Slater determinantal density matrix

The variational procedure in Eq. (100) is in the spirit of the Kohn-Sham ansatz. Since satisfies the (g, K) conditions, it is A-representable. In general, Pij ig corresponds to many different A-electron ensembles and one of them,, corresponds to the ground state of interest. However, for computational expediency in computing the energy, a Slater determinantal density matrix,... 

Density functional theory, 21, 31, 245-246 B3LYP functional, 246 Hartree-Fock-Slater exchange, 246 Kohn-Sham equations, 245 local density approximation, 246 nonlocal corrections, 246 Density matrix, 232 Determinantal wave function, 23 Dewar benzene, 290 from acetylene + cyclobutadiene, 290 interaction diagram, 297 rearrangement to benzene, 290, 296-297 DFT, see Density functional theory... 

That Eq. (44) and Eq. (34) are different is due to the fact that GHF exchange is quadratic in the first-order density matrix, whereas Slater s approximation depends on the 4/3 power of the density. Only for the special case of a single determinantal wavefunction that has constant direction of S (i.e. for conventional but not generalized single determinants) can we regroup terms in Eq. (43) to yield Eq. (34). For this case N and S can be simplified as... 

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