碳族元素氢化物与氢反应的量子含时动力学研究
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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得动力学规律是其重要课题之一。在过去的二十年里,量子散射理论得到了极大的发展,随着计算能力的不断提高,人们已经可以对四原子反应体系进行严格的全量子计算。然而在化学和生物等领域,往往涉及更多个原子的反应。对于超过四原子的反应体系,不可能对其进行全维的量子动力学计算。因此,为了对多原子分子反应进行精确定量的动力学计算,人们提出了一些约化维数的方法来降低计算难度,如绝热修正法、固定几何性质近似法、以及量子—经典动力学方法等。
本文采用一种新的约化维数模型—半刚性振转靶(SVRT)模型,参加反应的多原子分子(靶分子)被处理为两个不同的刚性部分,这两个刚性部分在其质心的连线方向作一维振动,它的空间运动被严格处理为一个一般的不对称转子。由于它较准确的处理空间转动,所以SVRT 模型能够正确地体现反应体系的立体动力学效应,这一点对研究多原子分子反应是非常重要的。此模型适用于反应体系的靶分子中有一键较弱,且反应结束后可分为两部分。对于一般的多原子—多原子分子反应体系,可以用7 个自由度来描述,而对于单原子—多原子分子反应仅需4 个自由度来描述。
本文首次将单原子—多原子分子反应体系的SVRT 模型运用到H + SiH_4 →SiH_3 + H_2 、H + GeH_4 →GeH_3 + H_2 两反应体系中。选取此反应体系的原因有三:其一,此反应是典型的单原子—多原子分子反应。其二,这两个体系在实验上可以测量,因此其理论结果可以与实验相对比,从而进一步验证理论的正确性以及所选势能面的准确性。其三,对于H + CH_4 →CH_3 + H_2反应体系,此理论已经对其进行了全面的详细地研究,通过研究碳族另外两种元素的氢化物与氢的反应,可以对比它们在能垒高度、反应程度,从而找出其内在的一些规律性的东西,纵向比较可以更好的验证理论及势能面的正确性。
根据这个理论,将反应多原子分子XH4(X=Si、Ge)看作双原子分子H -XH_3,反应H + XH_4 →XH_3 + H_2 看作单原子—双原子反应,把体系的反应简化为一个四维
Molecular reaction dynamics is a branch of chemical reaction dynamics. Researchwith quantum theory on the rule of molecular chemical reaction is one of the mostimportant topics. In the past twenty years, with the great development of quantum scattingtheory and the enhancement of calculating capacity, it was possible to take full quantumcalculation on reactions with no more than four atoms. But in chemical and biologicalfields, reactions always deal with more than four atoms. So, to take accurate full quantumcalculations on such reactions, some models and dimension-reduced calculating methodshave been provided to reduce the calculation difficulty such as adiabatic approach, fixedgeometry approximations and mixed quantum-classical dynamics methods.
In this thesis, a new reduced dimensionality method, semirigid vibrating rotortarget(SVRT) model, is introduced. In SVRT model polyatomic molecule whose speciallocomotion can be accurately treated as a regular non-symmetry rotor is dealt with as twodifferent rigid segments which both can vibrate one-dimensionally through the line of theircentroid. Since SVRT model can relatively deal with the special locomotion, it can exactlydemonstrate reaction system’s steric dynamics effect, which is very crucial in moleculereaction. This model is adaptive to polyatomic molecule one of whose bond is relativelyweaker and which can be divided into two segments at the end of the reaction. For thepolyatomic molecule reaction system, 7 degrees of freedom are necessary to describe it andfor atom-polyatom molecule reaction system, only 4 degrees of freedom are enough.
