tailieunhanh - Ideas of Quantum Chemistry P102

Ideas of Quantum Chemistry P102 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. | 976 I. SPACE- AND BODY-FIXED COORDINATE SYSTEMS h 2 A1 2m i - h2 IÏ 2mi M h2 a 2m2 2 m1 2 d2 d2 2 d2 dX M dx2 dXcMdx similarly for y and z h2 Vm2 2 d2 2m2 A M dXCM mi 2 d2 2mim2 d2 m dX2 M2 dXcMdX similarly for y and z - A icM - M ixxz - 2m2 M ixyz - 2m M -2Amt h2 2mim2 d2 2m2 M2 dXcMdX h2 h2 mi 2 h2 mi 2 - 2MAcm - 2mAm Sx - m. m xxz h2 a h2 mi -2MAcm - 2 m2M xyz It is seen that once again we have reached a situation allowing us to separate the motion of the centre of mass in the Schrodinger equation. This time however the form of the operator H is different . Axyz has only formally the same form as A only because the variables are different the operator remains the same . Once again this is the kinetic energy of a point-like particle9 with coordinates x y z defined in this example and mass equal to m - 9 Let us first denote the nucleus as particle 1 and the electron as particle 2. Then Rqm almost shows the position of the nucleus and x y z are almost the coordinates of the electron measured from the nu- cleus while m M s almost equal to the mass of the electron. Thus we have a situation which resembles Example 1. If the particles are chosen the other way the electron is particle 1 and the nucleus is particle 2 the same physical situation looks completely different. The values of x y z are very close to 0 while the mass of the effective point-like particle becomes very large. Note that the new coordinates describe the potential energy in a more complex way. We need differences of the kind X2 xi to insert them into Pythagoras formula for the distance. We have X mi m2 m2 _X mi m2 m2 X m2 xi XCM----------------- x2 XCM- x XCM XCM------x mi mi mi mi mi m2 m2 xi x2 XCM--------x x XCM x i ----- mi mi This gives immediately r stands for the electron-centre of mass distance V new - m. i mf r J. ORTHOGONALIZATION 1 SCHMIDT ORTHOGONALIZATION Two vectors Imagine two vectors u and v each of length 1 . normalized with the dot product u v a. If a 0 the two vectors are .

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