Ideas of Quantum Chemistry P64 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. | 596 11. Electronic Motion Density Functional Theory DFT potential vo will be written as cf. the formulas and E A 0 si To y p r vo r d3r. Inserting this into we obtain E A 1 . the energy of our original system E A 1 To I p r v r d3r 1 1 dA d3r1 d3r2 This expression may be simplified by introducing the pair distribution function naver which is the nA r1 r2 averaged over A 0 1 naver r1 r2 f nA r1 ri dA. o Finally we obtain the following expression for the total energy E E A 1 To j p r v r d3r 1 dWn naver r2 . Note that this equation is similar to the total energy expression appearing in traditional quantum chemistry36 without repulsion of the nuclei E T y p r v r d3r 2 d3r1d3ri 2 4 22 where in the last term we recognize the mean repulsion energy of electrons obtained a while before . As we can see the DFT total energy expression instead of the mean kinetic energy of the fully interacting electrons T contains To . the mean kinetic energy of the non-interacting Kohn-Sham We pay however a price which is that we need to compute the function naver somehow. Note however that the correlation energy dragon has been driven into the problem of finding a two-electron function naver. EXCHANGE-CORRELATION ENERGY vs naver What is the relation between naver and the exchange-correlation energy Exc introduced earlier We find that immediately comparing the total energy given in eqs. and and now in . It is seen that the exchange-correlation energy Exc 1 ii d3r1d3r2 naver r1 ri - p r1 p ri . 36It is evident from the mean value of the total Hamiltonian taking into account the mean value of the electron-electron repulsion eq. and . 37As a matter of fact the whole Kohn-Sham formalism with the fictitious system of the non-interacting electrons has been designed precisely because of this. On the physical justification for the exchange correlation energy 597 The energy looks as if
