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Communication: Constrained search formulation of the ground state energy as a functional of an idempotent one-matrix
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33.An important restriction here is that in a finite basis there may not be an idempotent density matrix that satisfies this relation,40,41 unlike the case for the first natural determinant which is always defined (assuming that the exact one-matrix is).
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Despite the fact that idempotent one-particle reduced density matrices are pervasive in quantum chemistry, the understanding of a general energy functional of such idempotent density matrices for the ground state energy has been lacking. By a constrained search, we show the structure of the general functional, illuminating the contributions from various terms. For the examples of the “best idempotent density matrix” and Kohn–Sham idempotent density matrices, we contrast the functional forms and suggest how the best idempotent density matrix approach may be a good starting point for further development.
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