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Ideas of Quantum Chemistry P53

Ideas of Quantum Chemistry P53 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. | 486 9. Electronic Motion in the Mean Field Periodic Systems bution which has been postponed in the long-range region p. 477 . It is time now to consider this again. The exchange term in the Fock matrix element Fpq had the form see 9.65 -l S S plhi0h lj 9 94 2 2- Psr pr sq 9.94 and gave the following contribution to the total energy per unit cell Eexch E Eexch j 9.95 j where the cell 0-cell j interaction has the form see 9.81 E h i -1 pj0plhi0h lj 9 96 Eexch j 4 PqpPsr pr sq - 9.96 It would be very nice to have the exchange contribution Eexch j decaying fast when j increases because it could be enclosed in the short-range contribution. Do we have good prospects for this The above formula shows the integral that the summation over l is safe the contribution of those cells l that are far from cell 0 is negligible due to differential overlaps of type x0p 1 xS 1 The summation over cells h is safe as well for the same reasons because it is bound to be limited to the neighbourhood of cell j see the integral . In contrast the only guarantee of a satisfactory convergence of the sum over j is that we hope the matrix element PJq p decays fast if j increases. So far exchange contributions have been neglected and there has been an indication suggesting that this was the right procedure. This was the magic word exchange . All the experience of myself and my colleagues in intermolecular interactions whispers this is surely a short-range type . In a manuscript by Sandor Suhai I read that the exchange contribution is of a long-range type. To our astonishment this turned out to be right just a few numerical experiments . We have a long-range exchange. After an analysis was performed it turned out that the long-range exchange interaction appears if and only if the system is metallic. A metallic system is notorious for its HOMO-LUMO quasidegeneracy therefore we began to suspect that when the HOMO-LUMO gap decreases the FJq p coefficients do not decay with j. Such things are most .