Kohn orbitals

Fig. 6. Many-to-one correspondance between wavefunctions in and one-particle densities is the Hohenberg-Kohn orbit, i.e., the orbit that contains the exact ground-state wavefunction...

Hohenberg-Kohn orbit. Clearly, within the application of local-scaling transformations to any initial wavefunction leads to the exact ground-state wavefunction as well as to the exact ground-state density. 

The optimal energy for intra-orbit variation is attained at < [pop,(r) y ]. Because the functional N-representability condition is fulfilled, this value is an upper bound to (i.e., to the optimal energy within the Hohenberg-Kohn orbit as W/Hn, C ] =... 

The question arises of why not to carry out this energy minimization for an energy functional that has been defined from the outset in the Hohenberg-Kohn orbit. The answer is that if we wish to construct the exact energy density functional d [p(r) we must depart from some orbit-generating... 

Hohenberg-Kohn orbit (Of course, it must be understood that this is... 

Hohenberg-Kohn" orbit, where the exact ground-state wavefunction is found. 

Notice that the optimal energy value within orbit O is [p%t(r, a) W]. This value is an upper bound to the optimal energy value within the Hohenberg-Kohn orbit, which, of course, is just the exact ground-state energy [, r,s) WK = E . 

The Hohenberg-Kohn orbit and the Kohn-Sham equations... 

The action of a local-scaling transformation of the density within the interacting Hohenberg-Kohn orbit carries the wavefunction 0 C,K C Cn into the transformed wavefunction [,WA l e c Cn- The same occurs within the noninteracting Hohenberg-Kohn orbital where the wavefunction s°lHK] g c SN... 

Eq. (51), the i-th optimal, ground-state wavefunction q G True, generally speaking, the latter is the approximate ground-state wavefunction that yields an upper bound to the exact ground-state energy 0 which is attained, by definition, only at the Hohenberg-Kohn orbit that is, = Eq. 

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