In this thesis, the dynamics of theH + SiH_4 →SiH_3 + H_2 、H+GeH_4 →GeH_3 +H_2 reactionsare studied for the first time by using atom-polyatom SVRT model. There are three mainreasons for selecting such reactions: First, they are typical atom-polyatom reactions;Second, these systems is measurable in experiments, so the results of the study will be ofmuch reference value for experiment researches and for further study of more complicated
systems; Third, researches onH +CH4 →CH3 + H2 reaction were taken fully in details withSVRT model. By studying the other two reactions between group IV hydride and hydrogen,then contrasting their reaction threshold energy, reaction probabilities, we can find theinner rules. The vertical contrast of these reactions can prove the credibility of SVRTmodel and the potential energy surface (PES). According to this theory, the reactive polyatomic molecule XH4 (X=Si,Ge)is regardedas a diatomic molecule H ? XH3, therefore the reaction system can be regarded as anatom-diatom reaction system, thus reducing the system to a four-dimensional scatteringsystem, and the ‘diatomic’molecule H ? XH3 always keeps the C3V symmetry. In theprocess of calculation, the time-dependent wave packet method is used; the split-operatormethod is employed to propagate the wave packet. To avoid boundary reflection of wavefunction, an optical absorbing potential is used in the calculation process. This thesisadapts Garcia’s PES got by ab initial calculation, and calculates the reaction probabilities,cross sections and rate constants of the two reactions. After comparing and analyzing the calculated results, we get the followingconclusions: First, each of the two reaction systems has observable reaction probabilitywhen it approaches the barrier, which indicates quantum tunnel effects exist obviously.Second, the behaving that vibrating exciting of target molecule H ? XH3 increases thereaction probability enormously while they decreases the threshold energy evidentlyillustrates that the molecule’s vibrating energy makes great contribution to collisionreaction. Third, the different rotating states for the molecule have on the reactionprobability influences, including that the increase of molecules’vibrating energy makesgreat contribution to abstract reaction while it has little effects on the reaction thresholdand that the initial geometry orientation for the reaction molecule has important influenceon the reaction probability. Fourth, the total cross-section of each of the reaction systemsincreases with the enlargement of the translational energy while the rate constant enhanceswith the rising of the temperature. By comparing the three Group IV hydride(X=C, Si, Ge),their rate constants increase respectively, then it shows that their stability much weaker in
本文采用一种新的约化维数模型—半刚性振转靶(SVRT)模型,参加反应的多原子分子(靶分子)被处理为两个不同的刚性部分,这两个刚性部分在其质心的连线方向作一维振动,它的空间运动被严格处理为一个一般的不对称转子。由于它较准确的处理空间转动,所以SVRT 模型能够正确地体现反应体系的立体动力学效应,这一点对研究多原子分子反应是非常重要的。此模型适用于反应体系的靶分子中有一键较弱,且反应结束后可分为两部分。对于一般的多原子—多原子分子反应体系,可以用7 个自由度来描述,而对于单原子—多原子分子反应仅需4 个自由度来描述。
本文首次将单原子—多原子分子反应体系的SVRT 模型运用到H + SiH_4 →SiH_3 + H_2 、H + GeH_4 →GeH_3 + H_2 两反应体系中。选取此反应体系的原因有三:其一,此反应是典型的单原子—多原子分子反应。其二,这两个体系在实验上可以测量,因此其理论结果可以与实验相对比,从而进一步验证理论的正确性以及所选势能面的准确性。其三,对于H + CH_4 →CH_3 + H_2反应体系,此理论已经对其进行了全面的详细地研究,通过研究碳族另外两种元素的氢化物与氢的反应,可以对比它们在能垒高度、反应程度,从而找出其内在的一些规律性的东西,纵向比较可以更好的验证理论及势能面的正确性。
根据这个理论,将反应多原子分子XH4(X=Si、Ge)看作双原子分子H -XH_3,反应H + XH_4 →XH_3 + H_2 看作单原子—双原子反应,把体系的反应简化为一个四维
Molecular reaction dynamics is a branch of chemical reaction dynamics. Researchwith quantum theory on the rule of molecular chemical reaction is one of the mostimportant topics. In the past twenty years, with the great development of quantum scattingtheory and the enhancement of calculating capacity, it was possible to take full quantumcalculation on reactions with no more than four atoms. But in chemical and biologicalfields, reactions always deal with more than four atoms. So, to take accurate full quantumcalculations on such reactions, some models and dimension-reduced calculating methodshave been provided to reduce the calculation difficulty such as adiabatic approach, fixedgeometry approximations and mixed quantum-classical dynamics methods.
