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Ideas of Quantum Chemistry P60

Ideas of Quantum Chemistry P60 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. | 556 10. Correlation of the Electronic Motions These are the equations of the many body perturbation theory in which the exact wave function and energy are expressed in terms of the unperturbed functions and energies plus certain corrections. The problem is that as can be seen these corrections involve the unknown function and unknown energy. Let us not despair in this situation but try to apply an iterative technique. First substitute for to in the right-hand side of 10.76 that which most resembles to i.e. t00 . We obtain to Ro E00 - Eo H 1 00 10.78 and then the new approximation to t0 should again be plugged into the right-hand side and this procedure is continued ad infinitum. It can be seen that the successive terms form a series let us hope that it is convergent . co to E Ro e00 - Eo Hl 1 00 - 10.79 n 0 Now only known quantities occur on the right-hand side except for Eo the exact energy. Let us pretend that its value is known and insert into the energy expression 10.77 the function t0 Eo e00 t 00 Hr 1 to M e 0 lt 0 H 1 TRn E 0 - E H 1 Hn t 0 10 80 Eo to lH Lr0 e0 Eo H i to r 1o.8o n 0 Let us go back to our problem we want to have Eo on the left-hand side of the last equation while - for the time being - Eo occurs on the right-hand sides of both equations. To exit the situation we will treat E0 occurring on the right-hand side as a parameter manipulated in such a way as to obtain equality in both above equations. We may do it in two ways. One leads to Brillouin-Wigner perturbation theory the other to Rayleigh-Schrodinger perturbation theory. 10.16.5 BRILLOUIN-WIGNER PERTURBATION THEORY Let us decide first at what n M we terminate the series i.e. to what order of perturbation theory the calculations will be carried out. Say M 3. Let us now take any reasonable value94 as a parameter of Eo. We insert this value into the right-hand side of eq. 10.80 for Eo and calculate the left-hand side i.e. Eo. Then let us again insert the new Eo into the right-hand side and .