| Transition theories pointed out that each adiabatic chemical process must pass through a state called transition state in which the energy is higher than the reactants or products, and the transition state, which configuration is very unstable lies between the states where the chemical bond is created and broken. The property of the transition state and its existent time can give large amounts of information of the chemical reaction. Therefore the characters of molecular and electronical structures of the transition state being understood would assist us greatly in the comprehension of reactive mechanism and the factors which would affect the speed of chemical reaction, and also has great meaning for us to comprehend the channels of the reaction and the species and properties of the products.At present, the configuration, the energy, and the mechanical property of the transition state are presented mainly by ab initio. Also, the spectroscopy experiments can give some information. But because the transition state is an unstable intermediate state, which exists so shortly, most spectra can not be measured, and only dynamic methods can do. So the experimental research is very difficult. Although ab initio have gotien many numerical potential energy surface (PES)s of the transition state molecules, which are just some simple reactive systems, the method has not universality. Besides, the workload calculating using ab initio method is so large that it is very hard to gain the global PES for the whole space, especially when the system which contains more than several atoms is dealed with.Molecule's PES can be conveniently given using dynamic Lie algebraic method. We can introduce one U(4) group for every bond of the triatomic molecule. Then the dynamical symmetry group of the triatomic molecule is the direct product of two U(4) groups. Thus the molecule's vib-rotation Hamiltonian (it contains several coefficients) can be written as the sum of Casimir operators and the Majorana operator of the very group chain involved in the direct product group. The Majorana operator is used to describe the interaction between the chemical bonds. Then start with the U(4) algebraic Hamiltonian of the molecular vibrational high excited state, classify it using Intensive Boson Operator proposed by Gilmore, and the classicaltotal energy of the molecule is obtained. Order the kinetic energy zero, and the PES of the triatomic molecule is derived.In order to calculate out the PES of triatomic reactive system, we regarded in this thesis the transition state as "sub-stable molecule", and the reactive PES as "sub-stable molecular PES". So the PES formula was gotten (several unknown coefficients are included) according to the above statements. The expansion coefficients were determined using the method of least square through fitting to the ab initio numerical data about the reactive PES. Thus the PES of triatomic reactive system was achieved. Taking examples of the linear reactive system Cl+Na2, H+NH, Sr+HF and the bent system H+O2, The PESs were fitted, the analytical formulas of the PESs were derived, and the contour plots of them were figured out. By analyzing the plots, it could be seen that the analytical PESs we got is in good agreement with those coming from the source papers, and the PESs fitted reflect the reactive characters fairly well.Through our study, a way to obtain the PES of the reactive system by fitting ab initio data has been found from the theory. This method has solved the problem of the theoretic calculation due to the lack of spectroscopic data on the experiment. Furthermore, only part of the ab initio data is needed, not the data of the whole PES. therefore the workload is much reduced. The PES we got is applicable not only to the transition state region but to the region beyond that region. That means the method has extensive applicability. The reactive PES is the extension of the triatomic molecular PES, therefore it has important theoretic meaning and application. The thesis considers that the method involved is applicable universally to the triatomic reactive systems.Having obtained the reactive PES provides a basis for the study of the chemical property and the spectrum of the reactions, for the coefficients of the Hamilton operators can be derived from those in the potential energy expression. So the vib-rotational Hamiltonian of the "transition state sub-stable molecule" can be achieved, whose eigenvalues are the spectra of the transition state. In this way the energy level and spectrum of the system can be predicted from the theory.From the above, we can see that dynamic Lie algebraic method is a powerful tool to study the PES of the reactive system, which provides another important tool for the research of the atomic and molecular dynamics and the property of the transition state.The whole thesis is divided into five chapters. Chapter 1 is the overview. §1.1 chiefly introduced the present state of the transition state from the experimental and theoretical aspects. § 1.2 was the introduction of dynamical Lie algebraic method both on its application and on how to use it to study PES. Chapter 2 gave the theory and formulas when constructing the PES of the triatomic molecule by using Lie algebraic approach. Chapter 3 introduced the contents about the transition state theory. Chapter 4 was the emphasis of the thesis, in which we represented how to extend the theory of constructing triatomic molecular PES by Lie algebraic method to the reactive system. Taking examples of reactive systems Cl+Na2, NH+H. Sr+HF and H+O2 we calculated the reactive PES, and gave the results and analyses. Chapter 5 summarized the method of constructing the PES of triatomic reactive system, also it gave the perspectives for the development of the method. |
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