In this thesis, a new reduced dimensionality method, semirigid vibrating rotortarget(SVRT) model, is introduced. In SVRT model polyatomic molecule whose speciallocomotion can be accurately treated as a regular non-symmetry rotor is dealt with as twodifferent rigid segments which both can vibrate one-dimensionally through the line of theircentroid. Since SVRT model can relatively deal with the special locomotion, it can exactlydemonstrate reaction system’s steric dynamics effect, which is very crucial in moleculereaction. This model is adaptive to polyatomic molecule one of whose bond is relativelyweaker and which can be divided into two segments at the end of the reaction. For thepolyatomic molecule reaction system, 7 degrees of freedom are necessary to describe it andfor atom-polyatom molecule reaction system, only 4 degrees of freedom are enough.
In this thesis, the dynamics of theH + SiH_4 →SiH_3 + H_2 、H+GeH_4 →GeH_3 +H_2 reactionsare studied for the first time by using atom-polyatom SVRT model. There are three mainreasons for selecting such reactions: First, they are typical atom-polyatom reactions;Second, these systems is measurable in experiments, so the results of the study will be ofmuch reference value for experiment researches and for further study of more complicated
systems; Third, researches onH +CH4 →CH3 + H2 reaction were taken fully in details withSVRT model. By studying the other two reactions between group IV hydride and hydrogen,then contrasting their reaction threshold energy, reaction probabilities, we can find theinner rules. The vertical contrast of these reactions can prove the credibility of SVRTmodel and the potential energy surface (PES). According to this theory, the reactive polyatomic molecule XH4 (X=Si,Ge)is regardedas a diatomic molecule H ? XH3, therefore the reaction system can be regarded as anatom-diatom reaction system, thus reducing the system to a four-dimensional scatteringsystem, and the ‘diatomic’molecule H ? XH3 always keeps the C3V symmetry. In theprocess of calculation, the time-dependent wave packet method is used; the split-operatormethod is employed to propagate the wave packet. To avoid boundary reflection of wavefunction, an optical absorbing potential is used in the calculation process. This thesisadapts Garcia’s PES got by ab initial calculation, and calculates the reaction probabilities,cross sections and rate constants of the two reactions. After comparing and analyzing the calculated results, we get the followingconclusions: First, each of the two reaction systems has observable reaction probabilitywhen it approaches the barrier, which indicates quantum tunnel effects exist obviously.Second, the behaving that vibrating exciting of target molecule H ? XH3 increases thereaction probability enormously while they decreases the threshold energy evidentlyillustrates that the molecule’s vibrating energy makes great contribution to collisionreaction. Third, the different rotating states for the molecule have on the reactionprobability influences, including that the increase of molecules’vibrating energy makesgreat contribution to abstract reaction while it has little effects on the reaction thresholdand that the initial geometry orientation for the reaction molecule has important influenceon the reaction probability. Fourth, the total cross-section of each of the reaction systemsincreases with the enlargement of the translational energy while the rate constant enhanceswith the rising of the temperature. By comparing the three Group IV hydride(X=C, Si, Ge),their rate constants increase respectively, then it shows that their stability much weaker in
引文
[1] R. D. Levine, R. B. Bernstein, Molecular reaction dynamics, Oxford University Press, (1974).
[2] R. Kosloff, J. Chem. Phys. 92, 2087 (1988).
[3] (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).
[4] D. Neuhauser, J. Chem. Phys. 100, 9272 (1994).
[5] (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).
[6] A. N. Brook and D. C. Clary, J. Chem. Phys. 92, 4178 (1990).
[7] Q. Sun and D. L. Yan, N. S. Wang, J. M. Bowman and M. C. Lin, J. Chem. Phys. 93, 4730 (1990).
