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Ideas of Quantum Chemistry P83 shows how quantum mechanics is applied to chemistry to give it a theoretical foundation. The structure of the book (a TREE-form) emphasizes the logical relationships between various topics, facts and methods. It shows the reader which parts of the text are needed for understanding specific aspects of the subject matter. Interspersed throughout the text are short biographies of key scientists and their contributions to the development of the field. | 786 14. Intermolecular Motion of Electrons and Nuclei Chemical Reactions the molecule undergoes when oscillating perpendicularly29 to xIRC s . Simply the valley bottom profile results from the fact that the molecule hardly holds together when moving along the reaction coordinate s a chemical bond breaks while other bonds remain strong and it is not so easy to stretch their strings. This suggests that there is slow motion along s and fast oscillatory motion along the coordinates Qk. Since we are mostly interested in the slow motion along s we may average over the fast motion. The philosophy behind the idea is that while the system moves slowly along s it undergoes a large number of oscillations along Qk. After such vibrational averaging the only information that remains about the oscillations are the vibrational quantum levels for each of the oscillators the levels will depend on s . VIBRATIONALLY ADIABATIC APPROXIMATION The fast vibrational motions will be treated quantum mechanically and their total energy will enter the potential energy for the classical motion along s. This approximation parallels the adiabatic approximation made in Chapter 6 where the fast motion of electrons was separated from the slow motion of the nuclei. There the total electronic energy became the potential energy for the motion of nuclei here the total vibrational energy the energy of the corresponding harmonic oscillators in their quantum states becomes the potential energy for the slow motion along s. This concept is called the vibrationally adiabatic approximation. In this approximation to determine the stage of the reaction we give two classical quantities where the system is on the reaction path s and how fast the system moves along the reaction path ps . Also we need the quantum states of the oscillators vibrating perpendicularly to the reaction path vibrational quantum number vk 0 1 2 . for each of the oscillators . Therefore the potential energy for the slow motion along the .
