多原子分子反应散射的含时量子动力学研究
摘要
分子反应动力学是化学反应动力学的一个重要分支。用量子理论来研究分子反应的动力学规律是当前研究的重要课题之一。近年来，随着量子散射理论的发展和计算机运算能力的提高，多原子分子反应的量子动力学研究有了长足的进步。特别是态-态化学反应的第一性原理的研究更是成为反应散射的主要任务。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。然而化学和生物所感兴趣的绝大多数是大分子(多于4个原子)。随着原子数目和自由度的增加，对四原子以上体系进行动力学研究困难很大。因此，探索和发展多原子分子化学反应的理论模型和计算方法是非常有必要的，为此，人们提出了一些处理多原子体系反应的理论模型和约化维数的计算方法。
本文采用一种最近提出的新的理论模型—半刚性振动转子靶(Semirigid Vibrating Rotor Target—SVRT)模型研究多原子分子反应。SVRT模型是一个处理多原子体系反应的约化维数模型。在这一模型中，参加反应的多原子分子被处理为两个不同的刚性部分，这两个刚性部分能沿通过它们质心的直线做一维振动，它的空间运动被严格处理为一个一般的不对称转子。由于它较准确地处理了空间转动，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。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体系。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。
本文运用原子—多原子分子反应的SVRT模型，首次对六原子反应体系D+CH_4→HD+CH_3，O(~3P)+CH_4→OH+CH_3，O(~3P)+CD_4→OD+CD_3进行了量子动力学研究。根据模型理论，反应多原子分子H-CH_3(D-CD_3)被看作一个半刚性振动转子，由一个H(D)原子和CH_3(CD_3)两部分组成。由于CH_3(CD_3)被处理成为刚体，CH_3(CD_3)的几何结构被固定，在反应过程中，CH_3(CD_3)保持C_(3v)对称性，所以，所有几何参数的选取都必须保持这种CH_3(CD_3)部分的C_(3v)对称，因此可用4个自由度描述反应体系。本文利用量子含时波包法来模拟D+CH_4→HD+CH_3，O(~3P)+CH_4
博士学位论文
摘要
一oH+eH;，o(3尸)+eD4~00+eD:反应，采用J。r-dan和Gilbert提出的从头计算
的势能面，分别计算了上述三个反应体系的基态、振动激发态和不同转动激发
态的反应几率，基态的总散射截面和热速率常数以及D+CH;反应的第一激发态
的总散射截面与热速率常数。
通过比较和分析计算结果，我们得到如下结论:第一，在接近能垒高度时，
个体系均有可观测的反应几率，这说明量子隧道效应显著;第二，H一CH3
(D一cD3)分子的振动激发极大地提高了反应几率，而反应闭能却随分子的振动
激发明显降低，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，
反应分子的不同转动态对反应几率的影响表明:(l)反应分子的转动能的增加，
对提取反应有重要贡献，但基本不影响反应阂能值;(2)三个体系的反应具有
很强的空间立体效应，反应分子的初始空间几何方位对反应几率起着重要的影
响作用;第四，三个反应体系的总反应截面都随平动能的增大而增大，热速率
常数都随温度的升高而增加。对D+CH;反应而言，振动激发极大地提高了总散
射截面曲线且反应阐能有显著降低，这与反应几率的变化规律是一致的，另外
振动激发态的速率常数远大于基态的速率常数，说明振动激发更有利于反应的
进行;第五，对D+CH;反应而言，反应几率随平动能的变化关系曲线呈现出显
著的量子共振结构。这一点与H+HZ，H+CH4等提取反应有类似的特征。但在总
散射截面中，这种强烈的共振结构不再存在。这是因为散射截面是通过对不同
J的反应几率进行求和得到，在求和时，不同J的振动结构相互抵消了。
总之，本文通过对。+eH4一HD+eH:，o(3尸)+eH4一。月+eH:，o(3P)+eo4一00+en3
反应的SVRT模型研究，揭示了体系中某些重要的动力学微观物理机制，为燃
烧化学提供了有价值的可参考数据。同时通过研究也证明在研究涉及多原子分
子的化学反应中，SVRT模型是一个比较准确和通用的模型。从理论上讲，SV尺T
模型可适用于任意的涉及原子一多原子分子的反应，值得应用到其它的多原子
分子反应体系中去。
Research with quantum theories on the rules of molecular reaction dynamics, which is a main branch of chemical reaction dynamics, is currently one of the most important research topics. With the already ongoing development of quantum scattering theory and the enhancement of computer calculating capacity, enormous progress has been made on the research of polyatomic molecule reaction dynamics, especially on that of the first principles for the state-to-state chemical reaction, which becomes the main task of reaction scattering. Although accurate full quantum calculations can be made currently on reaction systems for four-or-less-atom molecules, what biology and chemistry concerns most are large molecules containing more than four atoms. With the increase of atomic amount and the degrees of freedom, research on dynamics for more-than-four-atom systems becomes more and more difficult, which is why there is great necessity to explore and develop new theory models and calculating methods for polyatomic molecules'
chemical reaction. Therefore, some theory models and dimension-reduced calculating methods have been provided.
