Fields Coupling to the Spins SDFT

Up to this point we have discussed DFT in terms of the charge (or particle) density n r) as a fundamental variable. To reproduce the correct charge density of the interacting system in the noninteracting (Kohn-Sham) system, one must apply to the latter the effective Kohn-Sham potential Vs = w -f wh + Wxc, in which the last two terms simulate the effect of the electron-electron interaction on the charge density. This form of DFT, which is the one proposed originally, could also be called charge-only DFT. It is not the most widely used DFT in practical applications. Much more common is a formulation that employs one density for each spin, (r) and (r), i.e. works with two fundamental variables. To reproduce both of these 

The formulation of DFT in terms of n (r) and n4,(r) is known as collinear SDFT. ° Its fundamental variables n-i-Cr) and 4,(r) can be used to calculate the charge density (r) and the spin-magnetization density m (r) from 

There are, however, some exceptions to this simple rule. One is the fourth statement of the Hohenberg Kohn theorem, as discussed in Sect. ni.l. Another is the construction of functionals. For the exchange energy it is known, e.g., that  

The exchange-correlation magnetic field 5xc = Mo(fxc,t — Vxc,t) the origin of, e.g., ferromagnetism in transition metals. 

References to recent work with SDFT include almost all practical DFT calculation SDFT is by far the most widely used form of DFT. In fact, SDFT has become synonymous with DFT to such an extent that often no distinction is made between the two, i.e. a calculation referred to as a DFT one is most often really a SDFT one Some recent work on SDFT is described in Ref [168]. A more detailed discussion of SDFT can be found in Refs., [7, 8, 85] and a particularly clear exposition of the construction of exchange-correlation functionals for SDFT is the contribution of Kurth and Perdew in Refs. [17,18]. 

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