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Ideas of Quantum Chemistry P65 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. | 606 11. Electronic Motion Density Functional Theory DFT Fig. 11.9. Exchange potential. Efficiency analysis of various DFT methods and comparison with the exact theory for the harmonium with the force constant k according to Kais et al. Fig. a shows exchange potential vx as a function of the radius r and Fig. b as a function of the density distribution p. The notation of Fig. 11.8 is used. It is seen that both DFT potentials produce plots that differ by nearly a constant from the exact potential it is therefore an almost exact potential . The two DFT methods exhibit some nonphysical oscillations for small r. Reused with permission from S. Kais D.R. Herschbach N.C. Handy C.W Murray and G.J. Laming J. Chem. Phys. 99 1993 417 1993 American Institute of Physics. surely the most difficult to describe and no wonder that simple formulae cannot accurately describe the exact electronic density distribution. Correlation potential The correlation potential Ec is more intriguing Fig. 11.10 . The exact potential represents a smooth hook-like curve. The BLYP and BP correlation plots twine loosely like eels round about the exact curve 60 and for small r exhibit some vibration similar to that for vx. It is most impressive that the BLYP and BP curves twine as if they were in counter-phase which suggests that if added they might produce good61 results. Conclusion The harmonic helium atom represents an instructive example that pertains to medium electronic densities. It seems that the dragon of the correlation energy 60The deviations are very large. 61Such temptations give birth to Babylon-type science. Summary 607 Fig. 11.10. Correlation potential -efficiency analysis of various DFT methods and comparison with the exact theory for the harmonic helium atom with the force constant k 4 according to Kais et al. Fig. a shows correlation potential vc less important than the exchange potential as a function of the radius r a and of density distribution p b . Notation as in Fig. 11.8. The .
