section due to the summation of partial waves. At the same translational energy, the cross-section increases with the rising of the rotational quantum number j, and declines with the rising of the quantum number m. In the last, we find that the reaction rate c
onstant and the cross-section have the similar rule for the quantum numbers j and m.
Finally, at present our calculated results are one of the most accurate results of the reaction H+CD4→HD+CD3. And it also shows some microscope dynamics mechanism of the system. The present results also demonstrate that the SVRT model for atom-polyatom reaction provides a practical and accurate approach for studying chemical reactions involving polyatomic molecule.
半刚性振转靶(SVRT)模型把参加反应的多原子分子处理为两个基本的刚体，这两个刚性部分能沿通过它们质心的直线做一维振动，另外它还象一个刚性转子一样在3维空间中运动。实际上，就是把多原子分子处理为了准双原子分子，因而减少了体系的自由度，使得实际计算能够进行。这个模型适用于参加反应的多原子分子中有一个键较弱，且反应结束后可分为两部分的多原子分子。对一般的多原子-多原子分子反应体系，它用7个自由度来描述，对单原子-多原子分子反应体系仅仅需要4个自由度来描述，1999年SVRT模型成功地应用于H+H_2O和H+D_2O等4原子反应体系上，2000年应用SVRT模型对H+CH_4反应体系进行的量子计算又取得了比较好的结果。
我们把SVRT模型应用于H+CD_4→HD+CD_3反应体系上，把分子CD_4处理为D和CD_3两个刚性部分，建立了6原子反应体系的SVRT模型，并用4个自由度来描述此反应体系。然后在从头计算法得到的解析势能面(Jordan and Gilbert)上，采用含时波包法进行了量子计算。对CD_4分子在基态(v=O，j=0，m=0)和4个转动激发态(v=O，j=1，m=0)，(v=0，j=1，m=1)，(v=0，j=2，m=0)，(v=0，j=2，m=1)时分别计算出了体系的反应几率，总散射截面和速率常数。
本文中详细给出了H+CD_4→HD+CD_3反应体系的计算结果。通过分析和比较计算结果，我们得到如下结论。第一，体系的能量-反应几率变化曲线说明量子隧道效应显著。第二，能量-反应几率变化曲线呈现明显的振动结构。第三，转动
SVgr模型在H＋CD4—HD＋CD3反应散射中的应用 中文摘要
激发态时体系的反应几率随转动量子数j的增大有很大幅度的提高。表明在本体
系中，高的转动激发态对CD。分子中的C0键断裂有很大的贡献。这一点在选键
化学中有很重要的应用。另外在积分散射截面中，由于对各个分波求和，能量－
几率曲线的振动结构消失了。在相同入射能的情况下，总散射截面随转动量子数
j的增大而显著增大，随量子数m的增加而减小。最后比较各个量子态的速率常
数，我们也看出随量子数j的增加，速率常数升高，随量子数m的增加速率常数
降低，这些曲线在我们的图中都呈现相似的下降趋势，这和散射截面的规律是吻
合的。
总之，我们的结果是当前本体系全量子计算最精确的结果之一，它揭示了本
体系中某些重要的动力学微观物理机制，它为燃烧化学提供了有价值的数据。同
时也说明在研究多原子参与的化学反应中，SVRT模型是一种实际可行的方法，
值得应用到更一般的多原子分子反应体系中去。
Molecular reaction dynamics is a branch of chemical reaction dynamics. It is an important topic of molecular reaction dynamics to study the chemical reaction with the method of the quantum theories. At present, rigorous quantum dynamics calculations are limited only to systems involving not more than four atoms. For the further development, one will carry out quantitatively accurate quantum dynamic study for the systems including more than four atoms. But with decreasing of atomic number, the quantity of calculation will go up tremendously. In order to solve that. recently, the Semirigid Vibrating Rotor Target (SVRT) model has been proposed as a general theoretical model for practical dynamic polyatomic molecules. Reliable quantum dynamics calculation can be carried out for the system of more than four atoms using the SVRT method. Now the SVRT model is applied to study the reaction of H+CD4→HD+CD3 in four mathematical dimensions.
In the SVRT model, the target molecule is treated as a simirigid rotor composed of two rigid parts. The two rigid parts can exercise only one dimensional relative motion along the coordinate connecting the center-of-mass of the two parts. Their spatial motion is considered as a general asymmetric rotor. Practically, the SVRT model for the atom-polyatom reaction is a natural generalization of the exact atom-diatom reaction. So the quantity of calculation is reduced effectively. This model can be applied to the polyatomic molecule in that there is a weakly bond, and after the reaction the molecule can be split into two parts. In the study, the model permits realistic quantum dynamics calculation for a general atom-polyatom reaction with just four mathematical dimensions. Using the SVRT model, excellent quantum results have been obtained for the H+H2O, H+D2O and H+CH4 reactions.