In this paper a recently offered theory model-semirigid vibrating rotor target (SVRT) model, which is a dimension-reduced model handling polyatomic system reaction, is adopted to study polyatomic molecule reaction. In SVRT model polyatomic molecule whose spacial locomotion can be accurately treated as a regular non-symmetry rotor is dealt with as two different rigid segments which both can vibrate one-dimensionly through the line of their centroid. Since SVRT model can relatively correctly deal with the spacial locomotion, it can exactly demonstrate reaction system's steric dynamics effects, as is a very crucial factor in the research for
polyatomic molecule reaction. This model is adaptive to polyatomic molecule one of whose bond is relatively weaker and which can be divided into two segments at the end of the reaction. For polyatomic molecule reaction system, 7 degrees of freedom are necessary to describe it and for atom-polyatom molecule reaction system, only 4 degrees of freedom are much enough.
In this paper, the quantum dynamics research on the six-atom molecule reaction system for D+CHHD+CH, 0(P) +CHOH+CH, and 0(P) +CDOD+CD is for the first time explored with SVRT model. According to the model theory, the reaction polyatomic molecule H-CH (D-CD) is regarded as a semirigid vibrating rotor which is made up of one H(D) atom and one CH(CD) whose geometry structure is fixed. Since CH3(CD) is dealt as rigid and maintain C symmetry in the reaction process, four degrees of freedom are enough to describe the reaction system. In the paper, the time-dependent wave packet method is used to simulate D+CH4HD+CH3, O+CH OH+CH and O+CD4OD+CD3 reactions and the Jordan and Gilbert provided potential energy surface is adapted to calculate separately the above-mentioned three reaction systems' reaction probability for ground state, vibrating excited state and different rotating excited states, the total cross-section and the rate constant for the ground state, and the total cross-section as well as the rate constant for the D+CH4 reaction's the first excited state.
After comparing and analyzing the calculated results, we get the following conclusions: First, each of the three reaction systems has observable reaction probability when it approaches the barrier, which indicates quantum runnel effects exist obviously. Second, The fact that H-CH(D-CD) molecules' vibrating exciting increase the reaction probability enormously while they decreases the threshold evidently illustrates that the molecule's vibrating energy makes great contribution to collision reaction. Third, the different vibrating states for the molecule have on the reaction probability influences, including that the increase of molecules' vibrating energy makes great contribution to abstract reaction while it has little effects on the reaction threshold and that the initial geometry orientation for the reaction molecule has important influence on the
本文采用一种最近提出的新的理论模型—半刚性振动转子靶(Semirigid Vibrating Rotor Target—SVRT)模型研究多原子分子反应。SVRT模型是一个处理多原子体系反应的约化维数模型。在这一模型中，参加反应的多原子分子被处理为两个不同的刚性部分，这两个刚性部分能沿通过它们质心的直线做一维振动，它的空间运动被严格处理为一个一般的不对称转子。由于它较准确地处理了空间转动，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。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体系。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。
本文运用原子—多原子分子反应的SVRT模型，首次对六原子反应体系D+CH_4→HD+CH_3，O(~3P)+CH_4→OH+CH_3，O(~3P)+CD_4→OD+CD_3进行了量子动力学研究。根据模型理论，反应多原子分子H-CH_3(D-CD_3)被看作一个半刚性振动转子，由一个H(D)原子和CH_3(CD_3)两部分组成。由于CH_3(CD_3)被处理成为刚体，CH_3(CD_3)的几何结构被固定，在反应过程中，CH_3(CD_3)保持C_(3v)对称性，所以，所有几何参数的选取都必须保持这种CH_3(CD_3)部分的C_(3v)对称，因此可用4个自由度描述反应体系。本文利用量子含时波包法来模拟D+CH_4→HD+CH_3，O(~3P)+CH_4
博士学位论文
摘要
一oH+eH;，o(3尸)+eD4~00+eD:反应，采用J。r-dan和Gilbert提出的从头计算
的势能面，分别计算了上述三个反应体系的基态、振动激发态和不同转动激发
态的反应几率，基态的总散射截面和热速率常数以及D+CH;反应的第一激发态
的总散射截面与热速率常数。
通过比较和分析计算结果，我们得到如下结论:第一，在接近能垒高度时，
个体系均有可观测的反应几率，这说明量子隧道效应显著;第二，H一CH3
(D一cD3)分子的振动激发极大地提高了反应几率，而反应闭能却随分子的振动
激发明显降低，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，
反应分子的不同转动态对反应几率的影响表明:(l)反应分子的转动能的增加，
对提取反应有重要贡献，但基本不影响反应阂能值;(2)三个体系的反应具有
很强的空间立体效应，反应分子的初始空间几何方位对反应几率起着重要的影
响作用;第四，三个反应体系的总反应截面都随平动能的增大而增大，热速率
常数都随温度的升高而增加。对D+CH;反应而言，振动激发极大地提高了总散
射截面曲线且反应阐能有显著降低，这与反应几率的变化规律是一致的，另外
振动激发态的速率常数远大于基态的速率常数，说明振动激发更有利于反应的
进行;第五，对D+CH;反应而言，反应几率随平动能的变化关系曲线呈现出显
著的量子共振结构。这一点与H+HZ，H+CH4等提取反应有类似的特征。但在总
散射截面中，这种强烈的共振结构不再存在。这是因为散射截面是通过对不同
J的反应几率进行求和得到，在求和时，不同J的振动结构相互抵消了。
