Ideas of Quantum Chemistry P63 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. | 586 11. Electronic Motion Density Functional Theory DFT exchangecorrelation energy cf. p. 515 . Also a no-parking zone results because electrons of the same spin coordinate hate one another22 exchange or Fermi hole cf. p. 516 . The integral J does not take such a correlation of motions into account. Thus we have written a few terms and we do not know what to write down next. Well in the DFT in the expression for E we write in the lacking remainder as Exc and we call it the exchange-correlation energy label x stands for exchange c is for correlation and declare courageously that we will manage somehow to get it. The above formula represents a definition of the exchange-correlation energy although it is rather a strange definition - it requires us to know E. We should not forget that in Exc a correction to the kinetic energy has also to be included besides the exchange and correlation effects that takes into account that kinetic energy has to be calculated for the true . interacting electrons not for the noninteracting Kohn-Sham ones. All this stands to reason if Exc is small as compared to E . The next question is connected to what kind of mathematical form Exc might have. Let us assume for the time being we have no problem with this mathematical form. For now we will establish a relation between our wonder external potential v0 and our mysterious Exc both quantities performing miracles but not known. DERIVATION OF THE KOHN-SHAM EQUATIONS Now we will make a variation of E . we will find the linear effect of changing E due to a variation of the spinorbitals and therefore also of the density . We make a spinorbital variation denoted by 8 i as before p. 336 it is justified to vary either i or the result is the same we choose therefore 8 and see what effect it will have on E keeping only the linear term. We have see eq. 8 p p 8p N 8p r EE 8 r a i r a . We insert the right-hand sides of the above expressions into E and identify .