In this paper, the SVRT model is applied to study the reaction of H+CD4→HD+CD3. In the reaction, the target molecule is treated as two parts of D and CD3, and the whole system is described with four dimensions. Our dynamic calculation is carried out on a recent ab initio potential energy surface (PES) of Jordan and Gilbert. The TDWP method also is employed as a computational tool. Reaction probability, cross section and rate constant are calculated for the title reaction from the ground state (v=0, j=0, m=0) and from the four rotational excited states (v=0, j=1,
m=0), (v=0, j=1, m=1), (v=0, j=2, m=0)and (v=0, j=2, m=1) of the molecule CD4.
Numerical results including reaction probability, cross section and rate constant are discussed in this article. By analysis and comparison of the results, we draw the conclusion as follows: Firstly, the quantum tunneling effect is quite pronounced. Second, the reaction probability shows resonance-like oscillatory structures in its dependence on collision energy. Thirdly, the probability goes up obviously with the rising of the rotational quantum number j. This indicates that the ascension of the rotational excited state is propitious of the split of the C-D bond in the molecule CD4. This feature plays a very important role in the field of the bond-selected chemist. Fourthly, the resonance structure disappears in the energy dependence of integral cross-section due to the summation of partial waves. At the same translational energy, the cross-section increases with the rising of the rotational quantum number j, and declines with the rising of the quantum number m. In the last, we find that the reaction rate c
onstant and the cross-section have the similar rule for the quantum numbers j and m.
Finally, at present our calculated results are one of the most accurate results of the reaction H+CD4→HD+CD3. And it also shows some microscope dynamics mechanism of the system. The present results also demonstrate that the SVRT model for atom-polyatom reaction provides a practical and accurate approach for studying chemical reactions involving polyatomic molecule.
引文
1. R.D. Levine, R.B. Bernstein, Molecular reaction dynamics, Oxford University Press, (1974).
2. J.Z.H. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific, Singapore, (1999).
3. A.N. Brook and D.C. Clary, J. Chem. Phys. 92, 4178 (1990).
4. (a) Q. Sun and J.M. Bowman, J. Chem. Phys. 92, 5201 (1990). (b) Q. Sun and D.L. Yan, N.S. Wang, J.M. Bowman and M.C. Lin, ibid, 93, 4730(1990).
5. R. Kosloff, J. Chem. Phys. 92, 2087 (1988).
6. (a) D.J. Kouri and R.C. Mowrey, J. Chem. Phys. 86, 2087 (1987). (b) Y. Sun, R.C. Mowrey and D.J. Kouri, J. Chem. Phys. 87, 339 (1987). (c) Y. Sun, R.S. Judson and D.J. Kouri, J. Chem. Phys. 90, 241 (1989).
7. D. Neuhauser, J. Chem. Phys. 100, 9272 (1994).
8. (a) D.H. Zhang, J.Z.H. Zhang, Y.C. Zhang, D.Y. Wang and Q.G. Zhang, J. Chem. Phys. 102, 7400 (1995). (b) Y.C. Zhang, D.S. Zhang, W. Li, Q.G. Zhang, D.Y. Wang, D.H. Zhang and J.Z.H. Zhang, J. Phys. Chem. 99, 16824 (1995).
9. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 101, 1146 (1994).
10. Y.C. Zhang, Y.B. Zhang, L.X. Zhan, S.L. Zhang, D.H. Zhang, J.Z.H. Zhang, Chin. Phys. Lett. 15, 16 (1998).
11. D.H. Zhang, M.A. Collins and S.Y. Lee, Science. 290, 961 (2000).
12. J.Z.H. Zhang, J. Chem. Phys. 111, 3929 (1999).
13. M.J.T. Jordan and R.G. Gilbert, J. Chem. Phys. 102, 5669 (1995).
14. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 112, 585 (2000).
15. E.B. Wilson, Jr., and J.B. Howard, J. Chem. Phys. 4, 260 (1936).
16. B.T. Darling and D.M. Dennison, Phys. Rev. 57, 128 (1940).
17. J.K.G. Watson, Mol. Phys. 15,479 (1968).
18. R.C. Mowrey, J. Chem. Phys. 60, 633 (1991).
19. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 101, 1146 (1994).
20. J.A. Fleck, Jr., J.R. Morris and M.D. Feit, Appl. Phys. 10, 129 (1976).
21. M.D. Feit, J.A. Fleck, Jr., andA. Steiger, J. Comput. Phys. 47, 412 (1982).
22. (a) D.H. Zhang, O.A. Shrfeddin and J.Z.H. Zhang, Chem. Phys. 167, 137 (1992). (b) D. Neuhauser, M. Baer et.al., Comput. Phys. Commun. 63,460 (1991).
