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Ideas of Quantum Chemistry P56

Ideas of Quantum Chemistry P56 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. | 516 10. Correlation of the Electronic Motions disqualifying feature since the region of space in which this condition should be fulfilled is very small. The area of application of this method is - for practical computational reasons - relatively small. The method of Gaussian geminals has been applied in unusually accurate calculations for three- and four-electron systems.33 10.8 EXCHANGE HOLE FERMI HOLE The mutual avoidance of electrons in helium atom or in hydrogen molecule is caused by Coulombic repulsion of electrons Coulomb hole see above . As we have shown in this Chapter in the Hartree-Fock method the Coulomb hole is absent whereas methods which account for electron correlation generate such a hole. However electrons avoid each other not only because of their charge. The Pauli principle is an additional reason. One of the consequences is the fact that electrons with the same spin coordinate cannot reside in the same place see p. 33. The continuity of the wave function implies that the probability density of them staying in the vicinity of each other is small i.e. around the electron there is a NO PARKING area for other electrons with the same spin coordinate exchange or Fermi hole . Let us see how such exchange holes arise. We will try to make the calculations as simple as possible. We have shown above that the Hartree-Fock function does not include any electron correlation. We must admit however that we have come to this conclusion on the basis of the two-electron closed shell case. This is a special situation since both electron have different spin coordinates a 2 and a -2 . Is it really true that the Hartree-Fock function does not include any correlation of electronic motion We take the H- molecule in the simplest formulation of the LCAO MO method two atomic orbitals only 1sa Xa and 1sb xb two molecular orbitals bonding t V2 1 S Xa Xb and antibonding y2 V2 1-S Xa - Xb cf. p. 371 the overlap integral S Xa Xb . We have three electrons. As a wave function we