Summary of Kohn-Sham Spin-Density Functional Theory

2 Summary of Kohn—Sham Spin-Density Functional Theory 

This introduction closes with a brief presentation of the Kohn-Sham [6] spin-density functional method, the most widely-used method of electronic-structure calculation in condensed-matter physics and one of the most widely-used methods in quantum chemistry. We seek the groimd-state total energy E and spin densities n (r), n (r) for a collection of N electrons interacting with one another and with an external potential w(r) (due to the nuclei in most practical cases). These are foimd by the selfconsistent solution of an auxiliary (fictitious) one-electron Schrodinger equation  

Here a =f or 4- is the z-component of spin, and a stands for the set of remaining one-electron quantum numbers. The effective potential includes a classical Hartree potential 

Because (1.1) and (1.2) are interlinked, they can only be solved by iteration to selfconsistency. 

The second term of (1.6) is the interaction of the electrons with the external potential. The third term of (1.6) is the Hartree electrostatic self-repulsion of the electron density 

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