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Volumn 77, Issue 23, 2008, Pages

Generalized Kohn-Sham system in one-matrix functional theory

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EID: 46049121399     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.77.235121     Document Type: Article
Times cited : (44)

References (41)
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    • The following theorem (Ref.) implies that the functional Ev [γ] is stationary, i.e., δ Ev =0 with respect to all variations in the VR space. Theorem-A necessary condition for the differentiable functional J [y] to have an extremum (minimum) for y= y0 is that its first variation vanish for y= y0, i.e., that δJ [h] =0 for y= y0 and all admissible variations h. Thus, the functional Ev [γ] must be stationary because it is differentiable in the VR space and the Rayleigh-Ritz variational principle implies that it is minimum at the ground state one-matrix γ= γgs. The differentiability of Ev [γ] follows from the differentiability of the mapping γ→ Ψ0 in the VR space, if the ground state Ψ0 is nondegenerate.
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