[8] R. C. Mowrey and D. J. Kouri, J. Chem. Phys. 84, 6466(1986).
[9] J. Z. H. Zhang, J. Dai, W. Zhu, J. Phys. Chem. A, 101, 2746 (1997).
[10] D. Neuhauser, M. Baer, R. S. Judison, D. J. Kouri, Comput. Phys. Commun. 63, 460 (1991).
[11] N. Balakrishnan, C. Kalyanaraman, N. Sathyamurthy, Phys. Rep, 79,280,(1997).
[12] 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).
[13] D. H. Zhang, M. A. Collins and S. Y. Lee, Science. 290, 961 (2000).
[14] H. Szichman, I. Last, A. Baram, and M. Baer, J. Phys. Chem. 97, 6436 (1993).
[15] N. Balakrishnan and G. D. Billing, J. Chem. Phys. 101, 2785 (1994).
[16] U. Manthe, T. Seideman and W. H. Miller, J. Chem. Phys. 101, 4759 (1994).
[17] D. H. Zhang , J. C. Light and S. Y. Lee, J. Chem. Phys. 109, 79 (1998).
[18] W. Zhu, J. Z. H. Zhang, Y. C. Zhang and D. H. Zhang, J. Chem. Phys. 108, 3509 (1998).
[19] J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999).
[20] D. H. Zhang and J. C. Light, J. Chem. Phys. 104, 6184(1996).
[21] D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 1146 (1994).
[22] E. B. Wilson, Jr., J. C. Decius and P. C. Cross, Molecular Vibrations, Dover, New York,P273 (1980).
[23] E. B. Wilson, Jr., and J. B. Howard, J. Chem. Phys. 4, 260 (1936).
[24] B. T. Darling and D. M. Dennison, Phys. Rev. 57, 128 (1940).
[25] J. K. G. Watson, Mol. Phys. 15, 479 (1968).
[26] J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific, Singapore, (1998).
[27] R. C. Mowrey, J. Chem. Phys. 94, 7098 (1991).
[28] J. A. Fleck, Jr. J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[29] D. O. Harris, G. G. Engerholm et.al., J. Chem. Phys. 43, 1515 (1965).
[30] O. Sharafeddin and J. Z. H. Zhang, Chem. Phys. Lett. 204, 190 (1993).
[31] J. Echave and D. C. Clary, Chem. Phys. Lett. 190, 225 (1992).
[32] (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).
[33] (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).
[34] M. D. Feit, J. A. Fleck, J. Comput. Phys., 47, 412 (1982).
[35] C. Kreher, R. Theinl and K. H. Gericke, J. Chem. Phys. 104, 4481 (1996).
[36] J. Espinosa-Garcia, J. Sanson, J.C.Corchado, J. Chem. Phys.109, 466(1998)
[37] M. J. T. Jordan and R. G. Gilbert, J. Chem. Phys. 102, 5669 (1995).
[38] T. Joseph, R. Steckler and D. G.Truhlar, J. Chem. Phys. 87, 7036 (1987).
[39] K. D. Dobbs and D. A. Dixon, J. Phys. Chem.98, 5290(1994)
[40] T. Joseph, R. Steckler, and D. G. Truhlar, J. Chem. Phys. 87, 7036(1987)
[41] M. L. Wang, Y. M. Li and J. Z. H. Zhang, J. Phys. Chem. A. 105 2530(2001).
[42] M. L. Wang, J. Z. H. Zhang, J. Chem. Phys.116,6497(2002); 117,10429(2002)
[43] M. L. Wang and J. Z. H. Zhang, J. Chem. Phys.117, 3081(2002);117,10426 (2002).
[2] R. Kosloff, J. Chem. Phys. 92, 2087 (1988).
[3] (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).
[4] D. Neuhauser, J. Chem. Phys. 100, 9272 (1994).
[5] (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).
[6] A. N. Brook and D. C. Clary, J. Chem. Phys. 92, 4178 (1990).
