多原子分子反应体系的量子含时动力学研究
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摘要
近年来，随着量子散射理论的发展和计算能力的提高，多原子分子反应的量子动力学研究受到了人们的极大关注，态—态化学反应第一性原理研究将成为量子散射计算的主要任务。在过去的二十年里，量子散射理论得到了很大的发展，人们已经可以对四原子反应进行严格的量子计算。然而化学和生物领域涉及的是更多个原子的反应，因此，在目前的计算能力下，为了对多原子分子反应进行精确定量的动力学计算，发展一些实际可行的约化维数计算方法是非常必要的。为此，人们提出了一些用来处理多原子体系反应的约化维数方法，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。
本文引进了一种新的约化维数模型—半刚体振动转子靶(SVRT)模型。SVRT模型是一个处理多原子体系反应的约化模型，它对反应分子的空间转动作了精确处理，而反应分子的空间动力学性质在多原子分子反应中占有非常重要的地位，因此，SVRT模型保持了反应体系的空间动力学性质。
本文运用单原子与多原子分子反应的SVRT模型，首次对反应D+CD_4→CD_3+D_2进行了动力学研究。选取这个反应体系的原因有二：其一，D+CD_4→CD_3+D_2反应是一个典型的单原子与多原子分子的反应。其二，这个体系在实验上可以测量。因此，得到的结果对实验研究具有重要的参考意义，同时也有助于对更复杂的体系开展研究。目前对该反应体系，尚无全维量子动力学精确解。
根据这个理论，将反应多原子分子CD_4看作双原子分子D-CD_3，反应D+CD_4→CD_3+D_2看作单原子—双原子反应，把体系的反应简化为一个四维散射问题。在计算中，利用含时波包法得到了反应体系的哈密顿量，采用分裂算符法实现了波包的传播；为避免波函数的边界反射，采用了光学吸收势法。根据CD_4分子的C_(3v)对称性，选取了Jordan和Gilbert提出的半经验势能面。本文分别计算了该反应的反应几率、散
硕士学位论文 中文摘要
一
射截面和热速率常数。通过对反应几率的计算，得到了以下三个结论：第一，反应几率
随平动能的变化图象呈现出显著的量子共振特性。许多提取反应如H＋HZ、H＋＊巳反应
等都具有类似的特征。第二，D－CD3分子的振动激发极大地提高了反应几率，而反应阈
能却随分子的振动激发明显降低，这说明反应分子的振动能对分子的碰撞反应有重要贡
献。第三，反应分子的初始转动态对反应几率的影响表现出很强的空间效应。CD。处于
基态和振动激发态时，该反应的总散射截面随平动能的变化表明，振动激发极大地提高
了散射截面曲线，并且，当振动量子数由0变为1时，反应阈能降低约0．3eV这与由反
应几率得到的结果一致。此外，本文还计算了CD4分子处于基态和振动激发态时该反应
的热速率常数，并将CD。分子处于基态时的速率常数与相同情况下H＋CH。反应的速率
常数作了比较。
同时，本文首次运用多原子分子与表面反应的 SVRT模型，对 CH4和 CD4在 Ni门）
表面的解离吸附进行了动力学研究。这里，Ni表面被看作是光滑静止的。CH4在Ni＊）
表面的解离吸附是工业生产中的一个重要环节，所以这个课题一直被广为关注。由于二
维计算只考虑了分子的振动，其解离几率总是高于实验结果。而三维计算虽然考虑了分
子的转动对解离过程的影响，它的结论也只是与实验结果定性的保持一致。本文的四维
计算结果更为准确，达到了与实验结果较好的定量符合。
本文还计算了CH4分子处于不同振动态时解离几率随平动能的变化，结果表明，振
动激发极大地提高了解离几率。其反应趋势，与其它理论模型得到的结果一致。反应分
子处于基态时CH4分子的解离几率比CD4的要高得多，这是由它们不同的零点能和量子
隧道效应引起的，本文的结果，与实验结果及其它理论结果符合得较好。
论文共分为五章。第一章简要介绍了分子反应动力学的发展。第二章论述了单原子
与多原子分子反应的SVRT模型以及多原子分子与表面反应的SVRT模型。第三章介绍
了含时方法：含时波包法、分立变量表象、光学吸收势、分裂算符法、高斯型波包。第
四章中，将 SVRT模型应用于 D＋CD4 H CD3＋DZ反应，对该反应的反应几率、散射截面
以及热速率常数进行了计算，并对结果进行了理论分析。在第五章，运用多原子分子与表
面反应的 SVRT模型，对CH4和 CD4在Ni＊00）表面的解离吸附过程进行了研究，并对
同位素效应进行了讨论。
In recent years, the remarkable development of quantum scattering theory and the increasing abilities in relevant calculations have drawn more and more attention to the study of quantum dynamics of polyatomic reactions. The study of state-to-state chemical reaction dynamics from first principles is to be a major goal in quantum scattering calculations. During the last two decades, the quantum scattering theory has been substantially developed, and rigorous quantum reactive scattering calculations have already been done to reactions involving four atoms. The chemical or biological reactions, however, involve more than four atoms; therefore, considering the present calculation ability, it is necessary to develop some practical computational methods in order to carry out quantitatively accurate calculations in studying the quantum dynamics of polyatomic molecule reactions. To this end, some reduced dimensionality methods have been proposed for the study of polyatomic reaction systems such as adiabatic approach,
fixed geometry approximations and mixed quantum-classical dynamics methods.
