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Ideas of Quantum Chemistry P37

Ideas of Quantum Chemistry P37 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. | 326 8. Electronic Motion in the Mean Field Atoms and Molecules composed of molecular orbitals. At a certain level of approximation each molecular orbital is a home for two electrons. We will now learn on how to get the optimum molecular orbitals Hartree-Fock method . Despite some quite complex formulas which will appear below the main idea behind them is extremely simple. It can be expressed in the following way. Let us consider the road traffic the cars electrons move at fixed positions of buildings nuclei . The motion of the cars proves to be very complex as it does for the electrons and therefore the problem is extremely difficult. How can such a motion be described in an approximate way To describe such a complex motion one may use the so called mean field approximation paying the price of poor quality . In the mean field approximation method we focus on the motion of one car only considering its motion in such way that the car avoids those streets that are usually most jammed. In this chapter we will treat the electrons in a similar manner leaving the difficulties of considering the correlation of the motions of the electrons to Chapter 10 . Now the electrons will not feel the true electric field of the other electrons as it should be in a precise approach but rather their mean electric field i.e. averaged over their motions. Translating it into quantum mechanical language the underlying assumptions of the mean field method for the N identical particles here electrons are as follows there is a certain effective one-particle operator F i of an identical mathematical form for all particles i 1 2 . N which has the eigenfunctions k i.e. F k kfk such that Hf F F ef F where 1 is an approximate wave function to the exact wave function both functions normalized for the total system H is the electronic Hamiltonian in the clamped nuclei approximation Chapter 6 and Hef N-1 F i . In such a case the eigenvalue equation Hef 0 1 Vi i Eo 0 1 i i holds and the approximate .