[7] Q. Sun and D. L. Yan, N. S. Wang, J. M. Bowman and M. C. Lin, J. Chem. Phys. 93, 4730 (1990).
[8] R. C. Mowrey and D. J. Kouri, J. Chem. Phys. 84, 6466(1986).
[9] J. Z. H. Zhang, J. Dai, W. Zhu, J. Phys. Chem. A, 101, 2746 (1997).
[10] D. Neuhauser, M. Baer, R. S. Judison, D. J. Kouri, Comput. Phys. Commun. 63, 460 (1991).
[11] N. Balakrishnan, C. Kalyanaraman, N. Sathyamurthy, Phys. Rep, 79,280,(1997).
[12] 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).
[13] D. H. Zhang, M. A. Collins and S. Y. Lee, Science. 290, 961 (2000).
[14] H. Szichman, I. Last, A. Baram, and M. Baer, J. Phys. Chem. 97, 6436 (1993).
[15] N. Balakrishnan and G. D. Billing, J. Chem. Phys. 101, 2785 (1994).
[16] U. Manthe, T. Seideman and W. H. Miller, J. Chem. Phys. 101, 4759 (1994).
[17] D. H. Zhang , J. C. Light and S. Y. Lee, J. Chem. Phys. 109, 79 (1998).
[18] W. Zhu, J. Z. H. Zhang, Y. C. Zhang and D. H. Zhang, J. Chem. Phys. 108, 3509 (1998).
[19] J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999).
[20] D. H. Zhang and J. C. Light, J. Chem. Phys. 104, 6184(1996).
[21] D. H. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 1146 (1994).
[22] E. B. Wilson, Jr., J. C. Decius and P. C. Cross, Molecular Vibrations, Dover, New York,P273 (1980).
[23] E. B. Wilson, Jr., and J. B. Howard, J. Chem. Phys. 4, 260 (1936).
[24] B. T. Darling and D. M. Dennison, Phys. Rev. 57, 128 (1940).
[25] J. K. G. Watson, Mol. Phys. 15, 479 (1968).
[26] J. Z. H. Zhang, Theory and Application of Quantum Molecular Dynamics, World Scientific, Singapore, (1998).
[27] R. C. Mowrey, J. Chem. Phys. 94, 7098 (1991).
[28] J. A. Fleck, Jr. J. R. Morris, M. D. Feit, Appl. Phys. 10, 129 (1976).
[29] D. O. Harris, G. G. Engerholm et.al., J. Chem. Phys. 43, 1515 (1965).
[30] O. Sharafeddin and J. Z. H. Zhang, Chem. Phys. Lett. 204, 190 (1993).
[31] J. Echave and D. C. Clary, Chem. Phys. Lett. 190, 225 (1992).
[32] (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).
[33] (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).
[34] M. D. Feit, J. A. Fleck, J. Comput. Phys., 47, 412 (1982).
[35] C. Kreher, R. Theinl and K. H. Gericke, J. Chem. Phys. 104, 4481 (1996).
[36] J. Espinosa-Garcia, J. Sanson, J.C.Corchado, J. Chem. Phys.109, 466(1998)
[37] M. J. T. Jordan and R. G. Gilbert, J. Chem. Phys. 102, 5669 (1995).
[38] T. Joseph, R. Steckler and D. G.Truhlar, J. Chem. Phys. 87, 7036 (1987).
[39] K. D. Dobbs and D. A. Dixon, J. Phys. Chem.98, 5290(1994)
[40] T. Joseph, R. Steckler, and D. G. Truhlar, J. Chem. Phys. 87, 7036(1987)
[41] M. L. Wang, Y. M. Li and J. Z. H. Zhang, J. Phys. Chem. A. 105 2530(2001).
[42] M. L. Wang, J. Z. H. Zhang, J. Chem. Phys.116,6497(2002); 117,10429(2002)
[43] M. L. Wang and J. Z. H. Zhang, J. Chem. Phys.117, 3081(2002);117,10426 (2002).