In this thesis, a new reduced dimensionality method, semirigid vibrating rotor target (SVRT) model, is introduced. The SVRT model is a reduced model that is applicable to dealing with reaction dynamics of polyatomic systems and it can accurately describe spatial rotation of the reacting atoms. So the SVRT model preserves the correct stereodynamics of the reaction systems which is very important in polyatomic reactions.
In this thesis, the dynamics of the D+CD4 →CD3+D2 reaction is studied for the first time by using atom-polyatom SVRT model. There are two main reasons for selecting this reaction system: at first, D+CD4 reaction is a typical atom-polyatom reaction; secondly, this system is measurable in experiments. The results of the study will be of much reference value for
experiment researches and for further study of more complicated systems. At present, there is no full-dimensional accurate quantum dynamics solution available to this reaction system.
According to this theory, the reactive polyatomic molecule CD4 is regarded as a diatomic molecule D-CD3, therefore the reaction system can be regarded as an atom-diatom reaction system, thus reducing the system to a four-dimensional scattering system. In the process of calculation, the time-dependent wave packet method is used to obtain the Hamiltonian of reaction system; the split-operator method is employed to propagate the wave packet. To avoid boundary reflection of wave function, an optical absorbing potential is used in the calculation process. And considering the C3v symmetry of the molecule CD4, the
semiempirical potential energy surface developed by Jordan and Gilbert is employed for the calculation. In this thesis, reaction probability, scattering cross section and thermal rate constant are calculated. Three conclusions can be drawn from our calculations of the reaction probability: first, the graph of the calculated reaction probability changing with the energy dependence shows characteristic oscillatory structures, which are similar to those observed in many abstraction reactions such as H+H2 and H+CH4; second, the excitation of the stretching vibration of molecule D-CD3 enhances the reaction probability significantly, while the reaction threshold decreases with the vibrating excitation, which implies the substantial contribution made by the vibrating energy of the reacting molecules to the collision reaction of the molecules; third, detailed study of the effect of initial rotational states on reaction probability shows that the steric effect is strong. As demonstrated by the integral cross sections
varying with the translational energy when CD4 is at v=0 or v=l, the vibrational excitation improves the reaction cross section significantly, and the reaction threshold decreases by about 0.3eV when the vibrating quantum number changes from 0 to 1 , which is consistent with the result obtained by reaction probability. Besides, the rate constants of the rea
本文引进了一种新的约化维数模型—半刚体振动转子靶(SVRT)模型。SVRT模型是一个处理多原子体系反应的约化模型，它对反应分子的空间转动作了精确处理，而反应分子的空间动力学性质在多原子分子反应中占有非常重要的地位，因此，SVRT模型保持了反应体系的空间动力学性质。
本文运用单原子与多原子分子反应的SVRT模型，首次对反应D+CD_4→CD_3+D_2进行了动力学研究。选取这个反应体系的原因有二：其一，D+CD_4→CD_3+D_2反应是一个典型的单原子与多原子分子的反应。其二，这个体系在实验上可以测量。因此，得到的结果对实验研究具有重要的参考意义，同时也有助于对更复杂的体系开展研究。目前对该反应体系，尚无全维量子动力学精确解。
根据这个理论，将反应多原子分子CD_4看作双原子分子D-CD_3，反应D+CD_4→CD_3+D_2看作单原子—双原子反应，把体系的反应简化为一个四维散射问题。在计算中，利用含时波包法得到了反应体系的哈密顿量，采用分裂算符法实现了波包的传播；为避免波函数的边界反射，采用了光学吸收势法。根据CD_4分子的C_(3v)对称性，选取了Jordan和Gilbert提出的半经验势能面。本文分别计算了该反应的反应几率、散
硕士学位论文 中文摘要
一
射截面和热速率常数。通过对反应几率的计算，得到了以下三个结论：第一，反应几率
随平动能的变化图象呈现出显著的量子共振特性。许多提取反应如H＋HZ、H＋＊巳反应
等都具有类似的特征。第二，D－CD3分子的振动激发极大地提高了反应几率，而反应阈
能却随分子的振动激发明显降低，这说明反应分子的振动能对分子的碰撞反应有重要贡
献。第三，反应分子的初始转动态对反应几率的影响表现出很强的空间效应。CD。处于
基态和振动激发态时，该反应的总散射截面随平动能的变化表明，振动激发极大地提高
了散射截面曲线，并且，当振动量子数由0变为1时，反应阈能降低约0．3eV这与由反
应几率得到的结果一致。此外，本文还计算了CD4分子处于基态和振动激发态时该反应
的热速率常数，并将CD。分子处于基态时的速率常数与相同情况下H＋CH。反应的速率
常数作了比较。
同时，本文首次运用多原子分子与表面反应的 SVRT模型，对 CH4和 CD4在 Ni门）
表面的解离吸附进行了动力学研究。这里，Ni表面被看作是光滑静止的。CH4在Ni＊）
表面的解离吸附是工业生产中的一个重要环节，所以这个课题一直被广为关注。由于二
维计算只考虑了分子的振动，其解离几率总是高于实验结果。而三维计算虽然考虑了分
子的转动对解离过程的影响，它的结论也只是与实验结果定性的保持一致。本文的四维
计算结果更为准确，达到了与实验结果较好的定量符合。
本文还计算了CH4分子处于不同振动态时解离几率随平动能的变化，结果表明，振
动激发极大地提高了解离几率。其反应趋势，与其它理论模型得到的结果一致。反应分
子处于基态时CH4分子的解离几率比CD4的要高得多，这是由它们不同的零点能和量子
隧道效应引起的，本文的结果，与实验结果及其它理论结果符合得较好。
论文共分为五章。第一章简要介绍了分子反应动力学的发展。第二章论述了单原子
与多原子分子反应的SVRT模型以及多原子分子与表面反应的SVRT模型。第三章介绍