总之，本文通过对。+eH4一HD+eH:，o(3尸)+eH4一。月+eH:，o(3P)+eo4一00+en3
反应的SVRT模型研究，揭示了体系中某些重要的动力学微观物理机制，为燃
烧化学提供了有价值的可参考数据。同时通过研究也证明在研究涉及多原子分
子的化学反应中，SVRT模型是一个比较准确和通用的模型。从理论上讲，SV尺T
模型可适用于任意的涉及原子一多原子分子的反应，值得应用到其它的多原子
分子反应体系中去。
Research with quantum theories on the rules of molecular reaction dynamics, which is a main branch of chemical reaction dynamics, is currently one of the most important research topics. With the already ongoing development of quantum scattering theory and the enhancement of computer calculating capacity, enormous progress has been made on the research of polyatomic molecule reaction dynamics, especially on that of the first principles for the state-to-state chemical reaction, which becomes the main task of reaction scattering. Although accurate full quantum calculations can be made currently on reaction systems for four-or-less-atom molecules, what biology and chemistry concerns most are large molecules containing more than four atoms. With the increase of atomic amount and the degrees of freedom, research on dynamics for more-than-four-atom systems becomes more and more difficult, which is why there is great necessity to explore and develop new theory models and calculating methods for polyatomic molecules'
chemical reaction. Therefore, some theory models and dimension-reduced calculating methods have been provided.
In this paper a recently offered theory model-semirigid vibrating rotor target (SVRT) model, which is a dimension-reduced model handling polyatomic system reaction, is adopted to study polyatomic molecule reaction. In SVRT model polyatomic molecule whose spacial locomotion can be accurately treated as a regular non-symmetry rotor is dealt with as two different rigid segments which both can vibrate one-dimensionly through the line of their centroid. Since SVRT model can relatively correctly deal with the spacial locomotion, it can exactly demonstrate reaction system's steric dynamics effects, as is a very crucial factor in the research for
polyatomic molecule reaction. This model is adaptive to polyatomic molecule one of whose bond is relatively weaker and which can be divided into two segments at the end of the reaction. For polyatomic molecule reaction system, 7 degrees of freedom are necessary to describe it and for atom-polyatom molecule reaction system, only 4 degrees of freedom are much enough.
In this paper, the quantum dynamics research on the six-atom molecule reaction system for D+CHHD+CH, 0(P) +CHOH+CH, and 0(P) +CDOD+CD is for the first time explored with SVRT model. According to the model theory, the reaction polyatomic molecule H-CH (D-CD) is regarded as a semirigid vibrating rotor which is made up of one H(D) atom and one CH(CD) whose geometry structure is fixed. Since CH3(CD) is dealt as rigid and maintain C symmetry in the reaction process, four degrees of freedom are enough to describe the reaction system. In the paper, the time-dependent wave packet method is used to simulate D+CH4HD+CH3, O+CH OH+CH and O+CD4OD+CD3 reactions and the Jordan and Gilbert provided potential energy surface is adapted to calculate separately the above-mentioned three reaction systems' reaction probability for ground state, vibrating excited state and different rotating excited states, the total cross-section and the rate constant for the ground state, and the total cross-section as well as the rate constant for the D+CH4 reaction's the first excited state.
After comparing and analyzing the calculated results, we get the following conclusions: First, each of the three reaction systems has observable reaction probability when it approaches the barrier, which indicates quantum runnel effects exist obviously. Second, The fact that H-CH(D-CD) molecules' vibrating exciting increase the reaction probability enormously while they decreases the threshold evidently illustrates that the molecule's vibrating energy makes great contribution to collision reaction. Third, the different vibrating states for the molecule have on the reaction probability influences, including that the increase of molecules' vibrating energy makes great contribution to abstract reaction while it has little effects on the reaction threshold and that the initial geometry orientation for the reaction molecule has important influence on the
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