23. D.O. Harris, G.G Engerholm et.al., J. Chem. Phys. 43, 1515 (1965).
24. O. Sharafeddin and J.Z.H. Zhang, Chem. Phys. Lett. 204, 190 (1993).
25. J. Echave and D.C. Clary, Chem. Phys. Lett. 190, 225 (1992).
26. (a) J.V. Lill, G.A. Paker et.al., Chem. Phys. Lett. 89, 483 (1982). (b) J.C. Light, I.P. Hamilton et.al., J. Chem. Phys. 82, 1400 (1985).
27. (a) D.E. Manolopoulos et.al., Chem. Phys. Lett. 152, 23 (1988). (b) Z. Bacic, J.D. Kpress et.al., J. Chem. Phys. 92, 2344 (1990).
28. E. Kraka, J. Gauss, and D. Cremer, J. Chem. Phys. 99, 5306 (1993).
29. W.H. Miller, Annu. Rev. Phys. Chem. 41,245 (1990).
30. M.L. Wang, Y.M. Li and J.Z.H. Zhang, D.H. Zhang, J. Chem. Phys. 113, 1802 (2000).
2. J.Z.H. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific, Singapore, (1999).
3. A.N. Brook and D.C. Clary, J. Chem. Phys. 92, 4178 (1990).
4. (a) Q. Sun and J.M. Bowman, J. Chem. Phys. 92, 5201 (1990). (b) Q. Sun and D.L. Yan, N.S. Wang, J.M. Bowman and M.C. Lin, ibid, 93, 4730(1990).
5. R. Kosloff, J. Chem. Phys. 92, 2087 (1988).
6. (a) D.J. Kouri and R.C. Mowrey, J. Chem. Phys. 86, 2087 (1987). (b) Y. Sun, R.C. Mowrey and D.J. Kouri, J. Chem. Phys. 87, 339 (1987). (c) Y. Sun, R.S. Judson and D.J. Kouri, J. Chem. Phys. 90, 241 (1989).
7. D. Neuhauser, J. Chem. Phys. 100, 9272 (1994).
8. (a) D.H. Zhang, J.Z.H. Zhang, Y.C. Zhang, D.Y. Wang and Q.G. Zhang, J. Chem. Phys. 102, 7400 (1995). (b) Y.C. Zhang, D.S. Zhang, W. Li, Q.G. Zhang, D.Y. Wang, D.H. Zhang and J.Z.H. Zhang, J. Phys. Chem. 99, 16824 (1995).
9. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 101, 1146 (1994).
10. Y.C. Zhang, Y.B. Zhang, L.X. Zhan, S.L. Zhang, D.H. Zhang, J.Z.H. Zhang, Chin. Phys. Lett. 15, 16 (1998).
11. D.H. Zhang, M.A. Collins and S.Y. Lee, Science. 290, 961 (2000).
12. J.Z.H. Zhang, J. Chem. Phys. 111, 3929 (1999).
13. M.J.T. Jordan and R.G. Gilbert, J. Chem. Phys. 102, 5669 (1995).
14. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 112, 585 (2000).
15. E.B. Wilson, Jr., and J.B. Howard, J. Chem. Phys. 4, 260 (1936).
16. B.T. Darling and D.M. Dennison, Phys. Rev. 57, 128 (1940).
17. J.K.G. Watson, Mol. Phys. 15,479 (1968).
18. R.C. Mowrey, J. Chem. Phys. 60, 633 (1991).
19. D.H. Zhang and J.Z.H. Zhang, J. Chem. Phys. 101, 1146 (1994).
20. J.A. Fleck, Jr., J.R. Morris and M.D. Feit, Appl. Phys. 10, 129 (1976).
21. M.D. Feit, J.A. Fleck, Jr., andA. Steiger, J. Comput. Phys. 47, 412 (1982).
22. (a) D.H. Zhang, O.A. Shrfeddin and J.Z.H. Zhang, Chem. Phys. 167, 137 (1992). (b) D. Neuhauser, M. Baer et.al., Comput. Phys. Commun. 63,460 (1991).
23. D.O. Harris, G.G Engerholm et.al., J. Chem. Phys. 43, 1515 (1965).
24. O. Sharafeddin and J.Z.H. Zhang, Chem. Phys. Lett. 204, 190 (1993).
25. J. Echave and D.C. Clary, Chem. Phys. Lett. 190, 225 (1992).
26. (a) J.V. Lill, G.A. Paker et.al., Chem. Phys. Lett. 89, 483 (1982). (b) J.C. Light, I.P. Hamilton et.al., J. Chem. Phys. 82, 1400 (1985).
27. (a) D.E. Manolopoulos et.al., Chem. Phys. Lett. 152, 23 (1988). (b) Z. Bacic, J.D. Kpress et.al., J. Chem. Phys. 92, 2344 (1990).
28. E. Kraka, J. Gauss, and D. Cremer, J. Chem. Phys. 99, 5306 (1993).
29. W.H. Miller, Annu. Rev. Phys. Chem. 41,245 (1990).
30. M.L. Wang, Y.M. Li and J.Z.H. Zhang, D.H. Zhang, J. Chem. Phys. 113, 1802 (2000).