了含时方法：含时波包法、分立变量表象、光学吸收势、分裂算符法、高斯型波包。第
四章中，将 SVRT模型应用于 D＋CD4 H CD3＋DZ反应，对该反应的反应几率、散射截面
以及热速率常数进行了计算，并对结果进行了理论分析。在第五章，运用多原子分子与表
面反应的 SVRT模型，对CH4和 CD4在Ni＊00）表面的解离吸附过程进行了研究，并对
同位素效应进行了讨论。
In recent years, the remarkable development of quantum scattering theory and the increasing abilities in relevant calculations have drawn more and more attention to the study of quantum dynamics of polyatomic reactions. The study of state-to-state chemical reaction dynamics from first principles is to be a major goal in quantum scattering calculations. During the last two decades, the quantum scattering theory has been substantially developed, and rigorous quantum reactive scattering calculations have already been done to reactions involving four atoms. The chemical or biological reactions, however, involve more than four atoms; therefore, considering the present calculation ability, it is necessary to develop some practical computational methods in order to carry out quantitatively accurate calculations in studying the quantum dynamics of polyatomic molecule reactions. To this end, some reduced dimensionality methods have been proposed for the study of polyatomic reaction systems such as adiabatic approach,
fixed geometry approximations and mixed quantum-classical dynamics methods.
In this thesis, a new reduced dimensionality method, semirigid vibrating rotor target (SVRT) model, is introduced. The SVRT model is a reduced model that is applicable to dealing with reaction dynamics of polyatomic systems and it can accurately describe spatial rotation of the reacting atoms. So the SVRT model preserves the correct stereodynamics of the reaction systems which is very important in polyatomic reactions.
In this thesis, the dynamics of the D+CD4 →CD3+D2 reaction is studied for the first time by using atom-polyatom SVRT model. There are two main reasons for selecting this reaction system: at first, D+CD4 reaction is a typical atom-polyatom reaction; secondly, this system is measurable in experiments. The results of the study will be of much reference value for
experiment researches and for further study of more complicated systems. At present, there is no full-dimensional accurate quantum dynamics solution available to this reaction system.
According to this theory, the reactive polyatomic molecule CD4 is regarded as a diatomic molecule D-CD3, therefore the reaction system can be regarded as an atom-diatom reaction system, thus reducing the system to a four-dimensional scattering system. In the process of calculation, the time-dependent wave packet method is used to obtain the Hamiltonian of reaction system; the split-operator method is employed to propagate the wave packet. To avoid boundary reflection of wave function, an optical absorbing potential is used in the calculation process. And considering the C3v symmetry of the molecule CD4, the
semiempirical potential energy surface developed by Jordan and Gilbert is employed for the calculation. In this thesis, reaction probability, scattering cross section and thermal rate constant are calculated. Three conclusions can be drawn from our calculations of the reaction probability: first, the graph of the calculated reaction probability changing with the energy dependence shows characteristic oscillatory structures, which are similar to those observed in many abstraction reactions such as H+H2 and H+CH4; second, the excitation of the stretching vibration of molecule D-CD3 enhances the reaction probability significantly, while the reaction threshold decreases with the vibrating excitation, which implies the substantial contribution made by the vibrating energy of the reacting molecules to the collision reaction of the molecules; third, detailed study of the effect of initial rotational states on reaction probability shows that the steric effect is strong. As demonstrated by the integral cross sections
varying with the translational energy when CD4 is at v=0 or v=l, the vibrational excitation improves the reaction cross section significantly, and the reaction threshold decreases by about 0.3eV when the vibrating quantum number changes from 0 to 1 , which is consistent with the result obtained by reaction probability. Besides, the rate constants of the rea
引文
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